Probing atomic and nuclear structure
properties of promethium by laser
spectroscopy
Dissertation
zur Erlangung des akademischen Grades
”Doktor der Naturwissenschaften“
am Fachbereich Physik, Mathematik und Informatik (FB 08)
der Johannes Gutenberg-Universität Mainz
Dominik Studer
geb. in Wiesbaden
Mainz, den 22. Juni 2020
Tag der Prüfung: 18. Juni 2020
”There is a theory which states that if ever anyone discovers exactly what the Universe
is for and why it is here, it will instantly disappear and be replaced by something even
more bizarre and inexplicable. There is another theory which states that this has already
happened.”
Douglas Adams
Dominik Studer
Institut für Physik
Johannes Gutenberg-Universität Mainz
Staudingerweg 7
55128 Mainz
dstuder@uni-mainz.de
Abstract
Laser resonance ionization is a versatile technique for efficient ion source and sen-
sitive spectroscopy applications, based on step-wise optical excitation of atoms by
pulsed laser radiation, with the final step ionizing the atom. This work focuses on
in-source spectroscopy applications, i.e. laser probing directly within the ion source
environment, and therefore combines the experimental aspects of spectroscopy
and ”ion sourcery”. In this context atomic and nuclear structure properties of
dysprosium and promethium were determined, with a focus on so far widely un-
known parameters of the latter. The results are documented in five publications.
They can be thematically separated into atomic and nuclear structure research,
performed in broadband and high-resolution laser spectroscopic experiments, re-
spectively.
The first part of this thesis aims towards the determination of atomic level energies,
efficient resonance ionization pathways and the determination of the first ioniza-
tion potential. The technique of laser-induced resonant depopulation of excited
atomic levels is introduced, offering access to a specific low-lying energy level in
Dy. The corresponding ultra-narrow ground-state transition near 1001 nm was lo-
cated in preparation for high-precision spectroscopy on cold atoms. For the deter-
mination of the ionization potential, the techniques of Rydberg-spectroscopy and
saddle-point ionization were applied in Dy and Pm, respectively. While the for-
mer represents the conventional approach for this task, the sensitivity of the latter
was greatly improved and demonstrated in the challenging case of Pm. The ex-
tracted values of IPDy = 47 901.76(5) cm−1 and IPPm = 45 020.8(3) cm−1 improved
the precision of IPDy by one order of magnitude, while IPPm was experimentally
determined for the first time.
In the second part, dedicated to high-resolution spectroscopic applications, the
long-term stability and accuracy of wavelength meters in precision frequency mea-
surement was characterized as an important aspect for the extraction of reliable
spectroscopic data. Systematic patterns in deviations of relative frequency mea-
surements were discovered in comparison to complementary devices. Methods to
avoid or at least properly consider these effects in data post-processing are dis-
cussed. Lastly, the results of high-resolution spectroscopy on long-lived Pm iso-
topes are presented, using the novel PI-LIST ion source module. The experiment
on cyclotron-produced Pm isotopes demonstrates the capabilities of the PI-LIST
and represents a further step towards routine operation at on-line radioactive ion
beam facilities. The spectroscopic data obtained allowed for the extraction of sev-
eral nuclear ground state properties of the isotopic sequence of 143−147Pm, i.e.
magnetic dipole moments, electric quadrupole moments, and changes in mean
square charge radii.
iii

List of Included Articles
This cumulative dissertation is based on the five publications [1–5], which are
listed below. These articles are chosen to represent the key aspects of this work
in a comprehensive way. The author has made significant contributions to each of
these articles, which are pointed out in detail in an introductory section preceding
each article within this thesis. A complete list of all publications of the author is
given in the ??.
Publication [1] emerged from a collaborative activity within the QUANTUM re-
search group. It describes a specific case of resonance ionization scheme develop-
ment for the search of a low-lying meta-stable atomic level in dysprosium. The
direct ground-state transition to this level, which was also measured in this work,
is of high relevance for precision spectroscopy of cold atoms.
Publication [2] also describes the development of ionization schemes, in this case
directed towards the achievement of maximum ionization efficiency. In this scope
the first ionization potential (IP) of dysprosium was measured. This work exem-
plarily describes the evaluation of Rydberg convergences in a complex rare-earth
atomic system.
Publication [3] rounds up the part on measurements of atomic structure proper-
ties. It describes the extensive study of the atomic spectrum of the promethium
atom and the determination of its first IP, introducing the approach of electric
field ionization as a sensitive and complementary method to the analysis of Ryd-
berg convergences.
Publication [4] is a collaborative work between the University of Jyväskylä, the
University of Leuven, GSI Darmstadt and the University of Mainz. Within this
network the performance of wavelength meters is characterized, which has impor-
tant consequences on the accuracy of high-resolution laser spectroscopic studies.
Finally, Publication [5] presents the results of high-resolution spectroscopy on
long-lived promethium isotopes. This work concludes this thesis by demonstrating
the capabilities of laser resonance ionization spectroscopy for the study of nuclear
structure properties on minuit sample amounts of rare radioisotopes, significantly
refining and extending literature data.
[1] D. Studer, L. Maske, P. Windpassinger, K. Wendt, Laser spectroscopy of the 1001-
nm ground-state transition in dysprosium, Phys. Rev. A 98, 042504 (2018). doi:
10.1103/PhysRevA.98.042504.
[2] D. Studer, P. Dyrauf, P. Naubereit, R. Heinke, K. Wendt, Resonance ionization
spectroscopy in dysprosium: Excitation scheme development and re-determination of
the first ionization potential, Hyperfine Interact. 238, 8 (2017). doi:10.1007/
s10751-016-1384-4.
v
[3] D. Studer, S. Heinitz, R. Heinke, P. Naubereit, R. Dressler, C. Guerrero,
U. Köster, D. Schumann, K. Wendt, Atomic transitions and the first ionization
potential of promethium determined by laser spectroscopy, Phys. Rev. A 99, 062513
(2019). doi:10.1103/PhysRevA.99.062513.
[4] M. Verlinde, K. Dockx, S. Geldhof, K. König, D. Studer, T. E. Cocolios,
R. de Groote, R. Ferrer, T. Kieck, I. D. Moore, W. Nörtershäuser, S. Raeder,
P. van den Bergh, P. van Duppen, K. Wendt, On the reliability of wavelength me-
ters - Part 1: Consequences for medium- to high-resolution laser spectroscopy, Appl.
Phys. B 126, 85 (2020). doi:10.1007/s00340-020-07425-4.
[5] D. Studer, J. Ulrich, S. Braccini, T. S. Carzaniga, R. Dressler, K. Eberhardt,
R. Heinke, U. Köster, S. Raeder, K. Wendt, High resolution laser resonance ioniza-
tion spectroscopy of 143−147Pm, Eur. Phys. J. A 56, 69 (2020). doi:10.1140/epja/
s10050-020-00061-8.
vi
Contents
Abstract iii
List of Included Articles v
1 Introduction 1
1.1 Promethium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2 Resonance ionization techniques for mass separators . . . . . . . . . 5
2 Experimental instrumentation 9
2.1 Pulsed tunable laser systems . . . . . . . . . . . . . . . . . . . . . . . 9
2.1.1 Standard Laser . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.1.2 Grating-tuned laser . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.1.3 Injection-seeded laser . . . . . . . . . . . . . . . . . . . . . . . . 14
2.1.4 Frequency conversion . . . . . . . . . . . . . . . . . . . . . . . 16
2.2 Wavelength measurement . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.2.1 Wavelength meters . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.2.2 Absolute references . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.2.3 Fringe-offset technique . . . . . . . . . . . . . . . . . . . . . . . 22
2.3 RISIKO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.3.1 Ion source . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.3.2 Ion beam extraction and shaping . . . . . . . . . . . . . . . . . 28
2.3.3 Mass separation . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.3.4 Ion detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.4 MABU . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.5 ISOLDE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3 Atomic structure and the ionization potential 35
3.1 Atomic energy levels . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.1.1 Fine structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.1.2 Multi-electron systems . . . . . . . . . . . . . . . . . . . . . . . 37
3.1.3 Rydberg atoms . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.2 Electronic transitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.3 Spectral lineshapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
vii
Contents
3.3.1 Natural linewidth . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.3.2 Lifetime measurement . . . . . . . . . . . . . . . . . . . . . . . 42
3.3.3 Doppler broadening . . . . . . . . . . . . . . . . . . . . . . . . 43
3.3.4 Saturation and power broadening . . . . . . . . . . . . . . . . 45
3.4 Ionization scheme development . . . . . . . . . . . . . . . . . . . . . . 46
3.5 Determination of the ionization potential . . . . . . . . . . . . . . . . 49
3.5.1 Rydberg convergences . . . . . . . . . . . . . . . . . . . . . . . 50
3.5.2 Saddle-point ionization . . . . . . . . . . . . . . . . . . . . . . 51
3.6 Publication I: Laser spectroscopy of the 1001-nm ground-state tran-
sition in dysprosium . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
3.7 Publication II: Resonance ionization spectroscopy in dysprosium . . 59
3.8 Publication III: Atomic transitions and the first ionization potential
of promethium determined by laser spectroscopy . . . . . . . . . . . 71
4 High-resolution spectroscopy as a probe for nuclear structure 81
4.1 The shell model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
4.2 Nuclear moments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
4.2.1 Magnetic dipole . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
4.2.2 Electric quadrupole . . . . . . . . . . . . . . . . . . . . . . . . . 84
4.3 Mean square charge radius . . . . . . . . . . . . . . . . . . . . . . . . 86
4.4 Probing nuclear structure by laser spectroscopy . . . . . . . . . . . . 87
4.4.1 Hyperfine structure . . . . . . . . . . . . . . . . . . . . . . . . . 88
4.4.2 Isotope shift . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
4.5 Publication IV: On the reliability of wavelength meters - Part 1: Con-
sequences for medium- to high-resolution laser spectroscopy . . . . 92
4.6 Publication V: High-resolution laser resonance ionization spec-
troscopy of 143−147Pm . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
5 Summary and outlook 121
A Appendix 125
A.1 Laser prototypes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
A.1.1 Compact-footprint injection-seeded laser . . . . . . . . . . . . 126
A.1.2 Unseeded bowtie-resonator laser . . . . . . . . . . . . . . . . . 127
A.2 Supplemental Material for Publication I . . . . . . . . . . . . . . . . . 132
A.3 Supplemental Material for Publication III . . . . . . . . . . . . . . . . 134
List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154
List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
List of Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
Bibliography 163
Acknowledgements 181
viii
Chapter1
Introduction
Since the first evidence for the existence of an atomic nucleus by Ernest Rutherford,
revealed in the famous experiment by scattering α-particles on gold [1], theoretical
models for the description of its properties have developed tremendously. The liq-
uid drop model, describing the nucleus as a sphere of uniform density, composed
of protons and neutrons bound by the strong force, already allowed a qualitative
understanding of binding energy and radioactive decay [2]. Based on experimen-
tal evidence for so-called magic numbers, i.e. proton- or neutron numbers, at which
nuclei of particularly high stability occur, the nuclear shell model was introduced
by Maria Goeppert-Mayer and Hans Jensen [3, 4], who were awarded with the
physics Nobel Price in 1963 for their discovery. The shell model comprises a
quantum-mechanical treatment of the nucleus, resulting in proton- and neutron
orbitals similar to electrons in an atom, with the magic numbers corresponding
to filled shells. While the shell model successfully describes nuclear spins and
electromagnetic moments for spherical nuclei, it does not account for nuclear de-
formation. Therefore, it was extended by collective models in the 1950s, where a
collective motion of all nucleons, i.e. vibration and rotation, is considered [5, 6].
This allows for an accurate description of nuclear ground state properties and ex-
cited states. However, the predictive power of theory is limited by the complexity
in such systems of numerous interacting particles equal to the nucleon number A.
Calculations are usually based on mean field approaches and need to be tailored
to specific problems. In order to establish benchmarks for theoretical predictions,
the objective of experimentalists is to provide nuclear structure data in specific or
even exceptional regions of the Nuclear Chart, featuring e.g. extreme or unusual
deformation, abrupt shape transitions or shape staggering.
An access to the investigation of nuclear structure is offered indirectly through the
study of the atomic shell. Interactions of the nucleus with the surrounding elec-
tronic shell manifest as small perturbations in the atomic level structure, known
as hyperfine structure and isotope shift. Precise measurements of these effects
1
1. Introduction
allow the extraction of the nuclear spin I, the magnetic dipole moment µI , the
electric quadrupole moment Qs and changes in mean square charge radii δ〈r2〉,
all of which are closely related to the nucleus’ shape [7]. With energy scales of
atomic transitions in the range of few eV, rather than typically keV or MeV in nu-
clear excitation, they are accessible with lasers. For its versatility, the laser has
become the ultimate tool for the study and manipulation of atoms. However,
high-precision probing of individual atomic transitions for the study of nuclear
effects, with contributions in the order of 10−5 eV, requires prior knowledge of the
atomic spectrum. Elements with no stable isotopes often exhibit a severe short-
coming in this regard. Spectroscopic studies are impeded by limited availability
of samples, together with the necessity of high safety precautions for the han-
dling of radioactive material. One way to overcome these challenges is through an
efficient measurement technique, which is capable of analyzing minuscule sam-
ple amounts. The method of Resonance Ionization Spectroscopy (RIS) is perfectly
suited for this application. It relies on stepwise photoionization of sample atoms
by high-power, pulsed laser radiation and subsequent ion counting. This process
is highly efficient and inherently element-selective. RIS is usually combined with
conventional methods of mass spectrometry allowing the study of a single isotope
of interest.
This dissertation deals with the application of RIS for the study of both, atomic and
nuclear structure properties, with a special focus on the element promethium (Pm,
Z = 61) as the main physics case. Correspondingly, it is structured in two parts.
The first part describes broadband spectroscopy experiments for the exploration
of atomic spectra. In this scope many aspects of broadband RIS were developed
and applied in the rare-earth atomic system of dysprosium (Dy, Z = 66). This in-
cludes the development of ionization schemes aimed towards maximum efficiency,
but also covers a rather unusual case where specific ground state transitions are
probed indirectly by resonant de-population of excited levels. In addition, the first
ionization potential (IP) of Dy was determined via spectroscopy of Rydberg con-
vergences, using the most common and also most precise approach for this task.
The Dy experiments therefore offer an ideal overview of the basics and concepts
of RIS for atomic structure research in the rare-earth region. Afterwards, the chal-
lenging case of Pm is addressed. Pm has an extraordinarily rich atomic spectrum,
which on the one hand makes it easy to develop a laser ionization scheme, but
on the other hand complicates the determination of the IP, as all Rydberg-series
are obscured or strongly perturbed. An alternative approach, based on DC elec-
tric field ionization of weakly bound states, is introduced, which benefits from
the high atomic level density and remains applicable with extremely small sample
amounts. In addition to the first measurement of the IP of Pm, this experiment
also represents an important methodical preparation for IP measurements in the
region of medium mass to heavy actinides, where complex atomic systems are
likewise expected and only very limited atom numbers are accessible, resulting in
2
1.1. Promethium
low measurement statistics.
The second part of this work is dedicated to high-resolution spectroscopy in the
Pm isotopic chain. This experiment marks the first high-precision spectroscopy
measurements in the Pm atom, based on the ionization schemes developed ear-
lier within this work. It serves as an important test and preparation step for on-
line1 experiments, pushing further away from the valley of β-stability, towards
very short-lived Pm isotopes. In this context the experimental challenges of high-
precision experiments on exotic nuclei are discussed. As a basic prerequisite this
task specifically addresses precise absolute laser frequency measurements and ion
source developments, which are tailored for sensitive spectroscopy studies.
1.1 Promethium
The exclusively radioactive element promethium has been subject to an interesting
history of discovery, including the proposals of the names florentium and illinium
for the missing element between neodymium and samarium [8, 9]. In 1945, based
on research in the framework of the Manhattan project, Marinsky et al. success-
fully separated 147Pm from uranium fission products by means of ion exchange
chromatography [10], finally marking the discovery of element 61. Together with
technetium (Tc, Z = 43), Pm is one of two cases on the Periodic Table where an
element with an atomic number below Z = 83 has no stable isotope. An expla-
nation for this exceptional situation can be found in the liquid drop model of the
atomic nucleus, or more specifically the Bethe-Weizsäcker mass formula [2]. It de-
scribes parabola-like curves of nuclear mass for isobaric nuclei of a given number
of nucleons A, where the mass minimum (i.e. maximum binding energy) can be
reached through radioactive β-decay. The consequence, that no neighboring stable
isobars can exist, is formulated in Mattauch’s isobar rule [11]. Accordingly, any
stable Pm isotopes are ruled out by the existence of the large number of stable
Nd and Sm isotopes, as shown in the Nuclear Chart section in Fig. 1.1. Even
the longest-lived Pm isotopes 145,146,147Pm have half-lives in the order of only few
years, making Pm extremely rare in nature. Practical applications of Pm are based
on its radioactivity. 147Pm (T1/2 = 2.62 y), the most easily accessible isotope in
terms of production, is used in nuclear batteries [13] or β-thickness gauges [14].
Some shorter-lived isotopes, i.e. 142Pm (T = 40.5 s) and 1491/2 Pm (T1/2 = 2.21 d)
are promising candidates for medical imaging techniques [15, 16]. The synthesis
of weightable amounts of Pm is possible using nuclear reactors. 147Pm can be
produced by neutron activation of 146Nd, where the reaction product 147Nd de-
cays with a half-life of 11 days to 147Pm (cf. Fig. 1.1). Alternatively, it can be
extracted from fission products within nuclear reactor waste [17]. A different pro-
1In this context, on-line means the experiment is coupled to a production site of radioactive iso-
topes. In contrast, experiments which rely on externally introduced samples are referred to as
off-line.
3
1. Introduction
Z Sm 143 Sm 144 Sm 145 Sm 146 Sm 147 Sm 148 Sm 149 Sm 150 Sm 151 Sm 152 Sm 153 Sm 154
30 ms 1.10 m 8.75 m 3.07 340.00 d 1.00e8 y 14.99 11.24 13.82 7.38 90.00 y 26.75 10.6 ms 1.93 d 22.75
62 1.06e11 y 8e15 y 2.0e15 y primordial
Pm 142 Pm 143 Pm 144 Pm 145 Pm 146 Pm 147 Pm 148 Pm 149 Pm 150 Pm 151 Pm 152 Pm 153
2.0 ms 40.5 s 266.00 d 363.00 d 17.70 y 5.53 y 2.62 y 41.05 d 5.37 d 2.21 d 2.68 h 1.18 d 14.40 m 7.52 m 4.12 m 5.25 m
61
Nd 141 Nd 142 Nd 143 Nd 144 Nd 145 Nd 146 Nd 147 Nd 148 Nd 149 Nd 150 Nd 151 Nd 152
1.03 m 2.49 h 27.2 12.2 23.8 8.3 17.2 10.98 d 5.7 1.73 h 5.6 12.44 m 11.40 m
60 2.29e15 y 2.7e18 y 2.1e19 y
81 82 83 84 85 86 87 88 89 90 91 92 N
Figure 1.1.: Section of the Nuclear Chart in the Pm region close to the valley of
β-stability. The underlying data is taken from [12].
duction route is offered by cyclotrons, where stable Nd isotopes can be irradiated
with high-energy protons. Through (p, xn)-reactions (at a suitable proton energy
of some ten MeV) a large number of Pm isotopes can be accessed (cf. Fig. 1.1).
However, at reasonable irradiation times the amounts produced are usually small.
As a consequence of the generally low availability of Pm, accompanied by the high
specific radioactivity, some fundamental atomic and nuclear properties of Pm have
not been studied until today, although fundamental research interests in Pm are
quite strong. Pm marks the last element below Z = 100 where no experimental
value for the first ionization potential (IP) is available. The first IP specifies the en-
ergy required to remove one valence electron from the neutral atom and is closely
linked to an element’s chemical behavior. Closing this gap in the Periodic Table
is a very timely endeavor specifically in the year 2019, which has been declared
the International Year of the Periodic Table of Elements for the 150th birthday
of Mendeleev’s discovery2. As a mid- f -shell element Pm exhibits a particularly
complex atomic structure. Its ground-state configuration is [Xe]4 f 56s2. Already
at moderate excitation energies the 6p and 5d orbitals are populated, leading to
a system with four open shells and consequently forming an extraordinarily rich
atomic spectrum.
From a nuclear physics point of view, Pm with its 61 protons lies in an interest-
ing region with regard to nuclear shapes. 143Pm possesses a filled neutron shell
(N = 82) and thus is expected to exhibit a rather spherical shape, as no valence
neutrons contribute to its electromagnetic properties. Towards neutron deficient
isotopes, at N ≈ 75, a particularly sharp transition to strongly quadrupole de-
formed nuclei is predicted by Leander et al. [18]. In Nd (Z = 60) already clear
evidence for strong deformation was found at N < 76 [19]. On the neutron rich
side one can push towards the well-known region of shape transition between
N = 86− 90, which has been observed in several other lanthanide elements. The
characteristic of this transition, being either gradual (Ce [20], Nd [21, 22]) or abrupt
2Official website of the International Year of the Periodic Table of Elements: https://iypt2019.
org/ Accessed 12/2019.
4
1.2. Resonance ionization techniques for mass separators
(Sm [23], Eu [24]), is largely dependent on the element. This behavior can be re-
lated to the Z = 64 proton subshell closure [25]. The fact that Pm lies exactly at the
border between those two characteristics makes it a particularly interesting case.
1.2 Resonance ionization techniques for mass separators
In the 1970s the concept of step-wise photo-ionization by laser radiation was first
introduced as a highly selective ion source [26, 27]. This technique, today com-
monly known as Resonance Ionization (RI), exploits each element’s unique atomic
structure to achieve an inherent elemental selectivity in the ionization process. A
sketch of the RI principle is given on the left side in Fig. 1.2. Atoms are succes-
sively excited along strong optical dipole transitions, with the final step leading
to ionization. This process is not only selective, but also highly efficient in most
cases. Moreover, with the use of tunable laser systems, the adjustment of laser
ion sources to different elements is possible within a short period of time. The
elemental selection (respectively the atomic number Z) is often combined with
conventional mass spectrometry techniques, which allow an additional selection
of one set of isobars (nuclides of equal mass number A). As a result, one nuclide
of interest can be selectively addressed in the experiment, as illustrated in the
Nuclear Chart section on the right side in Fig. 1.2 for the specific case of 147Pm.
For its high versatility, the RI technique has evolved in different directions and is
used today for a wide variety of applications. Terminologies for the Resonance
Ionization principle vary dependent on the application case. A general distinction
is often made between Resonance Ionization Spectroscopy (RIS) and Resonance
Ionization Mass Spectrometry (RIMS), although the former usually relies on mass
separation, too. It should also be noted that laser ion sources are often referred to
as RILIS (Resonance Ionization Laser Ion Source), which strictly speaking does not
include the subsequent mass separation step. Most laser ion sources are based on
the hot-cavity approach, i.e. a resistively heated metal or graphite tube furnaces,
where the sample material is atomized at temperatures of up to 2500 ◦C. Atoms in
the source are resonantly ionized by the laser radiation and extracted with high-
voltage electrodes. Alternative atomization approaches are e.g. sputtering [28, 29]
or laser ablation [30, 31].
The RI technique, with its multitude of applications, is the field of expertise of the
LARISSA group (Laser Resonance Ionization Spectroscopy for Selective Applica-
tions) at Mainz University. Apart from dedicated off-line RIMS projects, such as
implantation of 163Ho in metallic micro-calorimeters for the ECHo-project (Elec-
tron Capture in 163Ho) [32–34], or trace analysis of actinide elements within the
SIRIUS project (Secondary Ionisation of Radioactive Isotopes for Ultra trace anal-
ysis) [35, 36], the group is closely collaborating with the laser ion source teams
at on-line radioactive ion beam (RIB)-facilities, e.g. ISOLDE at CERN, ISAC at
TRIUMF or IGISOL at JYFL. Related activities include fundamental research, e.g.
5
1. Introduction
Mass Separa�on
E Ion Con�nuum Eu 147 Eu 148 Eu 149 Eu 150 Eu 15124.00 d 54.50 d 93.10 d 12.80 h 36.40 y 47.81
Auto-ionizing state
IP
Sm 146 Sm 147 Sm 148 Sm 149 Sm 150
1.00e8 y 14.99 11.24 13.82 7.38
1.06e11 y 8e15 y 2.0e15 y
Pm 145 Pm 146 Pm 147 Pm 148 Pm 149
Excited states Laser Ioniza�on 17.70 y 5.53 y 2.62 y 41.05 d 5.37 d 2.21 d
Nd 144 Nd 145 Nd 146 Nd 147 Nd 148
23.8 8.3 17.2 10.98 d 5.7
Z 2.29e15 y 2.7e18 y
Pr 143 Pr 144 Pr 145 Pr 146 Pr 147
13.56 d 6.90 m 17.28 m 5.98 h 24.15 m 13.40 m
Atom
0 Ground state
N
Figure 1.2.: Left: Resonance Ionization scheme. The arrows indicate the step-wise
optical excitation from the atomic ground state to ionization. A detailed
description of different ionization mechanisms in the final excitation step is
given in section 3.4. Right: Selection principle of RIMS. The laser ionization
scheme selectively ionizes one chemical element (blue). A following mass
separation of the produced ion beam allows the selection of one set of isobars
(orange). In combination, one nuclide of interest is selected.
measurement of atomic properties of radioactive species , or high-resolution spec-
troscopy on long isotopic chains for nuclear structure research.
The major part of this dissertation was carried out within the Resonance Ionization
Techniques for Separators (RESIST) project, which is part of the Horizon 2020 re-
search initiative of the European Commission. The main goals of this project are
the refinement of laser RI techniques for applications at European on-line mass
separator facilities. This includes specifically
• Ionization scheme development: The applicability of RI depends on optical
excitation pathways populating excited atomic levels and leading to ioniza-
tion through the final step. Since these schemes are specific to each element,
extensive spectroscopic studies are necessary in order to make an element
accessible for laser ion sources. The efficiency of these schemes can be deter-
mined in dedicated measurements with calibrated samples. A compilation
of available ionization schemes is given in [37]. Since these schemes are the
key to RIS itself, it is of high relevance to extend such databases, in particular
towards previously unavailable elements.
• Ion source development: Although the RI process is fully element-selective,
it often competes with other ionization mechanisms in the hot ion source en-
vironment, predominantly surface ionization. Isobaric species, which cannot
be mass-separated, may consequently introduce significant contamination to
6
1.2. Resonance ionization techniques for mass separators
the ion beam and and impede on the experiment. In some extreme cases
this contamination might surpass the species of interest by several orders of
magnitude. Consequently, the feasibility and success of many experiments
depends on a stringent suppression of this contamination. A well-established
approach is the separation of the laser-atom interaction region from the hot
atomization region [38–40]. This technique has recently been refined to allow
high-resolution in-source spectroscopy through a perpendicular geometry
between atomic beam and probing laser beam [41]. This approach is com-
plementary to state-of-the-art spectroscopy techniques, e.g. collinear spec-
troscopy in fast beams, and needs to be well established thoroughly tested
before being used on-line on a routine basis.
• Laser development: Sensitive RI in hot cavities usually relies on pulsed,
high-repetition rate tunable laser systems. Almost twenty years ago, the
Mainz Ti:sapphire laser system has been developed specifically for this appli-
cation and is today in use at the majority of on-line laser ion sources world-
wide [42–44]. Based on the original design, specialized variants emerged
over the years. In particular pulsed narrow-bandwidth lasers are being re-
quested within the RIS community for use in high-resolution spectroscopy.
As part of the high-resolution capabilities of a laser system comes the chal-
lenge of precise laser wavelength measurement. In RIS, this is usually
done with wavelength-meters, which allow for absolute wavelength mea-
surements. With the steadily increasing precision in laser spectroscopy, it is
important to develop techniques to characterize and verify the accuracy of
such devices.
In conclusion, techniques of and around RI represent the methodical foundation
of this dissertation. In the following chapter, related instrumentation is intro-
duced as a basis for developments and experiments which were performed in this
framework. Afterwards, specific chapters on atomic- and nuclear structure stud-
ies are presented, including the related publications as the central pillars of this
thesis work. In order to establish a basis for the presented laser spectroscopy ex-
periments and to improve readability without the need to consult supplementary
literature, the publications are preceded by brief theory sections. Note that the
primary purpose of these sections is not to elaborate on basic textbook theory, but
rather to summarize the most important facts, equations and notations. For details
the reader is referred to the cited textbooks and articles.
7

Chapter2
Experimental instrumentation
2.1 Pulsed tunable laser systems
Hot cavity laser ion sources have special requirements for suitable laser systems.
In terms of efficiency, pulsed lasers have clear advantages over continuous wave
(cw) laser systems for several reasons. The peak power in pulsed laser radia-
tion is much higher compared to cw, on one side allowing for straightforward
frequency conversion using non-linear optics without dedicated resonators. On
the other side, the high power density also renders the saturation of relatively
weak transitions possible, which is often the bottleneck in the ionizing step (for
details see section 3.4). Moreover, considering the state population transfer in the
step-wise excitation, it is important to avoid optical pumping into states which
are not part of the excitation ladder. After typically 1 ns a population equilib-
rium between the lower and the upper state is reached as long as the external
laser field is sufficiently intense [45]. However, through additional loss channels
the population may be quenched into inaccessible states, which are not part of
the excitation ladder. These losses can be dramatically reduced by a laser pulse
length shorter than the excited state lifetime, which is typically in the order of
some ten nanoseconds [46]. Additional requirements on the laser system are in-
troduced by the thermal conditions within the ion source. At a typical temperature
of T = 2000 ◦C the most probable velocity in the Maxwell-√Boltzmann distribution
of a medium-mass-particle with mass m = 100 u is v̂ = 2kBT/m = 615 m s−1.
Considering a two-dimensional tubular atomizer of about 4 cm length (which is
the case at ISOLDE), a particle with a velocity vector pointing towards the exit
will require 60 µs to leave the tube (while strictly speaking still being exposed to
the collinearly entering laser radiation). At exemplary angles of 45◦ (75◦) towards
the exit, this time is extended to 90 µs (250 µs). As the release of atoms is con-
tinuous, a high laser pulse repetition rate is mandatory. Only in this case every
atom experiences at least one laser pulse before leaving the laser interaction re-
9
2. Experimental instrumentation
gion. At a repetition rate of 10 kHz, which is typically used at the majority of laser
ion sources (e.g. ISOLDE, ISAC and RISIKO), a sample atom is exposed to 1 to
3 laser pulse sequences, resulting in a high ionization probability. The thermal
movement of the atoms also causes a spectral Doppler broadening which is, de-
pending on atomic mass, laser wavelength and temperature, and lies in the order
of 1 to 5 GHz (for details see section 3.3). In order to achieve maximum ionization
efficiency, the spectral laser profile has to match the Doppler distribution. Note
that in dedicated high-resolution spectroscopy experiments, Doppler broadening
is greatly reduced, e.g. by a perpendicular laser-atom beam interaction geometry
[41] or by Doppler compression in accelerated beams [47, 48]. Naturally these ex-
periments rely on narrow-band laser radiation, raising the demand for different
and more complex laser types. Finally, and most essential, RIS depends on the
availability of tunable lasers with a wide spectral coverage as basis for a versatile
and universal ion source. Laser media fulfilling all the requirements are laser dyes
or, alternatively, titanium-doped sapphire (Ti:sapphire) crystals. All laser systems
in laser ion sources are based on these two types. Although dye and Ti:sapphire
are widely complementary with regard to their emission wavelength range, they
are rarely used in combination (with a prominent exception being the RILIS at
CERN-ISOLDE), since most elements can be reliably accessed by a laser system of
either type. Consequently, and for the sake of simplification of the experimental
expenditure, most ionization schemes rely on a single laser type rather than using
a mixed laser system. Dye lasers usually have a higher output power (≈10 W)
and a short pulse length (≈5 ns) [44] as laser dyes have high gain compared to
Ti:sapphire. However, they require high maintenance and degrade quickly during
operation due to break-up of dye molecules by the pump laser radiation. Partic-
ularly in the case of UV-pumped dye lasers, a dye change may be required every
6 to 10 h. The Mainz University laser system is based on home-built Ti:sapphire
lasers, which are widely maintenance free and provide a stable power output over
hours to days without readjustment. A commercial frequency doubled Nd:YAG
laser emitting at 532 nm serves a a pump source for the Ti:sapphire. Typical spec-
ifications for the pump laser are 10 kHz repetition rate, 150 ns pulse width and 40
to 200 W output power. One pump laser is usually used for pumping a number
of Ti:sapphire lasers, each with 10 to 20 W. An output pulse synchronization can
either be achieved by Q-switches (Pockels-cells) within the Ti:sapphire resonator
based on the linear electro-optical effect or by proper adjustment of the pump
power distribution.
2.1.1 Standard Laser
The basic Mainz University Ti:sapphire laser design was developed in 2003 by R.
Horn [42] and underwent constant refinement ever since. It is based on a Z-pinch
standing wave cavity with a Brewster-cut Ti:sapphire crystal in the central arm.
10
2.1. Pulsed tunable laser systems
Two curved mirrors (rcurv = 75 mm) focus the resonator mode inside the crys-
tal at a folding angle of 17.4◦ to compensate for the astigmatism induced by the
Brewster-cut of the crystal. The outer arms of the cavity are almost parallel beam
propagation and are terminated by a high-reflective end mirror and an output cou-
pler (R = 0.8), respectively. The latter has a slight wedge to avoid unwanted etalon
effects. The resonator layout is shown in Fig. 2.1 (a). The spectral bandwidth of
the laser output is given by two frequency selective elements, namely a Lyot-Filter
(LF) and a Fabry-Pérot-Etalon (FPE). The LF is based on a birefringent material of
thickness L. A sketch of the LF principle is given in Fig 2.2 (a). The electric field
components Ey, Ez of an incident beam are subject to a phase shift
2π
δLF(λ, L) = (n0 − ne)L, (2.1)
λ
where n0 and ne denote the ordinary and extraordinary refractive indices of the
birefringent material, respectively [49]. Generally this results in an elliptical po-
larization of transmitted light. Brewster surfaces within the laser resonator cause
high losses for the s-polarized component (normal to the plane of the resonator).
Considering a p-polarized beam traveling in the resonator, the phase shift δLF has
to match multiples of 2π for minimal losses. The transmission function is given
by ( )
T (λ, L) = T cos2
π(n0 − ne)L
LF 0 (2.2)
λ
[49]. Since the bandwidth (full width at half maximum (FWHM)) δν scales with L,
but the free spectral range (FSR) with L−1, multiple plates are often combined in
order to achieve a high finesse F = FSR/δν. The Mainz Ti:sapphire laser uses a
set of three quartz plates of thickness L1 = 0.3 mm, L2 = 4L1, L3 = 16L1, resulting
in a transmission profile of δν ≈ 250 GHz. The transmitted wavelength can be
tuned by rotation of the LF optical axis with respect to the propagation vector of
the incident beam, causing a change in ne.
The spectral profile of the laser is further narrowed by a solid intra-cavity FPE.
The principle is depicted in Fig. 2.2 (b). Subsequent reflection orders between the
plane parallel surfaces within the material are phase-shifted by
4π
δFPE(λ, d) = n2d cos(β). (2.3)
λ
Depending on the wavelength λ and the thickness of the substrate d, construc-
tive or destructive interference occurs. The transmission fringes of an FPE are
described by an Airy-function
(1− R)2
TFPE(λ, d, R) = T0 − (2.4)(1 R)2 + 4R sin2(δ/2)
11
2. Experimental instrumentation
CM
HR FPE QSW
Ti:sa
OC
CM LF
(a) L
G CMPBE
Ti:sa
CM QSW
OC
(b) L
PD
Ti:sa
L CM CM
Seed
LF
PAM OC
(c)
Figure 2.1.: Layout of the different Mainz University Ti:sapphire laser types. (a)
Standard laser. (b) Grating-tuned laser. (c) Injection-seeded laser. For details
see text. HR: high reflector; FPE: Fabry-Pérot etalon; QSW: Q-switch; CM:
curved mirror; Ti:sa: Ti:sapphire crystal; LF: Lyot-filter; OC: output cou-
pler; L: (biconvex) lens; G: reflective diffraction grating; PBE: prism beam
expander: PD: photodiode; PAM: piezo-actuated mirror.
12
2.1. Pulsed tunable laser systems
z
E E(0) y n =1 n >nz optnical axisEy 0 n y
1 2 1
e zEz E(L) yEy
x=0 x=L x α d β
(a) (b)
Figure 2.2.: Frequency Selection principles in a (a) Lyot-Filter and (b) Fabry-Pérot-
Etalon. Figures adapted from [49].
[49]. Similar to the LF, the finesse F is defined as the FSR to bandwidth δν ratio
of a transmission fringe. It scales with the parallelism of the surfaces and their
reflectivity R. In standard configuration the Mainz Ti:sapphire laser design uses
a FPE with d = 0.3 mm and√R = 0.4. This results in FSRFPE = c/2nd = 345 GHz
and a finesse of FFPE = π R/(1 − R) = 3.3. The bandwidth of this etalon is
δν = FSR/F ≈ 100 GHz, however, depending on the number of round-trips in the
resonator during pulse build-up (typically ≈ 100), the resulting laser bandwidth
is 3 GHz to 10 GHz, properly matching typical Doppler ensembles, as discussed
above. Note that the laser bandwidth can be further reduced to ≈1 GHz by
using an additional FPE (uncoated YAG, d = 6 mm, R = 0.08) [50]. Furthermore,
with a length of ≈ 450 mm the resonator itself acts as a FPE with Fcavity ≈ 0.8
and FSRcavity ≈ 330 MHz. Nonetheless, since the laser is running on multiple
longitudinal modes, the effective bandwidth is given by the FPE fringe which lies
within the LF transmission maximum. Fine-tuning of the emission wavelength
is performed through careful adjustment of the FPE tilting angle α. The output
characteristics are summarized in Table 2.1.
2.1.2 Grating-tuned laser
Although wide range spectroscopy can be performed using the standard resonator
geometry, frequency scanning is a tedious procedure, as the transmission peaks of
LF and FPE always have to be matched. Mode hops can often not be avoided.
Nonetheless, a continuous scanning operation can be realized by using a reflec-
tive diffraction grating as frequency-selective element, replacing LF and FPE. The
principle is depicted in Fig. 2.3. The grating has sawtooth-like grooves perpen-
dicular to the plane of incidence. Light reflected from two neighboring grooves
features an optical path difference ∆s. When the relation ∆s = mλ is satis-
13
2. Experimental instrumentation
grating normal grating normal
β dα ·sin(α)
α=β d·sin(β)
θB
Δs = d·(sdin(α)+sin(β)) Δs d= 2d·sin(α)
Figure 2.3.: Operation principle of a reflective diffraction grating. Left: general
case at an arbitrary angle of incidence α. Right: Littrow configuration. The
angle of incidence α equals the reflection angle β. Constructive interference
can be optimized for certain wavelengths with the so-called blaze angle θB.
Figure adapted from [49].
fied, where m denotes the interference order, constructive interference occurs. In
Littrow-configuration, shown on the right side in Fig. 2.3, the grating is used as a
wavelength-selective retro-reflector, which is particularly useful in lasers. Usually
the m = 1 interference order is coupled back to the resonator. The resolving power
of a diffraction grating scales with the number of illuminated grooves N according
to
λ
= mN. (2.5)
δλ
In the grating-tuned Ti:sapphire laser, a reflective grating with 1740 grooves/mm
(blazed for 800 nm) replaces the end mirror. A prism beam expander (PBE) is used
in front of the grating to horizontally widen the beam to 3 mm (1/e radius). This
laser type was developed in 2010 at Mainz University and TRIUMF [51, 52]. It
is shown in Fig. 2.1 (b). Tuning of the grating angle on a rotation stage allows
continuous frequency scanning. The grating-tuned laser features a more narrow
bandwidth than the standard design in the order of 1 to 3 GHz, which is favorable
in spectroscopy applications. However, it suffers from a lower output power by a
factor of ≈ 2. The output characteristics are summarized in Table 2.1.
2.1.3 Injection-seeded laser
In terms of spectral linewidth and stability, cw lasers are clearly superior to pulsed
lasers. Indeed, tunable cw Ti:sapphire lasers with linewidths of < 100 kHz and
output powers of few W are commercially available, although at relatively high
costs. Laser diodes can be used as an economical low-power alternative over a
limited wavelength range (typically ±10 nm around the specified emission wave-
length λc). Nonetheless, since the RI process highly benefits from pulsed laser
radiation, as discussed above, the advantages of cw and pulsed lasers have to be
14
2.1. Pulsed tunable laser systems
combined. This can be achieved by seeding a pulsed amplifier cavity (slave) with
a cw laser (master or seed). This concept was applied to the Mainz Ti:sapphire
laser system in 2010 [51], and refined in a collaboration with the University of
Jyväskylä [53, 54]. The layout is shown in Fig. 2.1 (c). A bowtie-shaped cavity is
designed to avoid spatial hole burning, which would prevent single-mode opera-
tion [55]. Standing waves are stationary, resulting in non-collected inversion in the
laser medium at the spatial nodes of the main resonator mode m. Consequently,
the m± 1 side-modes, which have their anti-nodes located at the nodes of the main
mode, are amplified. The bowtie-shaped design allows for a traveling wave and
thus avoids this effect. Selective amplification of the desired longitudinal mode is
achieved by proper focusing of stabilized cw light into the amplifier (slave) cav-
ity. Upon built-up of population inversion in the laser medium by injection of the
pump pulse, the seed light is already present in the resonator, strongly promoting
the corresponding longitudinal mode by stimulated emission. As a constructive in-
terference condition, the optical path length within the cavity needs to be matched
to multiples of λseed. Although the slave laser has a rugged design, it is prone
to temperature drifts and vibrations on the desired level of precision and requires
continuous active stabilization. For this purpose, one cavity mirror is mounted on
a piezo actuator, allowing for fast adjustments of the cavity length in the order of
few micrometers. A sensitive fast photodiode placed behind one of the curved mir-
rors collects leaking cw light from the cavity and provides the stabilization signal
to a fast lock-in voltage supply (TEM Laselock 3.0) controlling the piezo-actuated
mirror. The photodiode amplifier is blanked during pulse build-up preventing
disturbance from the high-intensity Ti:sapphire fluorescence and scattered pump
light. The electronic layout of the photodiode amplifier circuitry can be found
in [53]. Usually no frequency-selective elements are placed within the resonator,
however, at wavelengths far from the Ti:sapphire gain maximum Brewster-plates
or a LF may be required. Provided the seed laser is sufficiently stable and the
amplifier properly locked, the linewidth of the pulsed laser radiation can reach
the Fourier-limit of δν = TDP/δt ≈ 11 MHz (with a time-to-bandwidth product
of TDP = 0.44 for a Gaussian pulse shape and a pulse width of δt = 40 ns), while
the other characteristics are similar to the standard laser, as comprised in Table
2.1. At Mainz University, an external cavity diode laser (ECDL) with sophisticated
stabilization electronics and monitoring is used as master laser. For a description
of the cw laser system see Publication IV or [56, 57].
Note that two bowtie-resonator laser prototypes were designed in the scope of this
dissertation: a compact-footprint injection-seeded laser and an unseeded bowtie-
resonator laser with a dual-etalon configuration. The resonator geometry is based
on calculations using the Gaussian ray transfer matrix analysis, or ABCD formal-
ism, which is described e.g. in [58]. The optimized geometry results are directly
transferred to a paper-printed layout, which can be fixed to an optical bread-
board allowing for easy assembly and testing. The compact-footprint injection-
15
2. Experimental instrumentation
seeded laser is now in use at the ISOLDE-RILIS and is presented in [59]. The
unseeded bowtie-resonator laser development was later abandoned due to unsta-
ble single-mode operation and high spectral jitter. It is now being replaced by a
cw Ti:sapphire laser with a similar resonator geometry [60, 61], which can then
be used for seeding another pulsed Ti:sapphire amplifier. Since these prototypes
are widely unrelated to the spectroscopy results presented in this thesis (with the
exception of the 741 nm transition in Publication I, where the unseeded bowtie-
resonator laser was used), they are only briefly described in the appendix A.1.
Table 2.1.: Specifications for the output of the different Ti:sapphire laser types. The
values are based on the references [44, 51–54, 62], as well as measurements
which were performed in the scope of this dissertation. The given specifi-
cations correspond to 10 kHz repetition rate. For the injection-seeded laser,
values marked with an asterisk are directly transferred from the master laser.
In this case typical values for an ECDL, as used in Publication V, are given.
Standard Grating-tuned Injection-seeded
Repetition rate 7 to 15 kHz
Pulse width 40 to 60 ns
Average Power 3 to 5 W 1 to 2 W 3 to 5 W
Output range 700 to 1020 nm λ ± 10 nm∗c
Tuning range 100 GHz 700 to 1020 nm 10 to 20 GHz∗
Spectral bandwidth 1 to 10 GHz 1 to 3 GHz 20 MHz
Beam quality (M2) < 1.3
2.1.4 Frequency conversion
The fundamental emission range of Ti:sapphire of 700 to 1020 nm corresponds to
photon energies of 1.22 to 1.77 eV. With ionization potentials between 5 to 9 eV for
most metallic elements, typically 4 to 6 photons would thus be required for ion-
ization. Apart from the fact that a six-photon ionization scheme would be rather
impractical, most atomic ground state transitions can simply not be accessed by
the fundamental Ti:sapphire radiation. The atomic level density roughly scales
with the square of the principal quantum number n (for single-electron excita-
tions). Consequently, ground-state transitions in many elements lie in the blue
or ultraviolet (UV) wavelength regime. They can be accessed by higher harmon-
ics, i.e. multiples of the fundamental laser frequency. In this process a wave E is
passed through a so-called non-linear optical medium, which in response is polar-
ized. The electric polarization density P of the material can be expressed by the
16
2.1. Pulsed tunable laser systems
Taylor-series ( )
P (1) (2) (3)i = e0 χij Ei + χijk EjEk + χijklEjEkEl + ... , (2.6)
where e is the electric field constant and χ(n)0 the electric susceptibility tensor [63].
Considering a non-vanishing χ(2) and a plane wave E = Ez = E0 cos(kz− ωt) of
frequency ω traveling in z direction, the polarization density is given by
P (1) (2) 2 2z,SHG = e0χzz E0 cos(kz−ωt) + e0χzzzE0 cos (kz−ωt) (2.7)
2
(1) E
= e0χzz E0 cos kz− t (2)( ω ) + e0χ 0zzz (1 + cos(2kz− 2ωt)). (2.8)2
Obviously, the non-linear polarization generates a new wave with frequency 2ω,
referred to as the second harmonic of the incident wave, as well as a zero-frequency
component. This process is called second harmonic generation (SHG) and repre-
sents the simplest case of non-linear frequency conversion. The more general case
with two different waves E1(k1, ω1) and E2(k2, ω2) interacting within the medium
results in a polarization of the form
P = P(0) + P(ω1) + P(ω2) + P(2ω1) + P(2ω2) + P(ω1+ω2) + P(|ω1−ω2|), (2.9)
which includes sum-frequency and difference-frequency terms. Independent of
the specific process, the phase-matching condition
n3ω3 n= 1
ω1 n ω+ 2 2 (2.10)
c c c
has to be met, where ni are the wavelength-specific refractive indices of the mate-
rial. It is based on the fact that incident and generated waves should constructively
interfere along the entire length of the medium to achieve maximum intensity
in the corresponding term. Since non-linear media are often birefringent crys-
tals, where the refractive indices depend on direction and polarization of incident
waves, phase-matching can be achieved by a suitable crystal orientation with re-
spect to the optical axis (type I phase matching) or alternatively by temperature
adjustment (type II phase matching) [64].
SHG is routinely used as part of the Mainz Ti:sapphire laser system. The simplest
approach is focusing the fundamental output of a Ti:sapphire laser into a beta-
barium borate (BBO) crystal in single-pass geometry. The conversion efficiency
of this process is 10 to 20 %. Alternatively, the BBO is placed directly inside the
Ti:sapphire laser resonator. In this configuration the output coupler is replaced
by a broadband high-reflective mirror. As a result the cavity is completely closed
for the fundamental wave, leading to high power density within the cavity and an
efficient SHG process with ≈ 50 % conversion efficiency. The second harmonics
is coupled out with a dichroic mirror. A photograph of this configuration, as was
17
2. Experimental instrumentation
Figure 2.4.: Photograph of the standard Ti:sapphire resonator with intra-cavity
SHG, as used in [65]. A BBO crystal within the laser cavity generates the
second harmonic at λ(2) = 470 nm. In this configuration the output coupler
is replaced by a broadband high reflective mirror. The second harmonic is
coupled out with a dichroic mirror.
used in the work [65], is presented in Fig. 2.4.
Other processes employed at the Mainz laser setup are sum frequency genera-
tion and difference frequency generation [66]. The former is usually applied for
production of the third harmonic by mixing the fundamental and SHG waves. A
dedicated frequency tripling unit has been designed for this purpose, where a con-
version efficiency of ≈ 3 % can be achieved [44]. Moreover, the fourth harmonic
can be generated in a two-stage SHG process. However, wavelengths below 215 nm
cannot be reached as BBO absorbs light in this range, resulting in low output in-
tensity possible damage of the crystal.
Using non-linear frequency conversion, laser ionization schemes usually rely on
two to three photons, where higher harmonics are predominantly used for ground-
state transitions, which require high photon energies but relatively low laser power
for saturation.
2.2 Wavelength measurement
In laser spectroscopy an accurate frequency measurement is as important as the
bandwidth and stability of the probe laser. In particular the RIS technique de-
pends on reliable absolute frequency measurements, since usually several excita-
tion steps are involved and have to be added in order to extract high-lying level
energies. Even for relative frequency measurements, e.g. for the study of hyper-
fine spectra or isotope shifts, reproducibility has to be ensured since RIS most
often relies on the measurement of one isotope at a time. For this task usually
commercial wavelength meters are used, which are convenient in operation and
18
2.2. Wavelength measurement
CCD array
α α+(2m-1)θ
h wavemeter fringe patternθ to be added
Figure 2.5.: Left side: sketch of the Fizeau interferometer principle for use in a
wavelength meter. The interference creates a line pattern along the axis of
the wedge, which can be captured on a CCD array. Right side: fringe pattern
of a narrow-linewidth diode laser in the WSU-30 wavelength meter. The
spectrum is plotted as intensity vs. pixel number on the CCD array. The
lower graph shows the pattern of the thickest interferometer with a FSR of
≈ 2 GHz.
easily meet the required specifications in broadband spectroscopy experiments.
However, with increasing precision in high-resolution experiments, the accuracy
and long-term stability of such devices needs to be verified and, in specific cases,
extended by complementary measurements. This task was tackled by a collabora-
tion of European RIS groups and is presented in Publication IV. In the following,
the underlying basics of laser frequency measurement are briefly introduced.
2.2.1 Wavelength meters
Wavelength meters (or Lambdameters) are commercially available since many
years. Modern high-end devices reach an accuracy of few MHz in absolute fre-
quency measurement. The LARISSA lab uses two different commercial devices:
a High Finesse WS6-600 and a High Finesse WSU-30 with specified absolute 3σ
accuracy of 600 MHz and 30 MHz, respectively. The wavelength measurement is
based on the evaluation of fringe patterns from a set of Fizeau interferometers.
Since the exact assembly of the device is not known, only the basic principle is dis-
cussed here. Disassembly and upgrade of a similar, but also rather old wavelength
meter is presented in [67].
A Fizeau interferometer (FI) is very similar to a plane Fabry-Pérot interferometer
(FPI, see Fig. 2.2), except that the surfaces of the cavity are inclined at a small
angle θ (in the order of 10−5 rad [68]) to each other. A sketch is given on the left
side in Fig. 2.5. The phase shift of the m-th reflection order is given by
19
2. Experimental instrumentation
m 2π hδFI(λ, h, θ, α) = (sin [α + 2(m− 1)θ]− sin α) , (2.11)λ tan θ
where α is the angle of incidence and h the distance of the reflecting surfaces [68,
69]. Rather than a circular fringe pattern as obtained from a FPI, a FI forms a line
pattern along the axis of the wedge, which can be captured on linear CCD sensor
arrays. Note that the interferometer is often formed by two air-spaced reflecting
surfaces rather than a solid wedged substrate. Since the two partly reflecting
mirrors have to be wedged themselves in order to avoid etalon effects, this may
lead to confusion in some cases. However, the substrate wedge angle is much
larger than the actual Fizeau wedge. The free spectral wavelength range of FSRFI =
λ2/2h depends on the plate separation h and the wavelength λ [68, 69]. Combining
multiple FI of different FSR and evaluating the fringe patterns with a previously
recorded calibration pattern allows for a precise frequency measurement within
few milliseconds. The right side of Fig. 2.5 shows a measured sample pattern
of a diode laser close to 780 nm in the WSU-30 wavelength meter. According to
the data sheet, the FSR of the two finest (thickest) interferometers in the WSU-30
are 2 GHz and 15 to 20 GHz, whereas the design of the WS6-600 omits the finest
interferometer with a dedicated CCD array. However, the specified accuracy of
600 MHz is sufficient for all kinds of broadband spectroscopic experiments.
2.2.2 Absolute references
As mentioned in the previous section, wavelength meters rely on external ab-
solute references. Although commercial devices are initially calibrated, frequent
re-calibration is necessary to account for temperature, pressure or mechanical in-
fluences. A prerequisite for reference sources is the precise knowledge of the ab-
solute frequency as well as long-term stability. Suitable options are e.g. frequency
combs, stabilized single-frequency lasers or tunable lasers locked to an atomic
transition. From an economical point of view the former is undue for the sole use
as wavelength meter calibration source. The LARISSA lab formerly used a stabi-
lized HeNe laser (SIOS SL03) with a specified wavelength of 632.991 040(25) nm
as absolute reference. Despite offering a suitable stability of ∆ν = 2.5 MHz over
24 h, the absolute frequency uncertainty of 19 MHz exceeds the 1σ accuracy of the
WSU-30 wavelength meter. Moreover, the HeNe emission is relatively far away
from the Ti:sapphire laser output between 700 and 1000 nm, making it rather un-
suitable for calibration in that range, as the wavelength meter accuracy is specified
for a calibration within ±200 nm of the wavelength to be measured. For these rea-
sons a Rb saturated absorption spectroscopy (SAS) setup was recently installed as
replacement for the HeNe laser. A schematic view of the setup is shown in Fig.
2.6. As laser source an external cavity diode laser (Toptica DL Pro 780) is used,
which is coupled to a Rb spectroscopy assembly (TEM CoSy 4.0). SAS is based
on a pump-probe scheme. The laser beam is split into three beams: a reference
20
2.2. Wavelength measurement
optical
diode
ECDL
λ meter Laselock
Rb vapor cell
BS Ref. PD1 -
Probe +PD2
Pump
Figure 2.6.: Schematic of the Rb saturated absorption spectroscopy setup. ECDL:
external cavity diode laser; BS: beam splitter; PD: photodiode. Note that the
actual design of the commercial Rb spectroscopy module may differ slightly.
beam, a probe beam and a high intensity pump beam. The reference beam sim-
ply passes through the Rb vapor cell, whereas the pump and the probe beam are
counter-propagating within the cell. Both, the reference beam and the probe beam
are separately captured on photodiodes after transmission through the cell. The
difference signal can be monitored with an oscilloscope. The feedback signal from
the photodiodes is sent to an electronic laser stabilization system (TEM LaseLock
3.0), which controls a current offset for the ECDL, enabling fast frequency scan-
ning within a range of few GHz. Since the atomic transition frequency ν of moving
atoms at a velocity v in the Rb gas is shifted according to ν = ν0(1+ v/c), where ν0
is the frequency at rest, the reference beam imprints a Doppler-broadened absorp-
tion profile on the photodiode upon scanning1. The absorption of the probe laser,
on the other hand, shows additional features. For ν = ν0 both, the probe and the
pump beam address the same velocity class of atoms, i.e. v = 0. In this case the
high intensity pump beam burns a hole into the atomic ground state population,
thus lowering the absorption of the probe beam. This effect is visible as narrow
dip in the absorption structure, also known as Lamb-Dip. For multiple transitions
which are separated by less than the Doppler width, a number of Lamb-Dips plus
additional lines are visible. These so-called crossover lines occur at laser frequen-
cies exactly between the two transition frequencies. In this case the probe and the
pump beam address different transitions for atoms moving at velocities ±v and
∓v, respectively [70].
For wavelength meter calibration in the Ti:sapphire output range the D2 line in
the Rb atom at 780 nm was chosen, which is close to the Ti:sapphire gain max-
imum. The level scheme and recorded spectrum of the multiplet starting from
the F = 2 ground state is shown in Fig. 2.7. For reasons of a larger line separa-
1For details on atomic transitions and Doppler broadening see sections 3.2 and 3.3.
21
2. Experimental instrumentation
87Rb F'=3 
193.7 MHz
 2P 63/2 72.9 MHz F'=2 
229.9 MHz 5
302.1 MHz F'=1 F'=0 
4
780.241 209 7 nm
384.230 484 5 THz 3
F=2 2
2 563.0 MHz
 2S1/2 1
4 271.7 MHz 0 2 4 6 8
F=1 Time (ms)
Figure 2.7.: Left: level scheme for the D2 line in 87Rb. Data is taken from [71],
where also higher precision numbers and uncertainties can be found. Right:
saturated absorption spectrum for F = 2 in 87Rb, corresponding to the transi-
tions shown as blue arrows in the level scheme. Crossover lines are denoted
by an X with the participating F′ levels in brackets. The baseline structure
is caused by slight imperfections in the gain adjustment of the two photodi-
odes. The horizontal axis gives the timescale at which the ECDL is scanned
over the structure (i.e. the progress of the diode current offset sweep).
tion 87Rb was chosen over 85Rb and the F = 2 over the F = 1 ground state. The
F = 2 → F′ = 3 line is of advantage for fast re-locking. Upon losing the lock,
the laser approaches the structure from the high-frequency side. Stabilization is
based on a top-of-fringe dither lock. The F = 2 → F′ = 3 transition in 87Rb is lo-
cated at 780.246 020 886(22) nm (= 384.228 115 203(11)THz) [71]. This precision of
11 kHz in literature exceeds by far the long-term stability of the SAS setup, which
is specified as ∆ν = 2 MHz and acts as the limiting factor in calibration accuracy.
Since drifts in the wavelength meter readout may reach up to 5 MHz per hour (see
Publication IV), an automated re-calibration was implemented into the LabVIEW
data acquisition. The cycle can be set to a fixed time interval or to a number of
recorded data points.
2.2.3 Fringe-offset technique
In addition to laser frequency measurement using wavelength meters, a scanning
Fabry-Pérot interferometer (SFPI) offers a complementary, relative measurement.
It is based on a comparison of transmission fringes of a laser under investiga-
tion with those of a reference laser of known wavelength and high stability. In
the LARISSA lab this complementary measurement is only applied to the master
ECDL used for seeding of the injection-locked Ti:sapphire laser (see Sec. 2.1.3),
where highest accuracy is required. At the same time this technique is used for
(slow) stabilization and scanning of the the master ECDL. An additional fast stabi-
22
Photodiode signal (V)
F'=1
X(1,2)
F'=2 
X(1,3)
X(2,3)
F'=3
2.2. Wavelength measurement
Confocal Piezo
HeNe DM SFPI 6 t tDM tPD1 O,ref O I,ref(Ref.)
4
Ramp PD2
2
Signal 0
ECDL iScan PC processing
0 2 4 6 8 10
Time (ms)
Figure 2.8.: Left: Schematic layout of relative frequency measurement with a con-
focal scanning FPI. The feedback signal can be used for slow stabilization
of the ECDL. DM: dichroic mirror; PD: photodiode. Right: Signal readout
recorded with an oscilloscope. Signals are scaled for better visibility. The
blue envelope marks one piezo ramp. The photodiode signal of HeNe and
ECDL (near 930 nm) are plotted in the colors corresponding to the sketch.
The HeNe signal is generally low and features some electronic baseline noise,
however, fringes are clearly visible. Fringes are marked according to Eq. 2.12.
A detailed descriptiopn of the signal processing is given in [56].
lization is provided by a quadrature interferometer coupled to a fast electronic
lock-box (TEM iScan). For a technical description of the locking see [56]. A
schematic layout of the fringe-offset measurement setup is shown in Fig. 2.8. The
ECDL and a HeNe reference laser (SIOS SL03) are transmitted through a confocal
SFPI. A confocal FPI features curved mirrors, which are spaced at a distance d cor-
responding to the mirror radius of curvature. In contrast to the plane-parallel FPI,
the free spectral range is FSRFPI,conf = c/4nd [49]. Using a piezo-actuated mirror,
the cavity length is periodically changed on a micrometer scale, so that each ramp
covers several transmission fringes of both lasers. After passing the cavity, the two
laser beams are separated with a dichroic mirror and the intensities are captured
by fast photodiodes. From the fringe time differences, measured from the start of
the piezo ramp, the relative frequency νrel of the ECDL to an arbitrary anchor point
can be determined. The first and second fringes (offsetfringe and interfringe) of
the HeNe reference laser act as a kind of ruler in this measurement. The frequency
change of the ECDL between two piezo ramps is given by
(t′ − t′O O,ref)− (tO − tO,ref) λ
ν = nFSR · refrel , (2.12)tI,ref λ
where tO and tI mark the timings of the offset- and interfringe, respectively.
Primed symbols refer to fringe timings in a different piezo ramp [57]. From Eq.
2.12, it is obvious that the wavelength of both lasers and the FSR of the SFPI have
to be known. The latter was measured as FSR = 299.721 MHz [72]. With the spec-
23
Signal (arb. units)
2. Experimental instrumentation
ified wavelength of the HeNe of λref = 632.991 040(25) nm, a precision of λ in the
range of 0.1 nm is sufficient to reach ∆νrel < 40 kHz [57], so that in practice the
uncertainty of the master ECDL is dominated by the laser frequency jitter of few
MHz.
2.3 RISIKO
The RISIKO mass separator is the heart of the LARISSA lab at Mainz. It is an
exemplary apparatus for RIMS applications. Regarding its key features, i.e. a hot-
cavity laser ion source coupled to a magnetic mass separation, it is very similar
to the RIB facility ISOLDE at CERN. Obviously, with the main difference being
that ISOLDE is directly coupled to the radioactive isotope production site (on-line
method), whereas RISIKO uses externally introduced samples (off-line method),
but nonetheless acts as RIB facility with operation permission for a variety of
long-lived radionuclides.
The RISIKO separator was originally designed by K. Zimmer [73] for trace anal-
ysis of strontium radioisotopes in environmental samples, following the disaster
of the Chernobyl nuclear power plant in 1986. Today the main applications of
RISIKO are isotope separation and ion beam implantation into collector foils or
calorimetric detectors, most prominently within the ECHo project [32–34], or laser
spectroscopy of stable and long-lived isotopes [74–76], as e.g. funded within the
RESIST project. In this context, RISIKO is also used as an off-line research & devel-
opment laboratory for novel developments and refinements of the ISOLDE laser
ion source RILIS (see section 2.5).
The combined vacuum chambers of the separator have a total length of ≈ 7 m on a
pressure in the range of 10−7 to 10−8 mbar. Some parts of RISIKO are modular and
can be replaced depending on the current application. Since this work is focused
on laser spectroscopy, the apparatus is presented in the corresponding configura-
tion if not explicitly noted. An overview of the setup is given in Fig. 2.9. It can be
divided into four main parts: ion source, ion beam extraction and shaping, mass
separation and ion detection.
2.3.1 Ion source
The hot-cavity ion source of RISIKO is depicted in Fig. 2.10. The central parts
are the sample reservoir (also referred to as mass marker2) and the atomizer (also
referred to as hot-cavity or line2), both made of tantalum. The atomizer is a tubular
oven with 2.5 mm inner diameter, 1 mm wall thickness and 35 mm length, mounted
between a water-cooled multi-layer Ta spring and a water-cooled Ta panel, featur-
2The terms mass marker and line refer to the corresponding components at ISOLDE’s ion source,
where the line acts as transfer tube between target and ion beam extraction and the mass mark-
ers as independent reservoirs, containing stable samples which can be used for mass calibration.
24
2.3. RISIKO
Figure 2.9.: Overview of the RISIKO mass separator setup. Red: Ion source; green:
Ion beam extraction and shaping; blue: Mass separation; magenta: Ion de-
tection. Parts are not to scale for better visualization. For details see text.
Figure adapted from [34].
ing four through-holes to minimize heat dissipation. The sample reservoir is a bent
capillary with an inner diameter of 1 mm, a wall thickness of 0.5 mm and 165 mm
length, which is connected to the back side of the atomizer through a conical
push-in assembly. The atomizer mount is fixed to the Ta spring by a molybdenum
washer and nut, preventing irreversible welding of the connection surfaces.
Usually the sample material is dissolved in nitric acid (HNO3) and afterwards
dropped on a ≈ 5× 5 mm backing foil. The solution is dried on the foil, which is
then folded like an envelope and introduced into the sample reservoir. A photo-
graph of a 5 µL sample solution droplet on a 5× 5 mm Ti foil, as well as a folded
”envelope” is shown on the right side of Fig. 2.10, with an atomizer for compar-
ison. The choice of backing material depends on the ion source chemistry. Since
the dried sample is usually oxidized, the backing should act as a reduction agent
as the sample diffuses through the foil. Titanium, Zirconium or Hafnium are of-
ten used as backing material, depending on the required source temperature and
a priori thermal equilibrium simulations3. Atomizer and sample reservoir can be
heated resistively with a currents of up to 400 A and 150 A, respectively, allowing
operation at temperatures of up to 2500 ◦C. While the atomizer is always operated
at a sufficiently high temperature for atomization, the temperature of the sample
reservoir is carefully ramped up for a controlled release of the sample into the at-
omizer, where resonance ionization by the incident laser beams occurs. A uniform
temperature distribution in the whole assembly is crucial for sensitive studies on
limited sample amounts. Cold spots lead to adsorption of sample atoms on walls,
lowering the effective ionization efficiency. On the other hand, excessive heating
3HSC Outotec Chemistry 9.
25
2. Experimental instrumentation
Laser
Beams
HeHaeta sth sihelideilndgs
WasWhaesrher 50 mm
NNuutt
Sample
reservoir
AtoLmineizer
Figure 2.10.: Left: Cross section of the hot-cavity ion source assembly of the RISIKO
mass separator (CAD drawing). The sample is placed in the sample reservoir,
which can be heated independently of the atomizer. The incident laser beams
resonantly ionize sample atoms within the atomizer tube. Ions are extracted
with 30 kV upon leaving the atomizer. Right: Photograph of a 5 µL sample
solution droplet on a 5× 5 mm Ti foil and a folded sample ”envelope”, with
the 35 mm long atomizer tube for scale.
enhances surface ionization, as described(by the Saha)-Langmuir equation
n+ g+ e(W − IP)
= exp , (2.13)
n0 g0 kBT
where n+ and n0 denote the flux of ions and neutral atoms with their respective
statistical weights g+ and g0 (the atomic and ionic ground state degeneracy), e
the elemental charge, W the work function of the ion source material and IP the
ionization potential of the sample atoms [77].
Obviously the hot-cavity can act as a surface ion source by itself. However, in
most cases the efficiency is comparatively low and a very limited elemental selec-
tion is only provided by the respective ionization potentials of the different species
within the ion source. Therefore surface ion source operation is avoided for most
elements, with an exception in the groups of the alkaline and alkaline-earth ele-
ments due to their low ionization potentials.
In laser ion source operation, the effect of surface ionization introduces unspecific
contamination in the extracted ion beam, therefore reducing the selectivity of the
ion source. In order to keep the effect of surface ionization at minimum while
maintaining high efficiency, an optimization of the ion source temperature distri-
bution was recently performed and is described in [33]. With typical operation
parameters for rare-earth samples, the ion source temperature is between 1500 ◦C
to 2200 ◦C. Nonetheless, specific experiments can be impeded or even prevented
26
2.3. RISIKO
e- repeller Ion repeller Exit electrode
RF quadrupole
Laser
Atomizer beams
Atom beam
Perpendicular laser
Figure 2.11.: Left: Schematic layout of the Laser Ion Source and Trap LIST. The
dashed line indicates the perpendicular laser-atom interaction geometry (PI-
LIST mode). Right: Photograph of the ion source region with an installed
(PI-)LIST module.
by ion beam impurities from surface ionization. Such cases are, for example, when
a low-IP element has stable isobars to the nuclide of interest, or simply when the
number of sample atoms is so small that even surface ionization of metallic ele-
ments is in the order of the laser ion signal. Approaches for further reduction of
the surface ion contribution are the use of low-workfunction materials within the
ion source [78], or a separation of the laser-atom interaction region from the hot
atomization region. This latter concept is implemented in the Laser Ion Source
and Trap LIST [79–81].
The LIST is an optional ion source module, which can be installed directly in front
of the atomizer. A schematic view is shown in Fig. 2.11. It features two repeller
electrodes facing the atomizer, a radio frequency (RF) quadrupole structure and
an exit electrode. Like the Ta panel holding the atomizer, the exit electrode is set to
the local ground potential of 30 kV. The voltages applied to the two electrodes fac-
ing the atomizer define the mode of operation: In Ion-Guide mode both electrodes
are set to a negative potential of −20 V. Ions generated within the atomizer are
extracted, guided by the 1.2 MHz RF field towards the exit electrode, and are ex-
tracted from the source region with 30 kV. This configuration resembles operation
of the ion source in standard RILIS mode, i.e. without a LIST module, with an ef-
ficiency loss factor of < 2 [40]. In LIST mode, the second electrode is set to +20 V,
thus acting as an ion repeller. Surface ions from the atomizer are suppressed and
only laser-ionized species from the atomic beam effusing to the LIST volume are
extracted. In this case the first (negative) electrode acts as an electron repeller,
preventing electron-impact ionization within the LIST volume through electrons
emitted from the hot atomizer. Typical suppression factors in LIST mode are in
27
2. Experimental instrumentation
the order of 103 [76, 81]. However, LIST operation also introduces a loss factor,
as all charged species (including laser ions) within the atomizer are suppressed.
Typical loss factors lie between 20 and 50 [76, 81]. Therefore LIST operation is only
advisable if an experiment depends on additional isobar suppression.
The most recently introduced mode of operation, the PI-LIST-mode, is described in
detail in Publication V, as well as in the references [41, 74, 76]. Therefore it is only
mentioned here for the sake of completeness. As the name suggests, the perpen-
dicularly illuminated (PI) LIST features a different laser-atom interaction geometry.
Instead of guiding all laser beams directly into the atomizer, i.e. anti-collinearly
to the ion beam axis, one laser beam perpendicularly intersects the atomic beam
effusing from the atomizer. This geometry offers greatly reduced spectral Doppler
broadening. Some quantitative considerations about expected Doppler linewidths
in perpendicular laser-atom interaction are given in section 3.3.
2.3.2 Ion beam extraction and shaping
The RISIKO ion optics consists of an extraction electrode, an einzel lens, a set of
horizontal and vertical deflector plates and a quadrupole triplet, as schematically
depicted in Fig. 2.9 by the green parts. The ion beam is extracted in two stages
from the ion source region, which is set to a potential of +30 kV. The extraction
electrode, located 40 mm downstream of the LIST exit electrode (or the atomizer
outlet in standard RILIS operation) acts as a pre-acceleration stage, with a potential
of typically +20 kV. The tip of the extraction electrode features a conical shape in
order to counteract beam expansion due to space-charge effects. The full beam en-
ergy of 30 keV is reached at the grounded first electrode of the einzel lens, located
400 mm downstream of the extraction electrode. The einzel lens assembly consists
of three ring electrodes, with the outer two sitting on ground potential and the
middle electrode at typically +10 kV. Through deceleration and subsequent accel-
eration of the ion beam, a focusing effect can be achieved without changing the
beam energy. Together with the two-stage extraction, this configuration acts as a
telescope, allowing careful adjustment of beam size and divergence. For minor
corrections of the ion beam direction, which can be traced back to slight mis-
alignment of the atomizer, two sets of 140 mm long deflector plates are installed
downstream of the einzel lens, with an offset of ±50 mm to the ion beam axis. In
order to preserve the on-axis potential, opposite sign voltages of identical abso-
lute value are applied to facing plates. Typically low voltages |Udefl| < 50 V are
needed for optimal transmission. Note that the deflector plates can also be used as
kickers for active ion beam gating. Since the ion beam has a pulsed time-structure,
following the 10 kHz laser repetition rate, the continuously extracted surface ion
contribution can be actively suppressed by a factor of > 2 by fast switching of
the deflector plates to a higher potential of e.g. ≈ 300 V [76, 81, 82]. Finally, an
electrostatic quadrupole triplet allows for compensation of an astigmatism in the
28
2.3. RISIKO
ε' B ε" 1 mm m+Δm
FP
2x0 α=60° Slit
Figure 2.12.: Sketch of the mass separation principle with a focusing dipole mag-
net. For details see text. x0 : beam offset; e′/e′′ : entrance/exit angle; B :
magnetic field; r0 : nominal radius; α : nominal deflection angle; m : mass;
∆m : mass difference; FP: focal plane. Figure adapted from [73].
ion beam. Ideally, after passing the quadrupole triplet, the ion beam is adjusted
for optimal parallelism in both axes.
2.3.3 Mass separation
Magnetic mass separation is based on the circular deflection of charged particles
traveling in a magnetic field B. A sketch of the dipole magnet mass separation
principle is given in Fig. 2.12. With a fixed kinetic energy of eU0 = 30 keV of the
incident ion beam, the deflection radius r is given by the equilibrium of Lorentz
force and centrifugal force as √
1 2mU
r = 0 , (2.14)
B e
where m denotes the particle mass. A beam of finite width 2x0 is focused upon
passing the magnet, with the focal length exclusively depending on the geometric
parameters r, α, e′, e′′ (cf. Fig 2.12) and the particle mass m. With a proper shape
of the magnet yoke in y-direction, as well as the angles e′ and e′′, the foci in x
and y direction can be matched. At the focal plane of the nominal trajectory with
r = r0 a slit aperture is placed. In order to achieve a separation of two neighboring
masses m and m + ∆m, their geometric splitting at the position of the slit has to
be greater than the beam spot size. In case of a parallel beam, the mass resolution
can be expressed as
m D
x m= , (2.15)
∆m 0 ke
where D (r , α, e′, e′′m 0 ) is the mass dispersion, e the emittance representing the
beam quality, and k an imaging parameter [73]. Under optimal conditions the
RISIKO magnet reaches a resolving power of m∆m ≈ 700. Obviously the magnet
29
r0=0.75 m
2. Experimental instrumentation
can be tuned to transmit a mass of choice according to Eq. 2.14 by adjusting the
magnetic field. The maximum field strength of the RISIKO magnet is 0.62 T [73].
According to Eq. 2.14, the maximum mass is ≈ 350 u at 30 keV beam energy.
2.3.4 Ion detection
The ion detection region is shown in Fig. 2.9 (magenta). After passing the slit
aperture, ions can be detected either with a Faraday cup (FC) or a channel electron
multiplier (CEM). The home-built FC essentially consists of a conducting plate
for charge collection and an electron repeller. Implanted ions induce a current
flow from the plate, which can be measured with a sensitive electrometer. Since
an impinging particle may also release several electrons, an aperture set to -100 V
is placed 20 mm upstream, deflecting electrons back to the plate. The sensitivity
of the FC is limited by electrical noise on a level of ≈ 50 fA, corresponding to
≈ 3× 105 e s−1. On the other hand, the FC has practically no upper limit for the
ion beam load. Typical peak currents that can be achieved at RISIKO are some
hundred nA. For very low-intensity beams, as usually the case in spectroscopy
of radioactive species, the CEM offers a more sensitive measurement. In order to
guide the ions to the CEM, the FC is retracted from the beam axis with a pneumatic
piston. The diverging ion beam passes an einzel lens for post-focalization and a
set of deflectors for beam steering. Finally, ions reach the CEM. It consists of a
front aperture, a conversion electrode, installed at an angle of ≈ 30◦ to the beam
axis, and a conical insulating channel, which is layered with a high-resistance
material on the inside. By applying a potential to the front of the channel, an
electric field gradient is created towards the grounded electrode on the back side.
The RISIKO CEM is operated with −1 kV on the front aperture, −3 kV on the
conversion electrode and −2.5 kV on the front of the channel. Upon ion impact
on the conversion electrode, secondary electrons are released and guided into the
channel, where an electron avalanche is created through several wall collisions
towards the grounded electrode. The signal is converted to a TTL pulse by a
discriminator and acquired with an Arduino MCU. The dead time of an identical
CEM was measured in [83] as τ = 398(50)µs, allowing single ion counting up
105 s−1 with losses < 4 %. Higher counting rates should be avoided anyway to
prevent damage of the detector.
Data acquisition and storage is performed with a modular LabVIEW interface on
a personal computer. The data acquisition cycle is 300 ms.
2.4 MABU
The Mainz Atomic Beam Unit (MABU) is a compact laser ion source coupled to
a quadrupole mass spectrometer. This tabletop setup has a footprint of < 1 m2.
Since it is similar to RISIKO in many aspects, a detailed description is not given
30
2.5. ISOLDE
here to avoid repetition. The setup is briefly described in Publication I, Publication
II and Publication III. For details the reader is referred to [83, 84], where the design,
construction and characterization of the apparatus was performed.
The main differences to RISIKO are the low beam energy of ≈ 200 eV and the
use of a quadrupole mass filter (QMF) instead of a magnet. An in-depth treatise
of the QMF mass separation principle and a characterization of the same type
quadrupole as used in the MABU system (ABB Extrel) is given in [85]. The MABU
setup is coupled to a dedicated Ti:sapphire laser system and can thus be operated
independently of RISIKO. The main drawback is its relatively low ion transmission
efficiency through the apparatus, which is in the range of 10−3 and thus about one
to two orders of magnitude lower compared to RISIKO. In addition, the MABU
system only features ion detection by a CEM, so it can be operated only at low
ion currents. Therefore it is mainly used for laser spectroscopy applications, e.g.
ionization scheme development [36, 86], measurement of ionization potentials [87,
88], or high-resolution spectroscopy on stable isotopes or long-lived radioisotopes
[89–91].
2.5 ISOLDE
The ISOLDE facility is the on-line mass separator at CERN. The original facility, lo-
cated at the synchrocyclotron, started operation in 1967 and was moved to the pro-
ton synchrotron booster (PSB) in 1992 [92]. A recent technical overview is given in
[93]. ISOLDE delivers radioactive ion beams for fundamental atomic and nuclear
physics research to currently ten fixed experimental setups4, as well as a number
of temporary setups, such as the GANDALPH spectrometer [94, 95]. The produc-
tion of radioisotopes is achieved using the ISOL technique. Protons are accelerated
to an energy of 1.4 GeV in the PSB and impinge on a massive target, formed e.g.
by uranium carbide (UCx), producing a wide range of short lived nuclei all over
the Nuclear Chart through spallation, fission and fragmentation processes [96].
The reaction products effuse out of the target unit through a transfer line into the
ion source. Ions are extracted with 60 kV, followed by magnetic mass separation
and delivery to an experiment. ISOLDE uses different types of ion sources, based
on surface ionization, plasma ionization or resonance laser ionization (RILIS). The
latter has been producing the majority of beams in recent years due to its high se-
lectivity and efficiency. The target and ion source in RILIS configuration is shown
in Fig. 2.13. Obviously, this configuration is very similar to the RISIKO ion source
(cf. Fig. 2.10 and Fig. 2.11), so that both facilities directly benefit from the close
collaboration. Moreover, the RILIS is using the Mainz type Ti:sapphire lasers as
part of their laser system [44]. Consequently, the LARISSA group and the RILIS
team are working on similar developments. This includes upgrades to the laser
4http://isolde.web.cern.ch/experimental-setups. Accessed 12/2019.
31
2. Experimental instrumentation
Figure 2.13.: Layout of the ISOLDE target and ion source unit (CAD drawing). The
many common features to the RISIKO ion source are obvious (cf. Fig. 2.10
and Fig. 2.11). For details see text.
system, new laser ionization schemes, measurement of ionization efficiencies for
different elements [97, 98] or technical ion source developments, e.g. the LIST [79–
81]. Many successful in-source spectroscopy experiments were performed with
the RILIS technique [99, 100]. However, the resolution that can be achieved is lim-
ited by spectral Doppler broadening within the hot ion source. High-resolution
in-source spectroscopy techniques, such as the PI-LIST [41, 76] or Doppler-free
two-photon spectroscopy [59], are coming up only recently. In this context, it
should be noted that there are two fixed experiments at ISOLDE focusing on high-
resolution laser spectroscopy, namely COLLAPS [101, 102] and CRIS [48, 103, 104].
Both setups rely on collinear laser spectroscopy of fast atom or ion beams. The
initial energy distribution of atoms in the ion source is conserved during the ex-
traction of ions by 60 keV, resulting in a strongly compressed Doppler broadening,
to the order of the natural linewidth of strong atomic transitions [47, 48]. Like this
hyperfine splittings and isotope shifts in long isotopic chains can be measured and
may be used to extract nuclear structure parameters. A compilation of radioiso-
topes that have been subject to laser spectroscopy studies is given in Fig. 2.14.
A similar overview is given in [7]. Note that the presented data was not exclu-
sively taken at ISOLDE. Other facilities that should be mentioned in this context
are ISAC at TRIUMF or IGISOL at JYFL, among others5. In order to expand this
chart of nuclear structure data, is it important to provide suitable laser ionization
32
2.5. ISOLDE
Figure 2.14.: An overview of the status of laser spectroscopy on radioactive iso-
topes. This figure was taken from an online database maintained by the
group of W. Nörtershäuser at TU Darmstadt. Black tiles mark stable iso-
topes, red tiles mark radioactive isotopes which have been studied by laser
spectroscopy with the results published in peer reviewed articles. References
are given on the website5.
schemes for previously inaccessible elements, both for ion beam production and
probing of individual transitions. Additionally, the extension of high-resolution in-
source spectroscopy capabilities is of high relevance as complementary technique
to collinear laser spectroscopy. The benefits of in-source techniques are the inde-
pendence from dedicated beam lines, laser systems or charge exchange processes
for re-neutralization of ions, greatly reducing the complexity of the experiment.
5https://www.ikp.tu-darmstadt.de/gruppen_ikp/ag_noertershaeuser/research_wn/
exotic_nuclei_wn/uebersicht_2/laserspectroscopy_survey.de.jsp. Accessed 12/2019.
33

Chapter3
Atomic structure and the ionization
potential
3.1 Atomic energy levels
As a starting point for the treatment of many-electron systems we first consider
a simple atomic system with a single electron orbiting a nucleus with Z protons.
The quantum-mechanical energy levels of such a hydrogen-like system are given
by the solution of the time-independent Schrödinger equation H |ψ〉 = E′ |ψ〉. In
polar coordinates (r, θ, φ) and with the center of mass of the system as origin of
coordinates it can be written as
− h̄
2
∆ψ(r, θ, φ) + VC(r)ψ(r, θ, φ) = E′ψ(r, θ, φ), (3.1)2µ
2
where µ = meM/(me + M) is the reduced mass of the system and V ZeC(r) = −4πe0r
the Coulomb potential [105]. By double separation of variables the solution, i.e.
the wave function, can be expressed as
ψnlm(r, θ, φ) = R mnl(r)Yl (θ, ψ), (3.2)
where the quantum numbers n, l and m can assume the values
n ∈N (Principal quantum number)
l = 0, 1, ..., (n− 1) (Angular momentum quantum number)
m = −l,−(l − 1), ..., l (Magnetic quantum number).
In spectroscopic notation l = 0, 1, 2, 3, 4, ... is written as s, p, d, f , g, .... The spherical
harmonics Yml (θ, ψ) completely describe the angular dependence of Eq. 3.2. They
are tabulated and can be found in common atomic physics textbooks, e.g. [105,
35
3. Atomic structure and the ionization potential
106]. The differential equation for the radial wave function Rnl has a similar form
to Eq. 3.1, but is only one-dimensional. With the substitution Rnl(r) = unl(r)/r it
can be written as
h̄2 d2− unl2 + Veffu
′
nl = Enlunl, (3.3)2µ dr
2
introducing the effective potential V h̄ l(l+1)eff = 2 r2 + VC [107]. For a state with princi-µ
pal quantum number n the energy eigenvalue is given by
µZ2e4′ ≡ ′ − −Z
2R
E E µnl n = 2 = , (3.4)8e h2n2 20 n
where Rµ is the reduced Rydberg energy [106]. In the case of hydrogen, it cor-
responds to RH = 13.6 eV, the binding energy of the atomic ground state. The
energy in 3.4 only depends on n, leading to a ∑n−1l=0 (2l + 1) = n
2-fold degeneracy
of each state.
Note that in 3.4, n→ ∞ corresponds to a binding energy of E′∞ = 0. In order to go
along with the notation in the publications presented within this work, we define
the atomic ground state as the zero-point energy. Consequently, En describes an
excitation energy rather than a binding energy and E∞ corresponds to the ion-
ization potential (IP), i.e. the energy required to lift the electron from the atomic
ground state to the ionization continuum. Accordingly, Eq. 3.4 is modified to
− Z
2R
En = IP
µ
2 . (3.5)n
3.1.1 Fine structure
Relativistic corrections to the energy eigenvalues derived from the Schrödinger
equation 3.1 are summarized under the term fine structure (FS). The considera-
tion of these effects partly lifts the above mentioned degeneracy. The individual
contributions to the fine structure are
• The increase√in mass of the electron by taking into account the relativistic
energy E = m2c4 + p20 c2 −m 20c + V.
• Non-localization of the electron within the volume λ3c , where λc = h̄/mec is
the Compton wavelength of the electron, leading to a shift in s-wave energies.
• The spin-orbit interaction, based on the coupling of the electron spin moment
to the magnetic field caused by its orbital motion. The parallel or anti-parallel
orientation of the spin s to the orbital angular momentum l leads to a split-
ting of energy levels into doublets. The total angular momentum j = l + s
is introduced, with a new quantum number j = l ± 1/2 (or more generally
36
3.1. Atomic energy levels
j = |l− s|, .., l + s). Note that, analogous to l, s and j have associated magnetic
quantum numbers ms and mj.
Finally, taking into account the FS corrections, the excited energy levels of
hydrogen-like atoms are given by[ 2 2 ( )]
E = IP− E′ Z α 1nj n 1 + −
3
, (3.6)
n j + 1/2 4n
where E′n denotes the energy from Eq. 3.4 and α = e2/4πe0h̄c is the fine structure
constant [106]. In hydrogen the FS corrections are in the order of 10−4 eV, however,
the FS contribution scales with Z2, which leads to a relatively large effect in heavy
atoms.
3.1.2 Multi-electron systems
The exact calculation of energy levels in a multi-electron system is not possible
anymore, since the mutual Coulomb repulsion of each individual electron has to
be considered, leading to an N-particle problem. In practice one has to rely on
mean-field approaches, treating the individual electrons as independent particles
in an effective potential. Depending on the level of precision and the complexity
of the atomic system, theoretical calculation may become computationally very
intensive. The common approximation methods shall not be discussed here and
can be found e.g. in [107, 108]. As established above, each single-particle state is
fully characterized by a set of quantum numbers (n, l, ml, ms). In a multi-electron
system, two electrons may not share the same set of quantum numbers due to the
Pauli exclusion principle. The individual angular momentum quantum numbers
in multi-electron systems may couple in different ways to a total angular momen-
tum J. In light atoms the single-electron orbital angular momenta li and the spins
si couple through the exchange interaction to a total orbital angular momentum L
and a total spin S, respectively, which in turn couple to the total angular momen-
tum
N N
J = L + S with L = ∑ li and S = ∑ si. (3.7)
i=1 i=1
This is referred to as LS-coupling. The state is described with a term symbol
according to
2S+1LπJ , (3.8)
where L = 0, 1, 2, ... is written as S, P, D, ... in analogy to the lowercase letters for
single particles. The parity π is omitted for even parity states and denoted with a
superscript ’o’ for odd parity states.
In heavy atoms, where the spin-orbit interaction dominates the exchange inter-
action, individual electron spins and orbital angular momenta couple to single-
37
3. Atomic structure and the ionization potential
particle total angular momenta ji, which then couple to the total angular momen-
tum
N
J = ∑ ji with ji = li + si. (3.9)
i=1
This is referred to as jj-coupling. The term symbol of a state is written as
(j1, j π2, ...)J (3.10)
[107]. For example, the notation for the atomic ground state in dysprosium
is [Xe]4 f 106s2 5 I8. The preceding [Xe] denotes the full electron configuration
of xenon, which, as a noble gas configuration, need not be considered further
(L = 0, S = 0). Similarly, the 6s shell is completely filled by the two electrons
and may be disregarded. The ten 4 f valence electrons couple to a 5 I8 term via
LS-coupling. Particularly in excited states, one may also find couplings of a col-
lective electronic core to excited electrons. As an example, the excited state in Dy
at 9991 cm−1 with a configuration of 4 f 9(6Ho)5d6s2 7 Io9 [109], which is subject to
spectroscopy studies in Publication I, can be considered. Like the atomic ground
state, it is described in LS-coupling. The total spin and the total orbital angular
momentum of the electronic core term 6Ho couple with the outer 5d electron to a
7 Io9 term. As another example, the excited state in Dy at 24 709 cm
−1 with a con-
figuration 4 f 10(5 I8)6s6p(1Po1 ) (8, 1)
o
7 [109], as addressed in Publication II, exhibits
LS-coupling in an inner and an outer part of the electronic shell, which then cou-
ple to a term of (8, 1)o7 via jj-coupling (or strictly speaking J J-coupling).
Note that there are also the possibilities of J1K-coupling or LK-coupling, which are
rather rare and not of relevance for this work. A brief description is given e.g. on
the NIST Atomic Spectra Database website1.
3.1.3 Rydberg atoms
An atom with one electron excited to a high principal quantum number state is
referred to as a Rydberg atom - and correspondingly the excited state as Rydberg
state. Some atomic properties exhibit a strong n dependence, as tabulated e.g. in
[110], leading to the extraordinary nature of Rydberg atoms. Particularly interest-
ing for RI applications are the low binding energy, accompanied by long radiative
lifetimes and large collisional ionization cross sections. Moreover, Rydberg atoms
can be easily ionized with electric fields in the order of 100 V cm−1 [110] or by
blackbody radiation, e.g. within a hot-cavity ion source, rendering laser excitation
to high-lying Rydberg-states an efficient ionization method [111]. Another pecu-
liar property of Rydberg atoms is their similarity to a hydrogenic atomic system
due to the low overlap of the excited electron wave function with the electronic
1www.nist.gov/pml/atomic-spectroscopy-compendium-basic-ideas-notation-data-and-formulas/
atomic-spectroscopy-2. Accessed 12/2019.
38
3.2. Electronic transitions
core. The nuclear charge of Ze is effectively screened by the −(Z− 1)e charge of
the electronic core. Accordingly, the potential acting on the outer electron can be
well approximated with a Coulomb potential of Zeff = 1. Similar to Eq. 3.5, the
energy levels can be calculated with
− R RE IP µ µn = ∗ 2 = − 2 , (3.11)(n ) (n δ(n))
introducing the effective principal quantum number n∗ and the quantum defect
δ(n) [112]. Obviously, this rather simple relation can be used to determine the
IP in any atomic system by measuring excitation energies for a series of Rydberg
states, provided δ(n) can be described conclusively. This approach, together with
the underlying theory, is presented in Publication II, where the IP of dysprosium
was determined by evaluation of Rydberg convergences. For more details the
reader is referred to [113, 114], where the analysis of perturbed Rydberg series is
discussed and alternative fitting functions are compared.
3.2 Electronic transitions
Optical spectroscopy is all about the interactions of light with the atomic shell.
Considering the two states |i〉 and |k〉 with energies Ei > Ek of an atom within an
external light field, one can distinguish between three basic interaction processes:
• A photon is absorbed by the atom, changing its energy from Ek to Ei =
Ek + hν, where ν is the frequency of the photon (absorption).
• A photon may induce the excited atom to emit an identical photon under
relaxation to a lower state Ek = Ei − hν (stimulated emission).
• The atom with excitation energy Ei may spontaneously relax to a lower en-
ergy state Ek under emission of a photon with the energy hν = Ei − Ek
(spontaneous emission).
The rates for absorption and stimulated emission
Wki =Bkiu(ν) and (3.12)
Wik =Biku(ν)
depend on the spectral energy density of the external light field u(ν), where the
proportionality constants B are called Einstein coefficients for absorption and stimu-
lated emission. Their relation Bik =
gk
g Bki only depends on the statistical weights ofi
the states |i〉 and |k〉, meaning that the maximum population transfer from |k〉 to |i〉
is 50 % for gi = gk [106]. In practice, the cross section σ is more commonly used to
39
3. Atomic structure and the ionization potential
express the proportionality between the intensity of the light field I(ν) = u(ν)/cν
and the transition rate as
σI
W = (3.13)
hν
[107]. The Einstein coefficient Aik describes the probability for spontaneous emis-
sion, related to Bik via
8πhν3
Aik = Bik. (3.14)c3
It can be calculated from the expectation value of the transition dipole moment
〈pik〉 = Mik according to
16π3ν3 3 2 3
∣∣∫ ∣2
A = ik
∣
ik 3 |Mik|
2 16π e ν= ik ∣ ∗ ∣3 ∣ ψi rψkdτ∣ , (3.15)3e0c h 3e0c h
where r is position of the electron and Mik the so-called transition matrix element
[106]. From the properties of 〈pik〉 selection rules for atomic dipole transitions
can be derived, which are comprised in Table 3.1. Note that in pure LS-coupling
∆S = ±1 is forbidden. In heavy atoms, however, S is not a good quantum number
due to the strong spin-orbit interaction and inter-combination lines with ∆S =
±1 can be observed, although they are strongly suppressed [106]. Atomic dipole
transitions are also referred to as E1-transitions, denoting a first order electric
multipole transition. Similarly, E2, E3,... denote electric quadrupole, octupole and
higher order transitions, while M1, M2,... refer to different magnetic multipole
transitions. Higher order transitions exhibit different selection rules as those in
Table 3.1. However, they are strongly suppressed and usually not considered in
RIS.
40
3.3. Spectral lineshapes
General
π = −π′
∆J = 0,±1; J = 0 9 J′ = 0
∆mJ = 0,±1; mJ = 0 9 m′J = 0 if ∆J = 0
LS-coupling
∆S = 0
∆L = 0,±1; L = 0 9 L′ = 0
∆l = ±1 for the transition electron
Intermediate coupling
∆S = ±1
∆L = 0,±1,±2
jj-coupling
∆j = 0,±1 for one electron
∆j = 0 for all other electrons
Table 3.1.: Selection rules for electronic dipole transitions [105, 106]. Primed sym-
bols refer to the final state quantum numbers.
3.3 Spectral lineshapes
3.3.1 Natural linewidth
The minimum spectral width of an atomic transition is given by the natural
linewidth. In consideration of Heisenberg’s uncertainty principle, the finite life-
time τ of an atomic state leads to an energy uncertainty of ∆E = h̄/τ. The natural
linewidth ∆ν of an atomic transition between two excited levels |i〉 and |k〉 is de-
termined by the lifetimes of both states, resulting(in )
1 1 1 1
∆ν = (∆Ei + ∆Ek) = + . (3.16)h 2π τi τk
The intensity distribution I(ω) of the spectral line follows a Lorentzian profile
γ2/2π
I(ω) = I0 (3.17)
(ω−ω0)2 + (γ/2)2
around the center frequency ω0, with ω = 2πν. The natural linewidth corresponds
to the FWHM of the Lorentzian profile, i.e. ∆ν = γ/2π [49, 106]. Excited level
lifetimes and respectively natural linewidths of atomic transitions span many or-
ders of magnitude. For example, the lifetime of the excited state of the 1001 nm
ground-state transition in atomic dysprosium (Dy I), presented in Publication I,
was later determined as τ ≥ 82.2(6.7)ms [115], which corresponds to ∆ν / 2 Hz.
On the other hand, the excited state of the 405 nm ground-state transition in Dy I,
presented in Publication II, has a lifetime of τ ≈ 5 ns, corresponding to a natural
41
3. Atomic structure and the ionization potential
1000
= 19.1(10) ns
800 FWHMG = 45(2) ns= 79(4) ns
600
400
200
0
200 400 600 800
Ionization pulse delay (ns)
Figure 3.1.: Lifetime measurement of the excited state at 23 083.3 cm−1 in Cm I.
The orange curve shows a fit according to Eq. 3.18.
linewidth of ∆ν ≈ 30 MHz [116]. Note that both of these examples are electronic
dipole transitions (E1) according to the selection rules in Table 3.1. Nonetheless,
the former is a very uncommon case in RIS as one usually aims for high excitation
probability.
3.3.2 Lifetime measurement
Although the natural linewidth can often not be resolved in RIS due to several
line broadening effects, as will be discussed in the following sections, the lifetime
τ of excited states can be measured. In the experiment this is performed by a
temporal delay of the ionization laser(s) with respect to the excitation laser, so that
the ion count rate is a function of the population decay. For short lifetimes, which
are in the order of the laser pulse length, one has to consider a convolution of
the approximately Gaussian temporal laser profile with an exponential decay law,
which can be expr[essed as( )] ( )
· t− t
2
n(t) = A 1 + erf √ 0 − √σ σ − t− texp 02 + n2 0, (3.18)σ 2 τ 2 τ τ
where t0 and σ are the center and the standard deviation of the Gaussian distribu-
tion, τ the lifetime and erf the Gaussian error function. Additionally, the function
features an amplitude A and an offset n0 [117]. An example lifetime measurement
of the excited state at 23 083.3 cm−1 in neutral Cm is shown in Fig. 3.1. Obvi-
ously, for very short lifetimes the exponential decay may be obscured by the laser
pulse width, as seen in Publication V. Moreover, an upper limit of ≈ 3 µs for the
measured lifetime is given by the experimental conditions in the hot ion source
environment, related to the mean free path of excited atoms. This was observed in
Publication I and is supported by a similar lifetime measurement of a meta-stable
42
Ion counts (s 1)
3.3. Spectral lineshapes
state in neutral Ra [118].
3.3.3 Doppler broadening
For an observer in the lab frame, the Doppler effect shifts the frequency ν of light
emitted or absorbed by atoms moving at a speed v towards the light source ac-
cording to
ν = ν0(1 + v/c), (3.19)
where ν0 denotes the resonance frequency for a particle at rest. If we consider an
atomic vapor at a temperature T(, the velo)cities follow(a Bol)tzmann distribution
− mv
2 v2
p(v)dv ∝ exp dv = exp − 2 dv, (3.20)2kBT v̂
where p(√v)dv is the probability to find a particle in the velocity interval [v, v + dv]
and v̂ = 2kBT/m gives the most probable velocity [107]. Inserting Eq. 3.19 into
Eq. 3.20 yields a Gaussian(line profile of th)e form ( )
−mc
2(ν− ν0)2 c2(ν− ν )2I(ν) = I0 exp 2 = I0 exp −
0
2 (3.21)2kBTν0 ν0 v̂2
with a FWHM Doppler linewidt√h of
8k T ln 2 2ν v̂√
∆ν = ν B 00 2 = ln 2. (3.22)mc c
Let us reconsider the back-of-the-envelope example calculation from Sec. 2.1, i.e.
an ensemble of particles with m = 100 u and a Boltzmann velocity distribution at
T = 2000 ◦C. At an arbitrary resonance frequency of ν0 = c/400 nm, the Doppler
width of the resonance line is ∆ν ≈ 2.5 GHz. The mass and temperature depen-
dence of ∆ν is visualized in Fig. 3.2. In crossed-beam geometry, as is the case
with the PI-LIST ion source, we consider the conical atom beam effusing from the
atomizer at an opening angle β, which is perpendicularly intersected by the probe
laser beam and collinearly overlapped with an ionizing laser beam. The situation
is schematically depicted in Fig. 3.3. The original velocity distribution is now con-
strained by the opening angle β of the atomic beam. It was assessed as close to
45◦ in [119] for the RISIKO ion source. However, due to the finite cross section of
the ionizing laser, which limits the effective laser-atom interaction region radially,
it is further constrained to βeff. As a consequence, the velocity classes which are
addressed by the laser are limited to
v⊥ = v/ sin(βeff). (3.23)
43
3. Atomic structure and the ionization potential
3.5 3
3.0
2.5
2
2.0
1.5
1
50 1.0
100
m 150 1500 2000
(u) 200 500 1000250 0 T ( C)
Figure 3.2.: Mass and temperature dependence of spectral Doppler broadening ac-
cording to Eq. 3.22, plotted for ν0 = c/400 nm. Obviously ∆ν scales linearly
with ν0.
With this, Gaussian linewidths of ∆ν < 100 MHz could be demonstrated in Tc
(m = 99 u) at a transition frequency of ν0 ≈ c/425 nm [74]. Since this is already
in the order of the natural linewidth for∫strong transitions, one has to consider aconvolution ∞
IV(ν) = (IG ∗ IL)(ν) = IG(ν′)IL(ν− ν′)dν′ (3.24)−∞
of a Lorentzian profile IL(ν) with a Gaussian profile IG(ν). This is referred to as a
Voigt profile. It expresses the fact that the spectral line shape of each velocity class
within the Boltzmann distribution follows a Lorentzian profile. For fitting pur-
poses Eq. 3.24 is not practical, since there is no analytical solution to the integral.
A popular approximation for rapid calculation is given by
√
√2 ln 2IV(ν) = ( Re [w(z)]π∆νG√ ) (3.25)2(ν− ν0) ∆νwith z = ln 2 + i L ,
∆νG ∆νG
where ∆νG and ∆νL are the Gaussian and Lorentzian full widths, respectively, and
2
w(z) = e−z erfc(−iz) the Faddeeva function [120]. The FWHM of the Voigt profile
IV(ν) can be calculated as √
∆νV = 0.535∆νL + 0.2166∆ν2L + ∆ν
2
G (3.26)
44
(GHz)
3.3. Spectral lineshapes
β
Atomizer v⟂
βeIffonizing laser
Probe laser
Figure 3.3.: Laser-atom interaction in crossed-beam geometry. v⊥ denotes the per-
pendicular velocity component of effusing atoms, i.e. on the axis of the probe
laser.
[49]. An approximation of the form 3.25 is also used in the SATLAS python pack-
age [121], which was used for fitting of hyperfine structures in Publication IV and
Publication V.
3.3.4 Saturation and power broadening
As discussed in Sec. 3.2, the maximum population transfer from a state |k〉 to |i〉 in
a two-level system is 50 % for equal statistical weights of both states. A transition is
saturated when the excitation probability corresponds to the relaxation probability.
In this context, a saturation parameter S = Wki/Ri, given by the ratio of excitation
rate Wki to relaxation rate Ri, can be defined [106]. It can be understood as an
intensity ratio of an external light field to a saturation intensity Isat, with
W I
S = ki = (3.27)
Ri Isat
[72, 74]. Obviously, S(I = Isat) = 1 expresses that excitation and relaxation are in
equilibrium. The frequency-dependent absorption cross section α, describing the
spectral line profile, is modified through the saturation parameter to
Sα
( ) = 0
(ν)
α ν , (3.28)
1 + Sα0(ν)
where α0 is the unmodified cross section, i.e. without consideration of saturation
effects [72]. An experimental access to the saturation intensity is possible by mon-
itoring the absorption cross section on resonance (i.e. the ion rate in RIS) as a
function of laser intensity. Similar to Eq. 3.28, it can be expressed as
I/I
I a satα( ) = + bI + c, (3.29)
1 + I/Isat
45
3. Atomic structure and the ionization potential
where the linear contribution accounts for non-resonant ionization processes and
the constant term considers any background signal [74]. The saturation intensity is
an important parameter in RIS experiments. In ion source applications, where the
highest possible ionization rate is desired, all transitions in the excitation scheme
should be driven with sufficient laser power to ensure saturation. Correspond-
ingly, strong dipole transitions and high power laser radiation are used. As an
example, the reader is referred to Fig. 2 in Publication II or Fig. 4 in Publication
III, where the saturation behavior of RIS schemes is studied in detail. Saturation
effects involve a spectral line broadening, which can be observed in the same fig-
ures as mentioned above (particularly distinct in the latter). A typical feature of
transitions driven by a laser with I  Isat is the flat-top line profile. Upon reach-
ing the excitation-relaxation rate equilibrium at the resonance frequency, i.e. for
I(ν0) = Isat, the absorption cross section for slightly detuned frequencies still rises
with increasing intensity, effectively lifting the edges of the profile while the center
is unaffecte√d. In case of a Lorentzian profile, the modified linewidth corresponds
to ∆ν = ν0 1 + S [49].
On the other hand, in high-resolution spectroscopy experiments the effect of sat-
uration broadening has to be avoided in order to achieve highest possible spec-
tral resolution. The laser intensity is correspondingly kept slightly below Isat as
a reasonable trade-off between linewidth and efficiency. Nonetheless, when the
linewidth of a probed transition is small, broadening effects from other transitions
in the excitation scheme may become significant. This can be understood by an ef-
fective shortening of the excited state lifetime through a transfer of the population
to the ionization continuum. In order to minimize this effect, the ionization step
may be de-coupled from the probed transition by a temporal delay. This effect was
studied qualitatively in Publication V. An in-depth treatise of power broadening
in pulsed laser RIS on the high-precision level can be found in [122].
3.4 Ionization scheme development
As described in the introduction, the method of resonance ionization is based on
step-wise excitation and finally photo-ionization of sample atoms. Due to their
unique atomic structure, resonance ionization (RI) schemes are specific for each
chemical element. On the one hand this renders the RI process highly selective, but
on the other hand demands for extensive spectroscopic studies in order to make
an element accessible to RI. A database comprising available ionization schemes
for different elements can be found on the web presence of the RILIS group [37].
Depending on their application, ionization schemes have different figures of merit.
Most commonly, for the application in laser ion sources, one aims to achieve max-
imum efficiency in the ionization process. This is closely linked to saturation of all
46
3.4. Ionization scheme development
involved transitions. Combining Eqs. 3.13 and 3.27 yields
R hν
I isat = , (3.30)
σki
meaning that the required laser intensity for saturation of a transition |k〉 → |i〉
is proportional to the relaxation rate Ri and to the inverse of the absorption cross
section σki. The latter can also be related to the Einstein Aik coefficient via Eqs.
3.12, 3.13 and 3.14, resulting in
g 2
σ = i
c
ki 3 Aik. (3.31)gk 8πν
From the relations introduced so far one can already establish rate equations to
calculate ionization rates in a multi-step scheme, as presented e.g. in [111, 123].
However, this requires knowledge about natural linewidths, decay channels of ex-
cited states and the ion source temperature to estimate Doppler broadening. A
simpler approach is the qualitative assessment of ionization rates by the depen-
dencies 3.30 and 3.31, followed by experimental determination of the ionization
efficiency. Firstly, transitions in an ionization scheme should be chosen with re-
spect to σki. An example scheme, similar to the one depicted in [111], is shown
in Fig. 3.4. It shows a three step excitation with the wavelengths λ1, λ2, λ3 and
typical excitation cross sections for the individual steps. Obviously, the bottleneck
of a RI scheme is usually the final transition, with an excitation cross section of
up to 7 orders of magnitude lower than strong transitions between bound atomic
levels. In some cases a non-resonant final excitation step is driven by a high-power
fixed frequency laser, e.g. one of the harmonics of an Nd:YAG laser (1064 nm,
532 nm, 355 nm, 266 nm). However, high-power laser radiation may introduce un-
desired background through non-linear multi-photon processes. This effect can
only somewhat be reduced by choosing the lowest possible harmonics for reach-
ing the ionization potential, but in most cases not completely eliminated. Con-
sequently, non-resonant ionization is avoided whenever possible. The preferable
ionization mechanisms, i.e. transitions to auto-ionizing states (AIS) or high-lying
Rydberg states, require far less laser power for saturation. High-lying Rydberg
states, as discussed in Sec. 3.1.3, exhibit a very low binding energy and can be
efficiently ionized by collisions, external electric fields, an additional photon from
any laser in the excitation scheme or simply by blackbody radiation from the hot
atomizer, even in the far infrared (FIR) regime [111]. As indicated by the statistical
weight term in Eq. 3.31, excitation to Rydberg states can often be advantageous,
since the fine structure interval scales with n−3 and high-lying Rydberg-states may
be degenerate [110]. Lastly, there is the possibility of a resonant ionization process
via auto-ionizing states (AIS). An AIS is a collective excitation with the total energy
lying above the ionization potential. Rather than undergoing radiative decay to a
47
3. Atomic structure and the ionization potential
Continuum
E (non-res. ionization)
Auto-ionizing state
5-9 eV IP (spontaneous ionization)
Rydberg states
(FIR/electric field ionization)
10-17 cm2 10-13 cm2 10-12 cm2
Second excited state
10-10 cm2
First excited state
10-10 cm2
0 eV Ground state
Figure 3.4.: Schematic description of Resonance Ionization Spectroscopy. The ar-
rows indicate the step-wise optical excitation from the atomic ground state
to ionization. The ionization efficiency crucially depends on the final ex-
citation step, which may address the continuum, Rydberg-states or auto-
ionizing states. The lowered IP on the right indicates an electric field, which
effectively reduces the ionization threshold. Approximate excitation cross
sections are given. Figure adapted from [111]. For details see text.
bound atomic state, AIS preferably decay into an ion-electron pair with lifetimes
in the order of well below nano- down to picoseconds, which can be verified by the
huge natural linewidths of tens or even hundreds of GHz. The absorption cross
section of auto-ionizing transitions follows a Fano-profile of the form
(e + q)2 E− E
α(E) = α0 + α with e =
R , (3.32)
1 + e2 b Γ/2
where ER is the resonance energy, Γ = 1/τ the resonance FWHM, and q the
Fano-parameter, describing the asymmetry of the line profile [107, 124]. Since the
ionization of AIS is independent of experimental circumstances, i.e. the presence
of an electric field or the temperature of the atomizer, they are the most universal
choice for an efficient ionization scheme.
From a practical point of view, atomic transitions have to be accessible with the
laser system at hand. For the Mainz Ti:sapphire laser system, as described in Sec.
2.1, the fundamental wavelength range is 700 nm < λ < 1020 nm (see Table 2.1),
with a decreased output power towards the edges of the gain profile. This range
can be extended by second, third and fourth harmonic generation. Due to the rela-
tively high level spacing and high absorption cross section for ground-state transi-
tions or transitions between low-lying states, they are often driven by a second or
third harmonic laser output. Ionizing transitions, on the other hand, are preferably
48
3.5. Determination of the ionization potential
driven by the fundamental output in order to obtain maximum laser power. The
pulse length of the lasers of ≈ 50 ns is in the order of the lifetime of excited states,
so that the loss channel of spontaneous relaxation to inaccessible states, described
via Ri, is minimized. However, it can not always be avoided completely and strong
radiative decay channels to meta-stable states, as observed e.g. in Ra [118], can
lower the overall ionization efficiency. A similar effect is much stronger present
in a buffer-gas environment. Depending on the pressure, collisional quenching to
meta-stable states can be observed, e.g. in No [125] or Pu [126]. In such cases one
tends to prefer two-step ionization schemes over three-step ionization schemes in
order to keep the number of intermediate levels at minimum. Recently two-step
schemes are becoming more popular even in hot-cavity ion sources for the sake of
simplification and reliability. However, a potentially lower selectivity due to the
additional high-power, high-energy laser radiation required for the ionization step
has to be considered. Naturally, radiative de-excitation can also be induced by a
resonant laser through stimulated emission. Such a case is presented in Publica-
tion I, where resonant de-excitation was utilized to observe a meta-stable state in
dysprosium.
Lastly, one should keep in mind that the highest possible Einstein Aik factors, rep-
resenting shortest excited state lifetimes, might not be ideal for high-resolution
spectroscopy applications. As discussed in Sec. 3.3.4, the probed transition has to
be de-coupled from all other excitation steps to achieve highest spectral resolution
[122]. This can only be achieved if the excited state lifetime is longer than the laser
pulse length.
3.5 Determination of the ionization potential
One of the fundamental properties of each chemical element is the first ioniza-
tion potential (IP), specifying the binding energy of the outermost electron in the
neutral atom. It is closely related the chemical properties of an element, e.g. the
electronegativity, which is defined as χM = (IP− EA)/2 on the Mulliken scale,
where EA is the electron affinity [127]. Today the IP is precisely known for all
stable elements, with experimental precision in the order of µeV, apart from very
few exceptions (cf. Fig. 1 in Publication III). For radioactive elements the situation
is different, due to the challenges in experiments on radioactive species, i.e. small
sample amounts and high safety precautions. Methods for the determination of
the IP are, for example, measurement of ionization rates from a well defined and
controlled surface ion source, which can be used to deduce the IP via the Saha-
Langmuir equation 2.13, or alternatively spectroscopic methods, i.e. evaluation of
Rydberg convergences using Eq. 3.11. The latter usually offers the highest preci-
sion and can be perfectly realized in RIS due to the straightforward ionization of
Rydberg states. Moreover, RIS is highly sensitive and thus still applicable with low
sample amounts, making spectroscopy studies on rare radioactive species feasible.
49
3. Atomic structure and the ionization potential
Such studies for the determination of the IP were successfully performed within
the LARISSA group, including measurements on exclusively radioactive elements,
e.g. Tc or Ac [87, 88] among others. In this context one should also mention on-
line RIS experiments on very-short lived species, e.g. At or No, where off-line
studies are not feasible [100, 125]. Additionally, the RIS method can be used in
more sophisticated approaches for IP measurement, which become important in
complex spectra where a straightforward identification of Rydberg convergences
is not possible anymore. An extensive treatise on methods for the determination
of the IP, demonstrated on stable elements of the lanthanide series, is given in the
dissertation of T. Gottwald [128]. This includes the methods of isolated core exci-
tation and delayed field ionization for the identification of Rydberg states, which
are not subject of this work.
3.5.1 Rydberg convergences
The analysis of Rydberg convergences relies on the measurement of level energies
close to the IP. Within an easily realizable laser scanning range of ≈ 1000 cm−1
below the IP, corresponding to ≈ 70 nm in the fundamental Ti:sapphire laser out-
put, a high number of Rydberg states can be localized. In Publication II, principal
quantum numbers of 20 < n < 60 could be covered within this range. Higher
n-states can most often not be resolved in broadband RIS and would require high
resolution techniques involving narrow bandwidth cw lasers, as demonstrated in
Gd and Sm [129]. The usually large amount of data points obtained from Rydberg
convergences leads to a precise result for the IP when fitting the energy positions
En with Eq. 3.11. However, Rydberg series in rare-earth or actinide spectra are
often subject to strong perturbations due to the high number of open shells and
interacting valence electrons. In this case a shift in the Rydberg level energies
under the influence of an interloper state formed by a collective excitation can be
described in the framework of multichannel quantum defect theory [124, 130]. The
application to perturbed Rydberg series is presented in Publication II, or similarly
in [88], and will not be explained here in detail. For the sake of completeness just
the final fitting function for a perturbed Rydberg series with interloper states at
energies ER,i and of width ΓR,i is given here as
En = IP− Rµ  
  
− δ1 − 1 Γn + arctan R,i/2δ0 
−2
(n− ,δ0)2 π ∑i IP− Rµ(n− 2 − Eδ ) R,i0
(3.33)
where δ0 and δ1 are the zero- and first order terms in the Ritz expansion of the
quantum defect [114].
50
3.5. Determination of the ionization potential
E
VF= eFz
W= VC+ VF zs
IP z
2
VC= IP Zeffe Field4 0|z| ionization
Tunneling
Figure 3.5.: Graphical representation of electric field ionization. The external elec-
tric field F along the z-axis distorts the Coulomb potential. Excited atomic
states (orange lines) with an energy En greater than the saddle-point of the
potential W(zS) are field-ionized. Meta-stable states may also tunnel through
the potential barrier.
3.5.2 Saddle-point ionization
An alternative approach for the determination of the IP is found by applying DC
electric field ionization. This method does not rely on an assignment of specific
states and benefits from high level density in the region close to the IP. Thus,
it is perfectly suited for the extraction of the IP from complex atomic spectra,
where the analysis of Rydberg convergences fails. The principle of electric field
ionization, or classically speaking saddle point ionization, is depicted in Fig. 3.5.
Considering an atom within a homogeneous electric field F along the z-axis, the
Coulomb potential is superimposed by an electric potential VF = −eFz, resulting
in an effective potential of the form
2
W(r, F) = IP− Zeffe| | − eFz (3.34)4πe0 r
[107]. By solving ∂/∂z W(zS) = 0, the potential at the location of the saddle point
zS can be written as √
Z e3F
W(zS, F) ≡WS(F) = IP− 2 eff , (3.35)4πe0
where the effective charge of√the nucleus is Zeff ≈ 1 for highly excited states,
resulting in WS = IP− const · F. This simple relation can be used to determine
51
3. Atomic structure and the ionization potential
the IP by measurement of several field ionization thresholds and extrapolation to
zero field strength. Note that Eq. 3.35 is purely classical and does not account
for tunneling, which leads to ionization already at field strengths lower than the
classical saddle point, as indicated in Fig. 3.5 by a dashed lined. However, since
the experiment relies on the measurement of a sharp increase in the ionization rate
upon reaching the saddle point, rather than a gradual increase as expected from
tunneling [131], the latter can be disregarded from our experimental point of view.
Another effect to keep in mind is the increased ionization threshold for states with
a magnetic quantum number m 6= 0. This additional centrifugal barrier
W ∝ |m|F3/4 3+ m2m F (3.36)16
leads to additional ionization thresholds with W = WS + Wm [131–133]. If the ex-
periment relies only on the first increase in the ionization rate, Eq. 3.35 is sufficient
for data evaluation. However, this only holds valid when m-states are not selec-
tively populated, i.e. through specific laser polarization with the corresponding
selection rules for Zeeman sublevels.
52
3.6. Laser spectroscopy of the 1001-nm ground-state transition in dysprosium
3.6 Publication I: Laser spectroscopy of the 1001-nm ground-state transition in
dysprosium
The following work was published as a regular article in Physical Review A 98,
042504 (2018) DOI 10.1103/PhysRevA.98.042504. The experiment addressed a re-
quest from the group of Prof. Dr. Patrick Windpassinger to determine the ground
state transition wavelength to the low-lying excited state at 9991 cm−1. From
theoretical calculations in [134], this state is predicted to have an exceptionally
long lifetime of 3 ms, which makes it highly interesting for precision studies and
quantum-optical engineering. According to the selection rules presented in Sec.
3.2, this ground-state transition falls in the category of an intercombination line
with ∆S = +1. Correspondingly, it features an ultra-narrow linewidth in the range
of ∆νtheo ≈ 50 Hz, making it a perfect candidate for high precision spectroscopy
within the magneto-optical trap (MOT) setup of the Windpassinger group. How-
ever, since the transition could not be observed by another group with a similar
setup [135], and because the laser scanning capability of the laser system coupled
to the MOT is limited to few GHz, a pre-search of the atomic level at 9991 cm−1 was
undertaken in the LARISSA group using RIS method. This task was particularly
challenging due to the extremely low absorption cross section in the transition un-
der investigation, together with the required wavelength of 1001 nm, close to the
edge of the Ti:sapphire gain profile. Therefore, in the first phase of the experiment
the transition was searched and observed by resonant de-excitation of a higher ex-
cited level, which was to our knowledge applied for the first time in the context of
RIS. Subsequently direct excitation spectroscopy was successfully performed, in-
cluding measurements in the 741 nm ground-state transition, which is a promising
candidate for high-resolution RIS.
Based on the results from this publication, the Windpassinger group succeeded
in spectroscopy of the 1001 nm-transition on cold atoms within a MOT [115]. The
excited state lifetime was measured as τ ≥ 82.2(6.7)ms, even surpassing the pre-
dictions from theory.
Note that this article was published together with a supplemental data table, which
is given in the appendix A.2.
Author contribution
The author contributed to this work by preparing the experimental setup for the
measurements, i.e. complete set-up of the laser system and optimization of the ex-
perimental apparatus towards dysprosium spectroscopy. Data taking, evaluation
and preparation of the manuscript was done jointly with the master student Lena
Maske from the group of Prof. Dr. Patrick Windpassinger, who also presented this
work as part of her master thesis [136].
53
PHYSICAL REVIEW A 98, 042504 (2018)
Laser spectroscopy of the 1001-nm ground-state transition in dysprosium
D. Studer, L. Maske, P. Windpassinger, and K. Wendt
Institut für Physik, Johannes Gutenberg-Universität Mainz, 55128 Mainz, Germany
(Received 20 July 2018; published 10 October 2018)
We present a direct excitation of the presumably ultranarrow 1001-nm ground-state transition in atomic
dysprosium. By using resonance ionization spectroscopy with pulsed Ti:sapphire lasers at a hot cavity laser
ion source, we were able to measure the isotopic shifts in the 1001-nm line between all seven stable isotopes.
Furthermore, we determined the upper level energy from the atomic transition frequency of the 164Dy isotope as
9991.004(1) cm−1 and confirm the level energy listed in the NIST database. Since a sufficiently narrow natural
linewidth is an essential prerequisite for high-precision spectroscopic investigations for fundamental questions,
we furthermore determined a lower limit of 2.9(1)μs for the lifetime of the excited state.
DOI: 10.1103/PhysRevA.98.042504
I. INTRODUCTION In order to detect this weak transition, we use the highly
efficient technique of laser resonance ionization spectroscopy
Narrow-linewidth atomic transitions can serve as highly (RIS) [15]. The aims of this work are to (i) determine the exact
sensitive probes for various inner and outer atomic interaction transition frequency and extract first values for the isotope
potentials and respective forces, and have become a general- shifts of all stable isotopes and (ii) give a lower limit for the
purpose tool in the field of quantum many-body physics [1,2]. lifetime of the excited state, since a sufficiently narrow natural
In addition, narrow linewidth is usually accompanied with linewidth is a prerequisite for precision spectroscopy.
long lifetimes of the excited states, such that these transitions
offer precise, coherent control over metastable state popula-
tions and therefore allow for, e.g., the study of quantum gas II. EXPERIMENTAL
mixtures and Kondo-type physics [3,4] or the implementation A. Setup
of qubits [5,6]. Beyond that, precision isotope shift measure- Laser resonance ionization is based on multistep photoion-
ments [7] have been suggested as a vehicle to reveal high- ization via characteristic transitions of the element under
energy physics contributions to atomic spectra and search for investigation. Because of the typically high efficiency and
physics beyond the standard model [8–10]. Various atomic selectivity, this technique is often applied at radioactive ion
species possess ultranarrow transitions; however, dysprosium beam facilities, such as ISOLDE at CERN, both for ion beam
is a particularly interesting case. Because of its high mag- production [16,17] and spectroscopy of short-lived radioiso-
netic moment and consequent anisotropic long-range interac- topes [18–20].
tion, dysprosium is highly attractive for quantum many-body Similarly, our setup is optimized with respect to high sen-
physics. On the other hand, many high-energy effects scale sitivity and relies on the hot-cavity laser ion source technique,
with atomic mass. Thus, dysprosium, with about 160 nucleons combined with a low-energy quadrupole mass spectrometer.
and seven stable isotopes, is an ideal study case. Finding and Figure 1 shows a sketch of the apparatus. A detailed de-
characterizing a particularly narrow optical transitions in this scription is given in Ref. [21]. In our experiment, we use a
system therefore is of high relevance. sample of ≈1015 Dy atoms, prepared from a standard nitric
Some promising narrow-linewidth transitions are dis- acid solution,1 which is enclosed in a 3×3 mm2 Zr carrier
cussed in Ref. [11], including calculated level energies foil and introduced into a tantalum oven 35 mm long with an
and lifetimes which are compared to experimental val- inner diameter of 2 mm. Dysprosium atoms are ionized by
ues, if available. One is the 1001-nm 4f 10 6s2(5I8) → three properly synchronized laser pulses at a repetition rate
4f 9(6Ho)5d6s2(7I o9 ) ground-state transition with a theoreti- of 10 kHz. The laser beams are overlapped anticollinearly
cally predicted linewidth of 53 Hz [11]. It was first observed with the ion beam axis, so that ionization takes place directly
indirectly in the spectrum of an induction lamp filled with inside the atomizer oven. Alternatively, one may guide the
162Dy [12]. The NIST database [13] reports an energy of laser beams through a side window of the vacuum chamber,
9990.97(1) cm−1 for the upper level, which corresponds to perpendicularly intersecting the effusing atomic beam in front
a transition wavelength of 1000.904(1) nm. In contrast, calcu- of the oven. This significantly reduces spectral Doppler broad-
lations using the configuration interaction (CI) method yield ening at the cost of approximately two orders of magnitude in
a value of 9944 cm−1 (corresponding to 1005.6 nm) [11]. ionization efficiency.
This and the fact that the transition at 1001 nm could not
be detected via fluorescence laser spectroscopy in an atomic
beam [14] motivate the verification of either result. 1Alfa Aesar Dysprosium AAS.
2469-9926/2018/98(4)/042504(5) 042504-1 ©2018 American Physical Society
Reprinted article with permission from D. Studer, L. Maske, P. Windpassinger and K. Wendt, Phys. Rev. A, 98, 042504 (2018). 
Copyright 2018 by the American Physical Society. https://doi.org/10.1103/PhysRevA.98.042504
D. STUDER, L. MASKE, P. WINDPASSINGER, AND K. WENDT PHYSICAL REVIEW A 98, 042504 (2018)
perpendicular 
laser beam
90° quadrupole 
deflector
tantalum 
ion optics + - anticollinearatomizer laser beams
( )
Dy sample - +
(1015 atoms) extraction ions
quadrupole
mass filter ( )
single ion counting
FIG. 2. Indirect measurement of the upper energy level belong-
ing to the 1001-nm transition. (a) Measurement scheme consisting
FIG. 1. Sketch of the atomic beam mass spectrometer with ion of a three-step resonant excitation, addressing an autoionizing state
flight path (yellow) and laser beams in anticollinear (solid red, solid (AI) above the first ionization potential IP = 47901.76 cm−1 of dys-
blue) and perpendicular, crossed beam (dashed red) geometry. In the prosium [28], together with the additional dip step. (b) Ion counts as
latter case, the first extraction electrode is put on a positive voltage a function of the dip-step wave number.
to act as an ion repeller.
and 437 nm. A third laser at 780 nm (the gain maximum
The laser system consists of up to four pulsed Ti:sapphire
of Ti:sapphire) is used for nonresonant ionization of excited
lasers, each of them pumped with 12 to 18 W of average
2 atoms. The spectrum shows over 100 lines, with some ofpower of a commercial 532-nm pulsed Nd:YAG laser. The
the upper states known in literature [13]. A complete list of
Ti:sapphire lasers have pulse lengths of typically 50 ns with up
recorded lines is given in the Supplementary Material [27]. In
to 4 W average output power. They can be tuned from about
most cases, a resonant third excitation step to an autoionizing
680 to 940 nm and have a spectral linewidth of 1–10 GHz
state can be easily found in the dense spectrum of dysprosium
depending on the specific resonator components used. The
by detuning the ionization laser output by few nanometers.
tuning range can be extended with second, third, and fourth
To connect our photoionization scheme to the 1001-nm
harmonic generation. Details of the laser system are given in
transition, we use a fourth laser to de-excite atoms from
Refs. [22–24]. For wide-range scans, we use a modified laser
the second excited state into the 4f 9(6Ho)5d 6s2(7I o) state.
design, featuring a diffraction grating in Littrow configuration 9
When the laser is resonant to the transition, the de-excitation
for frequency selection [25]. This laser type has an output
competes with the ionization and a dip in the ion signal can be
power of up to 2 W and can be tuned mode-hop-free from
observed, as shown in Fig. 2.
700 to 1020 nm. Under optimal conditions the linewidth is
The rather weak dip signal of less than 10% of the total
1.5 GHz; however, at wavelengths far from the Ti:sapphire
ion counts may be related to the fact that the specifically
gain maximum the pump power and the Ti:sapphire crystal
induced de-excitation competes with a number of loss chan-
position in the resonator have to be adjusted specifically so
nels through spontaneous decay into other lower lying levels.
that the linewidth increases to 5 GHz. The fundamental output
3 With the dip technique, we cannot only indirectly measure theof each laser is measured with a wavelength meter.
level energy of the excited state but also prepare for a full-
resonant three-step ionization scheme for the direct excitation
B. Spectroscopic technique of the 1001-nm ground-state transition. To further reduce the
Spectroscopy is performed by detuning one laser in the ex- uncertainty of the 4f 9(6Ho)5d 6s2(7I o9 ) level energy, which
citation scheme while monitoring the ion count rate. Since this depends on three wavelengths in the dip measurements, we
requires a photoionization scheme to begin with, the initial proceed by using the settled ionization scheme involving the
measurements were carried out with a scheme based on the direct excitation of the 1001-nm transition.
4f 106s2(5I8) → 4f 9(6Ho)5d 6s2(5Ko9 ) ground-state transi-
tion at 741 nm. The excited state has a configuration similar III. DIRECT EXCITATION SPECTROSCOPY
to the one at 1001 nm, but the line intensity is a factor of ≈50
higher [11,26]. This enormously facilitates the development A. The 1001-nm transition
of a full resonant three-step ionization scheme. Starting from In this section, we discuss a direct excitation of the
the excited state of the 741-nm transition, a wide range spec- 1001-nm ground-state transition. For the measurements, all
trum of high-lying states was accessed by scanning the second laser beams are oriented anticollinearly to the atom beam
harmonics of a grating-assisted Ti:sapphire laser between 401 (see Fig. 1). A perpendicular geometry does not lead to an
improvement at this point, since the expected Doppler broad-
ening of ≈600 MHz within the tantalum oven is in the order
2Photonics Industries DM100-532. of the laser linewidth. The beam diameter at atom position
3High Finesse WS6-600 for wide-range scans and High Finesse is about 2 mm which corresponds to the inner diameter of
WSU-30 for isotope shift measurements. the oven. For the photoionization a Ti:sapphire laser with
042504-2
Reprinted article with permission from D. Studer, L. Maske, P. Windpassinger and K. Wendt, Phys. Rev. A, 98, 042504 (2018). 
Copyright 2018 by the American Physical Society. https://doi.org/10.1103/PhysRevA.98.042504
LASER SPECTROSCOPY OF THE 1001-NM GROUND- … PHYSICAL REVIEW A 98, 042504 (2018)
( )
( )
FIG. 3. Isotope shift measurement for the 1001-nm ground-state
FIG. 4. Isotope shift measurement for the 741-nm ground-state
transition. (a) Excitation scheme. (b) Ion counts as a function of first transition. (a) Excitation scheme. (b) Ion counts as a function of first
excitation step frequency ν relative to the atomic transition frequency
= 164 excitation step frequency ν relative to the atomic transition frequencyν164 299.5228(1) THz of the Dy isotope. ν = 404.5990(1) THz of the 164164 Dy isotope. Laser side modes are
clearly visible.
a wavelength of 1001 nm first excites the atoms into the
4f 9(6Ho)5d 6s2(7I o9 ) state. From this state, the atoms are B. The 741-nm transition
resonantly excited to the second excited state with an energy
−1 In the course of the indirect detection of the upper energyof 26499.1 cm with a wavelength of 377 nm by using a level belonging to the 1001-nm transition, we were also able
second, this time frequency-doubled, Ti:sapphire laser. In the to measure the isotope shift in the first excitation step along
last step, a third laser with a wavelength of 777 nm addresses the 741-nm ground-state transition. These data were measured
an autoionizing state to resonantly ionize the atoms. The with a different implementation of the standard Ti:sapphire
complete excitation scheme is shown in Fig. 3(a). laser featuring a bow-tie resonator design. Similar to the
While the frequencies of the upper two steps are fixed standard laser, frequency selection is achieved by a combina-
for the whole measurement, the frequency of the first step tion of a birefringent filter and a solid etalon (d = 0.3 mm,
is scanned. Because of its wide tuning range, the grating
R= 0.4), but with the option to add an additional piezo-
assisted laser, as described in Sec. II A, was used to probe the
= actuated air-spaced etalon (d = 12 mm, R = 0.4). This po-1001-nm transition, while an additional etalon (d 2 mm,
= tentially allows operation on a single longitudinal mode;R 0.4) was inserted to reduce the linewidth to 1 GHz. however, since the cavity lacks active stabilization at this
Figure 3(b) shows the resulting direct excitation of all seven stage, it suffers from an occasional rise of side modes, which
stable dysprosium isotopes. For the individual isotopes, we appear at δν = ±443 MHz and are suppressed by only about
adapted the mass spectrometer setting accordingly. a factor of ≈10.
From the measurement, we calculated the isotopic shifts in Figure 4 shows the direct excitation of the five stable
the 1001-nm transition, which are listed in Table I. bosonic isotopes and Table II shows the resulting isotope
The specified error corresponds to the sum of the fit shifts. Since the isotope shifts of the stable odd-mass isotopes
error and an estimated error of 30 MHz for the drift of with nonzero nuclear spin I as well as the isotope shifts
the wavelength meter during the measuring time. Any other of the three stable even-mass isotopes (I = 0) with highest
systematics are comparatively small and were neglected. The abundance are already given in Ref. [26], we omitted a re-
error estimation is based on later measurements in which we
≈ measurement of the odd-mass isotopes at this point. Thedetermined the drift as 10 MHz per hour as well as the isotope shifts obtained here for the even-mass isotopes with
long measuring time due to the individual mass spectrometer highest abundance are in accordance with Ref. [26]. However,
setting for each isotope. Furthermore, we determined the here we have also provided an isotope shift measurement in
upper level energy from the atomic transition frequency of the
164 −1 this line for the two rarest stable isotopes,
158Dy and 156Dy.
Dy isotope as 9991.004(1) cm . Taking the isotope shift
into account, the latter is in good agreement with the value
listed in the NIST database [13]. IV. LIFETIME MEASUREMENTS
Lower limits for the lifetimes of the excited states
at 9990.96 and 13495.96 cm−1 can be determined by
TABLE I. Isotope shift in the 1001-nm transition in Dy, relative
to the isotope 164.
TABLE II. Isotope shift in the 741-nm transition in Dy for the
Isotope shift δν [MHz] five isotopes with even mass number.
δν164–163 907(36) Isotope shift δν [MHz]
δν164–162 1233(35)
δν164–161 2337(37) δν164–162 1245(32)
δν164–160 2566(36) δν164–160 2583(32)
δν164–158 3685(45) δν164–158 3874(32)
δν164–156 5976(39) δν164–156 6042(32)
042504-3
Reprinted article with permission from D. Studer, L. Maske, P. Windpassinger and K. Wendt, Phys. Rev. A, 98, 042504 (2018). 
Copyright 2018 by the American Physical Society. https://doi.org/10.1103/PhysRevA.98.042504
D. STUDER, L. MASKE, P. WINDPASSINGER, AND K. WENDT PHYSICAL REVIEW A 98, 042504 (2018)
of the investigated states are orders of magnitude shorter
than theoretical values [11], which actually was expected due
to the experimental circumstances. De-excitation of atoms
within the hot atomic vapor may occur by collisions with the
oven wall or other atoms. In comparison to an experimental
value for the lifetime of the 13495.96 cm−1 excited state of
89.3(8) μs [26] and the fact that both of our measured values
agree with each other we can conclude that, in our experiment,
the extracted lifetimes predominantly depend on the mean free
path of the hot atoms within the atomic beam oven cavity.
Consequently, the 2.9(1) μs lifetime for the 9990.96 cm−1
excited state should be treated as a very conservative lower
limit, which corresponds to an upper limit for the 1001-nm
FIG. 5. Lifetime measurements in the 741- and 1001-nm tran- transition linewidth of 55(2) kHz.
sitions obtained by delaying the ionization laser pulse. For better
readability, we added a random offset to the ion signal of the 741-nm
transition. V. CONCLUSION
investigating the population decay after the pulsed laser exci- We presented a direct excitation of the 1001-nm ground-
tation. The population is probed by delayed ionization laser state transition for all seven stable dysprosium isotopes for
pulses, according to the excitation schemes in Secs. III A the first time by applying high-repetition-rate pulsed laser
and III B, and subsequent ion counting. The temporal profiles resonance ionization. Furthermore, we measured the isotopic
and delays between the individual Ti:sapphire laser pulses shift in the 1001-nm transition and determined the upper level
are captured by fast photodiodes and monitored with an energy from the atomic transition frequency of the
164Dy
−1
oscilloscope. In order to maintain stable laser power during isotope as 9991.004(1) cm , which is in accordance with
the measurement, the first excitation step laser is pumped by the value listed in the NIST database [13]. We obtain an
a separate Nd:YAG laser4 and pulse delays are controlled by upper limit of 55(2) kHz for the transition linewidth of the
means of shifting the pump laser trigger accordingly. Figure 5 excited state. Our results open the route toward investigation
shows the excited-state population decay at oven temperatures of physics beyond the standard model of particle physics
of 700(100) ◦C and 950(100) ◦C for the states at 9990.96 and enable the study of many-body physics with magnetic
and 13495.96 cm−1, respectively. The excited state at 9990.96 quantum gases by atomic high-resolution spectroscopy within
cm−1 shows an exponential decay with a lifetime of 2.9(1) s, the 1001-nm transition.μ
whereas the 13495.96 cm−1 state clearly features two compo-
nents with lifetimes of 32(2) ns and 2.8(3) μs. The short-lived
contribution is an artifact, which is related to the ionization ACKNOWLEDGMENTS
scheme for the 741-nm transition where the first excitation The authors would like to point out that this work is part
step has enough energy to ionize atoms parasitically from the of the M.Sc. thesis of L. Maske, who not only contributed to
second excited state. This effect is completely suppressed by the experimental activities but also did a major part of the data
a delayed second excitation pulse; thus, the 32(2)-ns lifetime evaluation. We thank N. Petersen and F. Mühlbauer for their
corresponds to the laser pulse length. Nonetheless, lifetimes ideas and fruitful discussions. We gratefully acknowledge
the financial support of the EU through ENSAR2-RESIST
(Grant No. 654002) and DFG Großgerät: DFG FUGG (INST
4Quantronix Hawk-Pro 532-60-M. 247/818-1).
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Copyright 2018 by the American Physical Society. https://doi.org/10.1103/PhysRevA.98.042504
LASER SPECTROSCOPY OF THE 1001-NM GROUND- … PHYSICAL REVIEW A 98, 042504 (2018)
[13] A. Kramida, Y. Ralchenko, J. Reader, and the NIST ASD [21] V. Sonnenschein, S. Raeder, A. Hakimi, I. D. Moore, and
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pml/atomic-spectra-database. (2012).
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[16] V. N. Fedosseev, Y. Kudryavtsev, and V. I. Mishin, Phys. Scr. Reponen, Hyperfine Interact. 227, 113 (2014).
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V. N. Fedosseev et al., Nat. Commun. 4, 1835 (2013). starting from the 13495.96 cm−1 excited state.
[20] R. P. de Groote, M. Verlinde, V. Sonnenschein, K. T. Flanagan, [28] D. Studer, P. Dyrauf, P. Naubereit, R. Heinke, and K. Wendt,
I. Moore, and G. Neyens, Phys. Rev. A 95, 032502 (2017). Hyperfine Interact. 238, 02A916 (2017).
042504-5
Reprinted article with permission from D. Studer, L. Maske, P. Windpassinger and K. Wendt, Phys. Rev. A, 98, 042504 (2018). 
Copyright 2018 by the American Physical Society. https://doi.org/10.1103/PhysRevA.98.042504
3.7. Resonance ionization spectroscopy in dysprosium
3.7 Publication II: Resonance ionization spectroscopy in dysprosium: Excitation
scheme development and re-determination of the first ionization potential
The following article was published in Hyperfine Interactions 238, 8 (2017) DOI
10.1007/s10751-016-1384-4. It is part of the Topical Collection on Proceedings of
the 10th International Workshop on Application of Lasers and Storage Devices in
Atomic Nuclei Research: ”Recent Achievements and Future Prospects” (LASER
2016) Poznan, Poland. It comprises the results of a series of spectroscopic experi-
ments of the element dysprosium. New three-step laser ionization schemes were
assessed as alternatives to previously used schemes, relying on dye lasers or non-
resonant ionization steps [37]. This included extensive spectroscopy in various
three-step excitation ladders and measurements of saturation powers for individ-
ual transitions. A series of dedicated efficiency measurements was performed for
a suitable ionization scheme, where all transitions could be saturated with the
available laser power. This scheme was used later on to determine isotope ratios
of a Dy contamination in holmium samples produced for the ECHo project [137].
The second part of the article presents spectroscopy of Rydberg states, accessed in
a two-step excitation scheme. The analysis of perturbed Rydberg convergences is
presented and a value for the ionization potential of IPRydDy = 47 901.76(5) cm
−1 is
extracted. Note that this value is in perfect agreement with results from electric
field ionization, where IPSPDy = 47 901.8(3) cm
−1 was measured [128, 138]. This con-
firms the accuracy of the classical saddle point model, which is used in Publication
III for the determination of the IP of promethium.
Author contribution
Part of the data for this work, i.e. the two-step spectroscopy of Rydberg conver-
gences, was jointly measured with Patrick Dyrauf, who presented the respective
results in his master thesis [113]. These results were later re-evaluated by the au-
thor in preparation for publication. The three-step spectroscopy measurements
were partly presented in the diploma thesis of the author [114], and then further
extended in the scope of this dissertation. After the assessment of an optimal ion-
ization scheme, the author performed efficiency measurements. P.D. is listed as
second author for the experimental work and data evaluation during his master
thesis. The other co-authors, P.N. and R.H. contributed to the experimental work.
The author presented this data on the International Conference on Application of
Lasers and Storage Devices in Atomic and Nuclei Research (Poznan, Poland) and
prepared the manuscript as conference proceeding.
59
Hyperfine Interact (2017) 238: 8
DOI 10.1007/s10751-016-1384-4
Resonance ionization spectroscopy in dysprosium
Excitation scheme development and re-determination of the first
ionization potential
D. Studer1 ·P. Dyrauf1 ·P. Naubereit1 ·
R. Heinke1 ·K. Wendt1
Published online: 19 December 2016
© Springer International Publishing Switzerland 2016
Abstract We report on resonance ionization spectroscopy (RIS) of high-lying energy levels
in dysprosium. We developed efficient excitation schemes and re-determined the first ion-
ization potential (IP) via analysis of Rydberg convergences. For this purpose both two- and
three-step excitation ladders were investigated. An overall ionization efficiency of 25(4) %
could be demonstrated in the RISIKO mass separator of Mainz University, using a three-
step resonance ionization scheme. Moreover, an extensive analysis of the even-parity 6sns-
and 6snd-Rydberg-series convergences, measured via two-step excitation was performed.
To account for strong perturbations in the observed s-series, the approach of multichannel
quantum defect theory (MQDT) was applied. Considering all individual series limits we
extracted an IP-value of 47901.76(5) cm−1, which agrees with the current literature value
of 47901.7(6) cm−1, but is one order of magnitude more precise.
Keywords Resonance ionization spectroscopy · Ionization potential · Ionization scheme
development · Dysprosium
1 Introduction
Resonance ionization spectroscopy has been proven to be a most versatile experimental
technique with a wide range of applications in both atomic and nuclear research. The step-
wise excitation and ionization using strong optical dipole transitions provides excellent
This article is part of the Topical Collection on Proceedings of the 10th International Workshop on
Application of Lasers and Storage Devices in Atomic Nuclei Research: “Recent Achievements and
Future Prospects” (LASER 2016), Poznań, Poland, 16–19 May 2016
Edited by Krassimira Marinova, Magdalena Kowalska and Zdzislaw Błaszczak
 D. Studer
dstuder@uni-mainz.de
1 Institut für Physik, Johannes Gutenberg-Universität Mainz, 55099 Mainz, Germany
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8 Page 2 of 11 Hyperfine Interact (2017) 238: 8
elemental selectivity by utilizing each elements unique atomic structure, while being highly
efficient at the same time. In particular on-line mass separators, such as ISOLDE at CERN
and others, benefit from laser ion sources and related spectroscopic work. The production
of high-purity radioactive ion beams (RIBs) is achieved by applying resonance ionization
in combination with mass spectrometers (RIMS) and enables research on shortest lived
exotic radioisotopes far off stability [1, 2]. In addition to fundamental research, practical
applications of RIMS span from ultratrace analysis [3] to the production of medically rel-
evant radioisotopes, where highest purity against any radioactive interference is mandatory
to meet ethical standards [4].
While laser ion sources have undergone constant development in the last decades, their
efficiency is finally determined by the sequence of transitions used for resonant ionization
process. Optimum ionization schemes have to be theoretically prepared from literature data
and experimentally developed individually for each element. In complex atomic systems
like the lanthanide and actinide elements, reliable spectroscopic data towards higher excita-
tion energies is most often rather scarce or incomplete in literature. In particular high-lying
Rydberg-states and auto-ionizing states (AI) are often unknown but of primary interest,
since they represent promising candidates for strong ionizing transitions, as required to
maximize ionization efficiency.
Besides scheme development, the spectroscopic data obtained is useful for the analy-
sis of Rydberg convergences, which allows for a detailed study of the atomic system and
for a precise determination of the first ionization potential. This fundamental quantity is
closely linked to the chemical behavior of each element and can be used for the identifica-
tion of various trends across the periodic table [5]. Due to their complex electronic structure,
theoretical estimates of the IP for lanthanide elements can even today just be computed
with precisions several orders of magnitude below experimental uncertainties [6]. Corre-
spondingly, precise experimental data serves also as a valuable reference for optimizing
calculations.
The rare earth element dysprosium (Z = 66) has been subject to a number of RIS
studies in the past, during which different excitation schemes were developed and uti-
lized. Worden et al. used two-step excitation schemes with first excitation steps between
456 and 461 nm for spectroscopy of auto-ionizing Rydberg-series [7]. A similar approach
was applied by Zhou et al. [8], using a different first step at 554.7 nm. Both bound and
auto-ionizing Rydberg-series were studied in that publication. By minimization of vari-
ations in the quantum defect for individual series (for details see Section 4), a value
for the first ionization potential of IPDy = 47901.7(6) cm−1 was determined. Excita-
tion scheme development for efficient ionization of Dy was carried out by Fedosseev
et al. [9]. An overall efficiency of 20 % was measured using a three-step scheme. Two
dye lasers at 625.9 nm and 607.5 nm were used for the first and the second excitation
step, respectively, and the 510.6 nm component of a copper vapor laser for non-resonant
ionization.
The work presented here aims to refine these previous approaches. Excitation scheme
development is primarily oriented for the production of the radioisotopes 152Dy and 155Dy,
which are used for medical imaging in the framework of the CERN-MEDICIS-project [4].
In the course of spectroscopy of high-lying states, so far unknown Rydberg series were
discovered and convergences are analyzed to improve the accuracy of the first ionization
potential.
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Hyperfine Interact (2017) 238: 8 Page 3 of 11 8
2 Experimental
The laser system used here for resonance ionization consists of two to three high-power
pulsed Ti:sapphire lasers, pumped by a commercial frequency doubled Nd:YAG laser (Pho-
tonics DM100-532). They are operated at a repetition rate of 10 kHz with typical pulse
lengths of 50 ns. With an accessible spectral range of 690 to 960 nm and the option of higher
harmonic generation, the ionization of 38 elements with Ti:sapphire lasers could be demon-
strated so far [10]. Output powers of up to 4 W in the fundamental wavelength range and
about 1 W in the second harmonics are achieved. For wide range scans a grating-assisted
resonator in Littrow geometry is used, which allows mode-hop free tuning over the whole
Ti:sapphire range. Linewidths for the standard- and the grating Ti:sapphire laser are in the
range of 5 GHz and 1 GHz, respectively. The wavelength of the fundamental laser beam is
measured using a High Finesse WS6-600 wavelength meter with a specified 1σ -uncertainty
of 200 MHz. For the studies of two step excitation schemes the grating-laser was frequency
doubled with an extra-cavity BBO crystal. During scanning operation the crystal angle was
manually tuned to maintain phase matching, while the blue laser power was constantly mon-
itored with a sample beam reflected from a wedged glass plate. Walkoff effects due to crystal
angle adjustment were compensated with a commercial TEM Aligna Beamlock system.
The spectroscopic measurements were carried out at the Mainz Atomic Beam Unit
(MABU), a compact low-energy quadrupole mass spectrometer, combined with a laser
ion source. The mass spectrometer is a commercial device by ABB Extrel, including the
quadrupole mass filter and the detection system. For a detailed description see [11, 12]. A
sketch of the apparatus is given in the upper left of Fig. 1. The sample material is atom-
ized in a resistively heated graphite tube at approximately 1500 ◦C. Resonance ionization
of the atomic vapor occurs directly inside the atomizer cavity by irradiating the lasers in
anti-collinear geometry to the extracted ion beam. The ions are accelerated by a three-stage
extraction electrode, followed by an Einzel-lens and a telescopic lens for focusing and beam
shaping. All ion optics components operate with low voltages < 1 kV. Suppression of neu-
tral species is ensured by a 90◦ quadrupole deflector. The isotope of interest is selected with
a quadrupole mass filter, operated at 1.2 MHz. Transmitted ions are detected with a channel
electron multiplier in single ion counting mode.
While the MABU is a reliable instrument for spectroscopy, it is unfavorable for a quan-
tification of the ionization efficiency due to its low acceleration voltage and ion transmission
through the apparatus (which is primarily limited by the QMF settings). A more suitable
apparatus for efficiency measurements is found in the RISIKO mass separator (see lower
part of Fig. 1). Here the sample reservoir and the atomizer cavity can be heated indepen-
dently, allowing a well controlled release of the sample material. Laser ions are accelerated
to 30 keV before entering a 60◦ sector field magnet for mass separation. Depending on the
intensity of the beam, ions are detected with a Faraday cup (FC) or a secondary electron
multiplier (SEM) just behind the focal plane of the magnet. The RISIKO mass separator has
a resolving power of M/M > 500.
3 Excitation scheme development and efficiency measurements
The strongest transition probability into a suitable first excited state (FES) in dysprosium
is predicted for 4f 106s2(5I8) → 4f 10(5I8)6s6p(1P1)7,8,9 [13]. A-values are in the order
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Mainz Atomic Beam Unit Laser System
Ion Detecon
SHG grang
Ti:sapphire
QMF
Ti:sapphire
90° Deflector
SHG Ti:sapphire
Extracon
Ion Opcs
Atomizer Flip Mirror
2ν Nd:YAG
RISIKO Mass Separator
HV 
Plaorm
Faraday 
60 ° Dipole Magnet Slits SEMCup
Extracon & 
Ion Opcs
Atomizer &
Sample Reservoir
Fig. 1 Schematic view of the experimental setup, divided into the laser system (upper right), the Mainz
Atomic Beam Unit MABU (upper left) and the RISIKO mass separator (bottom). Abbreviations: QMF -
quadrupole mass filter, SHG - second harmonic generation, SEM - secondary electron multiplier. The dashed
SHG-unit represents the option to frequency-double the grating laser as well
of 108 s−1 [14]. With 404 nm, 418 nm and 421 nm they are accessible with a frequency
doubled Ti:sapphire laser. From the FES, one can either directly ionize the atom with an
additional blue laser photon or populate a second excited state (SES) to subsequently ionize
with a third excitation step, both in the fundamental wavelength regime. Two-step schemes
were successfully used for spectroscopy in [7] and [8]. A three-step scheme for dysprosium
was proposed by T. Gottwald et al. [15], but the ionizing transition was not specified. Based
on these transitions known from literature, several two- and three-step excitation ladders
were developed and tested. A summary of all utilized schemes with the respective transition
wavenumbers and configurations of the intermediate steps, as well as the scanning range of
the ionizing laser, is given in Table 1. Schemes #1 to #3 represent three-step ladders, where
the third laser excitation is scanned for odd-parity AI- or Rydberg-states, while schemes #4
to #6 are two-step ladders with scanning in the second step for even-parity states. Regarding
relative intensities and laser power requirements to saturate each transition, the three-step
scheme #1, aiming for an auto-ionizing state at E = 49101.8 cm−1 was chosen for a
series of efficiency measurements. Line profiles and saturation curves were measured at the
MABU with a laser beam diameter of approximately 2 mm, which corresponds to the inner
diameter of the atomizer tube of 2.2 mm. The obtained graphs for the individual transitions
are shown in Fig. 2. The intermediate steps were saturated with few mW laser power, while
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Hyperfine Interact (2017) 238: 8 Page 5 of 11 8
Table 1 Summary of all studied excitation schemes, starting from the atomic ground state 4f 106s2(5I8)
ν̃ −11 [cm ] FES ν̃2 [cm−1] SES ν̃scan [cm−1]
1 24708.97 4f 10(5I8)6s6p(1Po o1 )(8, 1)7 12454.20 J = 6 11080 − 12450
2 23877.74 4f 10(5I8)6s6p(1Po1 )(8, 1)
o
8 12882.89 J = 8 11040 − 13640
3 23877.74 4f 10(5I8)6s6p(1Po1 )(8, 1)
o
8 12721.70 J = 8 11200 − 13800
4 23877.74 4f 10(5I8)6s6p(1Po1 )(8, 1)
o
8 − − 22800 − 25130
5 23832.07 4f 9(6Ho)5d2(3F)(8Ko)8 − − 23150 − 25200
6 23736.60 4f 10(5I8)6s6p(1Po1 )(8, 1)
o
9 − − 23640 − 25420
The level energies and the configurations of the FES and SES are taken from [16]. For the SES only a J
value is given since the configurations are not known, with the exception of the SES in scheme #2, where
the configuration 4f 106s6d? J = 8 is given in NIST. The question mark indicates a doubtful configuration
assignment
AI at 49101.8 cm-13
837.661 nm
2
IP = 47901.7 cm-1
Dy
1
0
11937,6 11938,8 11940,0 0 500 1000 1500 2000
3 37163.16 cm
-1
J = 6
802.721 nm
2 A = 8.352 ∙ 106 s-1
1
0
12453,0 12454,2 12455,4 0 250 500 750 1000
3
24708.97 cm-1
4f10(5I )6s6p(1P o)(8,1)o
8 1
2 J = 7
404.711 nm
A = 1.92 ∙ 108 s-1
1
0
24708 24709 24710 0 50 100 150 200
-1 0 cm
-1
Excitation Energy [cm ] Laser Power [mW]
4f106s2(5I )
8
Fig. 2 Line profiles and saturation curves for the three-step excitation scheme used for efficiency measure-
ments. The peaks from the first step and second step are fitted with power-broadened Gaussian profiles. The
peak from the third step is fitted with a Fano profile [17]
the ionizing transition showed saturation at approximately 1.5 W, which was reached easily
with the available laser system.
Quantification of the ionization efficiency was achieved by complete exhaustion of a
calibrated sample and integration over the ion current. For singly charged ions, as obtained
with the employed excitation scheme, the overall efficiency is given by Q/eNA, where Q
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 Ion Signal [arb. units]
8 Page 6 of 11 Hyperfine Interact (2017) 238: 8
10n 50
1n 40
100p 30
10p 20
1p 10
0
0 1 2 3 4
Time [h]
Fig. 3 Typical course of an efficiency measurement at the RISIKO mass separator. The black curve shows
the measured ion current for mass 164. The optimization phase of the apparatus (mass scans, adjustment of
temporal and spatial laser overlap) is indicated by the red area. The gray area marks the background due to
surface ionized species, which is determined by interpolation over the shutter phases (sharp signal drops).
The measurement was stopped shortly after 4 hours of accumulation time at low ion signal
is the total accumulated charge in the detector (minus the laser-independent background sig-
nal), e the elemental charge, N the number of sample atoms and A the isotopic abundance.
For sample preparation dysprosium atomic absorption standard solution (Dy2O3 in 5 % HNO3)
with 997(5) μg/ml, supplied from Alfa Aesar, was used. Samples with a total of 5 · 1014
atoms for all natural Dy isotopes were produced by applying and heating the solution on a
3x3 mm2 piece of zirconium foil until the nitric acid and any water were completely vapor-
ized. The left over dysprosium oxide is enclosed in the Zr-foil, which serves as a reduction
agent. For further details on the efficiency measurement process at RISIKO see [18].
A typical efficiency measurement is shown in Fig. 3. Most of the sample is evaporated
over a period of about two hours. The ion current is stabilized at approximately 1 nA by
gradual heating of the sample reservoir until the sample is exhausted. This measurement was
repeated four times, yielding values of 28.3 %, 18.0 %, 26.6 % and 27.5 %. Even though one
of the values is significantly lower, which can be caused by an improper alignment of the
ion source, the obtained values show an overall good reproducibility. In conclusion we can
extract a value of 25(4) % by averaging over the series of measurements. The uncertainty is
given by the standard deviation of the set of efficiency values.
4 Analysis of Rydberg series
An extensive analysis of Rydberg-convergences was carried out for bound even-parity
Rydberg-states populated in three different two-step excitation schemes (schemes #4, #5
and #6 in Table 1), starting from the atomic ground state 4f 106s2(5I8). All three scans cover
a wide spectral range of up to 2300 cm−1 around the IP, so that Rydberg-series converg-
ing to the ionic ground state 4f 10(5I8)6s1/2(8, 1/2)17/2 and the higher lying fine-structure
component 4f 10(5I8)6s1/2(8, 1/2)15/2 located 828.314 cm−1 above the ionic ground state
can be observed [16]. The obtained spectra are shown in Fig. 4. An assignment of reso-
nances to Rydberg series is achieved by identification of trends in the quantum defect δ(n),
which can be calculated using the Rydberg-Ritz formula
Rμ Rμ
En = E∞ − = E∞ − (1)
(n− δ(n))2 (n∗)2
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Ion Current [A]
Efficiency [%]
Hyperfine Interact (2017) 238: 8 Page 7 of 11 8
Fig. 4 Measured spectra of the ionization step of the excitation schemes given in Table 1. The vertical
red lines mark the series limits, i.e. the ionic ground state 4f 10(5I8)6s1/2(8, 1/2)17/2 and the higher lying
fine-structure component 4f 10(5I8)6s1/2(8, 1/2) −115/2, located at 828.314 cm
where n is the principal quantum number, E∞ the series limit (e.g. the IP) and Rμ the
mass reduced Rydberg constant. Unless a principal quantum number n can be assigned to
the measured resonances, it is sufficient to consider the remainder of the quantum defect
δ′ = mod (δ(n)) = mod (−n∗1 1 ) since a shift of a series by an integer number does not
influence its convergence. For E∞ ≈ IP, high-lying Rydberg-states of one series possess a
nearly constant quantum defect, as described by the Ritz expansion [19]
δ(n) ≈ + δ1 + δ2δ0 − + [...] (2)(n δ0)2 (n− δ )40
where δ0 is expected to be in the range of 0 < δ0 < 6 [20] and the higher order δi param-
eters in the range of 10−3 to 101 [21]. Therefore the IP can be coarsely approximated by
minimizing the overall slope of δ(n) [7]. In Fig. 5 the spectrum obtained through excitation
scheme #6 is plotted against the effective principal quantum number n∗ for the literature
value IPDy = 47901.7 cm−1 [8], with the corresponding values of δ′ for each individual
resonance peak extracted into the graph above the spectrum. Three Rydberg-series can be
distinguished, together with some unassigned peaks. The series at δ′ ≈ 0.35 and δ′ = 0.8
are identified as the 6sns (red) and 6snd-series (blue), by comparing the respective δ′ with
the calculations of Fano et al. [20]. The high-intensity series, which approaches δ′ = 0.2
towards high n, could not be identified due to its unexpected steady and strong variation of
the quantum defect all along the measured series for 25 < n∗ < 45. Nevertheless above
n∗ = 55 a stable value of δ′ is approached, which supports the IP determination via the
other two identified series.
For the 6snd-series we observe a fine structure splitting, which cannot be resolved above
n∗ = 33 due to the experimental linewidth of > 5 GHz and the decreasing splitting between
individual fine structure components according to EFS ∝ n−3 [22]. To extend the series
towards lower n, the center of gravity of each fine structure multiplet is taken from n∗ = 28
to 33. Below n∗ = 28 peak intensities are too low for reliable assignment. For a fit of this
series we neglect second and higher order terms of the Ritz expansion, as the variations
in δ(n) are expected to lie well within the experimental uncertainty for the considered n-
interval.
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Fig. 5 Rydberg spectrum obtained through excitation scheme #6, plotted against the effective principal
quantum number n∗ as calculated from E∞ = 47901.7 cm−1. The corresponding value of δ′ = mod1(δ(n))
for each resonance is shown in the upper part. Three series can be distinguished: the 6sns-series (red), the
6snd-series (blue) and an unidentified series (black). Diamond signs on the lower part of the d-series mark the
center of gravity of a fine-structure multiplet. Individual components in that range are not shown for the sake
of clarity. Points of the same series are interconnected by lines to guide the eye. Grey points are unassigned
peaks
The other series in Fig. 5 show some distinct deviations from a constant quantum defect,
which are accompanied by strong fluctuations in peak intensities. For the 6sns-series the
very obvious perturbation around n∗ = 28 can be described within the framework of multi-
channel quantum defect theory (MQDT) [23]. Rydberg-states in the vicinity of an interloper
state with energy EI and width I are shifted away f(rom the int)erloper according to
= − 1 I /2δshift(n) δ(n) arctan . (3)
π En − EI
The perturbation in the s-series, which is observed in the spectra of all three excitation
schemes, can be accurately considered through this modification of the quantum defect. A
fit of this series is shown in Fig. 6, including the Ritz expansion to the second order term.
Towards lower n the course of the series is predominantly governed by δ1. The fitting errors
of this parameter are in the order of the value itself, yet the much higher consistency in
the values observed for all three spectra (see Table 2) leads to the assumption that the fit is
indeed very accurate. Even under consideration of the entire error range of δ1 only two levels
at 30560.56 cm−1 and 30979.53 cm−1 with the configuration 4f 10(5I8)6s7s(3S1) (8, 1)8,9
[16] represent possible band heads for the series. By using either one of these states as
anchor point for the series, the integer digit of the quantum defect can be determined. As a
result we obtain δ ≈ 4.33 for high n, which is in good agreement with calculations of Fano
et al. [20].
The unidentified series, represented by the black points in Fig. 5, is subject to quantum
defect variations over an extended range, which cannot be described with Eq. 3. The attempt
of fitting this series even with up to fourth order corrections from Eq. 2 is possible, however
resulting parameters for δ1 and δ2 are in the range of 102 and 105, respectively, which does
not seem appropriate. For this reason the series was excluded from evaluation.
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Hyperfine Interact (2017) 238: 8 Page 9 of 11 8
Fig. 6 Rydberg-Ritz fit of the 6sns-series (excitation scheme #6) in the energy representation (middle) and
the quantum defect representation (top). Dashed lines indicate the error range of δ1. The stars at n = 7
represent possible series heads with the configuration 4f 10(5I8)6s7s(3S1) (8, 1)J [16]. The lower graph
shows the fit residuals
Table 2 Summary of the IP values obtained from Rydberg-Ritz fits of the 6sns and 6snd-series with the
respective statistical uncertainties
scheme # series n∗-interval #peaks E∞[ cm−1] δ0 mod 1 δ1
4 6snd 27 − 45 20 47901.81(5) 0.749(9) −
6sns 12 − 47 14 47901.81(7) 0.329(9) 1.1(1.0)
5 6snd 25 − 40 16 47901.55(22) 0.69(2) −
6sns 12 − 48 23 47901.79(10) 0.33(1) 1.0(1.5)
6 6snd 28 − 49 20 47901.77(5) 0.766(7) −
6sns 15 − 46 24 47901.71(4) 0.327(5) 0.95(86)
Taking the weighted average yields a value of E∞ = 47901.76(2)stat
A summary of all series limits obtained from the different excitation schemes is given
in Table 2. The large deviation of value from the 6snd-series in scheme #5 is most likely a
consequence of missing fine structure components within the fitted n-interval, which were
not observed due to the low intensity of this series. Correspondingly the uncertainty of this
series limit is comparatively high, which is also a result of the limited n-interval and the
number of fitted peaks.
Taking the weighted average yields a value of E∞ = 47901.76(2) cm−1. Uncertainties
in the energy position of the FES, as well as systematic errors in the wavelength mea-
surement linearly propagate to E∞ and are thus added as a systematic uncertainty to the
error of the IP. In comparison to this, stark shifts are neglectable due to the low electric
field of < 1 V/cm inside the atomizer cavity. In conclusion we extract a final value of
IPDy = 47901.76(2) −1stat(3)sys cm , which is in good agreement with the results from Zhou
et al. [8].
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8 Page 10 of 11 Hyperfine Interact (2017) 238: 8
5 Conclusion
The spectra of altogether six different excitation schemes, covering spectral ranges of up
to 2500 cm−1 around the first ionization potential of Dy, were studied. In the spectra
obtained from two-step excitation we observed the bound 4f 106sns and 4f 106snd Rydberg-
series as well as a so far unidentified series, all of them converging to the ionic ground
state. Considering the second-order Ritz expansion and an approach from MQDT for the
characterization of a strong perturbation of the s-series around n = 32, we could re-
determine the first ionization potential of dysprosium. With the obtained value of IPDy =
47901.76(5) cm−1 we can confirm the literature value of Zhou et al. [8] and improve
the precision by about one order of magnitude. Auto-ionizing Rydberg-series converging
to the level 4f 10(5I8)6s1/2(8, 1/2)15/2 at 828.314 cm−1 were observed but not studied
in detail due to high non-resonant background and strong perturbing interactions of the
Rydberg-states with broad continuum states.
Spectroscopic data obtained in three-step excitation schemes was primarily used for
scheme development. Bound Rydberg-series could not be observed, most likely due to unfa-
vorable experimental conditions of low accessible laser power for the required third step
wavelengths of >931 nm as well as high background from additional photons of the second
excitation step laser. For scheme development several high-intensity auto-ionizing reso-
nances were studied with respect to their saturation power and laser ion signal intensity.
Utilizing the excitation scheme given in Fig. 2 an ionization efficiency of 25(4) % could be
reproducibly demonstrated at the RISIKO mass separator at JGU Mainz.
References
1. Lecesne, N.: Laser ion sources for radioactive beams (invited). Rev. Sci. Instrum. 83, 02A916 (2012)
2. Fedosseev, V.N., Kudryavtsev, Y., Mishin, V.I.: Resonance laser ionization of atoms for nuclear physics.
Phys. Scrip. 85, 58104 (2012)
3. Trautmann, N., Passler, G., Wendt, K.D.A.: Ultratrace analysis and isotope ratio measurements of long-
lived radioisotopes by resonance ionization mass spectrometry (RIMS). Anal. Bioanal. Chem. 378, 348
(2004)
4. dos Santos Augusto, R., Buehler, L., Lawson, Z., Marzari, S., Stachura, M., Stora, T.: CERN-MEDICIS
collaboration: CERN-MEDICIS (medical isotopes collected from ISOLDE): A new facility. Appl. Sci.
4, 265 (2014)
5. Wendt, K., Gottwald, T., Mattolat, C., Raeder, S.: Ionization potentials of the lanthanides and actinides
– towards atomic spectroscopy of super-heavy elements. Hyp. Inter. 227, 55 (2014)
6. Liu, W., Dolg, M.: Benchmark calculations for lanthanide atoms: Calibration of ab initio and density-
functional methods. Phys. Rev. A 57, 1721 (1998)
7. Worden, E.F., Solarz, R.W., Paisner, J.A., Conway, J.G.: First ionization potentials of lanthanides by
laser spectroscopy*. J. Opt. Soc. Am. 68, 52 (1978)
8. Zhou, H.J., Xu, X.Y., Huang, W., Chen, D.Y.: Study of high-lying excited states of rare-earth element
Dy by laser resonance ionization spectroscopy. Acta Physica Sinica (Overseas Edn), 19 (1992)
9. Fedosseev, V.N., Marsh, B.A., Fedorov, D.V., Köster, U., Tengborn, E.: Ionization scheme development
at the ISOLDE RILIS. Hyp. Inter. 162, 15 (2006)
10. Rothe, S., Marsh, B.A., Mattolat, C., Fedosseev, V.N., Wendt, K.: A complementary laser system for
ISOLDE RILIS. J. Phys. Conf. Ser. 312, 52020 (2011)
11. Blaum, K., Geppert, C., Müller, P., Nörtershäuser, W., Otten, E.W., Schmitt, A., Trautmann, N., Wendt,
K., Bushaw, B.A.: Properties and performance of a quadrupole mass filter used for resonance ionization
mass spectrometry. Int. J. Mass Spectrom. 181, 67 (1998)
12. Blaum, K., Geppert, C., Müller, P., Nörtershäuser, W., Wendt, K., Bushaw, B.A.: Peak shape for
a quadrupole mass spectrometer: Comparison of computer simulation and experiment. Int. J. Mass
Spectrom. 202, 81 (2000)
13. Cowan, R.D.: The theory of rare earth energy levels and spectra. Nucl. Instrum. Methods 110, 173 (1973)
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14. Wickliffe, M., Lawler, J., Nave, G.: Atomic transition probabilities for Dy I and Dy II. J. Quant. Spectros.
Rad. Transfer 66, 363 (2000)
15. Gottwald, T., Lassen, J., Liu, Y., Mattolat, C., Raeder, S., Wendt, K.: Laser resonance ionization spec-
troscopy of the lanthanides Tb, Dy and Ho as homologues to actinides and super heavy elements. AIP
Conf. Proc., 138 (2009)
16. Kramida, A.E., Ralchenko, Y., Reader, J.: NIST ASD Team. NIST Atomic Spectra Database (ver. 5.3).
(2016). http://physics.nist.gov/asd
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18. Kron, T., Liu, Y., Richter, S., Schneider, F., Wendt, K.: High efficiency resonance ionization of palladium
with Ti: Sapphire lasers. J. Phys. B: Atom. Molec. Opt. Phys. 49, 185003 (2016)
19. Ritz, W.: Zur Theorie der Serienspektren. Annalen der Physik 317, 264 (1903)
20. Fano, U., Theodosiou, C.E., Dehmer, J.L.: Electron-optical properties of atomic fields. Rev. Modern
Phys. 48, 49 (1976)
21. Weber, K.H., Sansonetti, C.J.: Accurate energies of nS, nP, nD, nF, and nG levels of neutral cesium.
Phys. Rev. A 35, 4650 (1987)
22. Harvey, K.C., Stoicheff, B.P.: Fine Structure of the nD2 Series in Rubidium near the Ionization Limit.
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23. Seaton, M.J.: Quantum defect theory. Reports Progress Phys. 46, 167 (1983)
Reprinted by permission from Springer Nature : Springer Hyperfine Interactions. D. Studer et al., Hyperfine Interact. (2017) 238:8 
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3.8. Atomic transitions and the first ionization potential of promethium
3.8 Publication III: Atomic transitions and the first ionization potential of
promethium determined by laser spectroscopy
The following work was published as a regular article in Physical Review A 99,
062513 (2019) DOI 10.1103/PhysRevA.99.062513. It presents extensive laser spec-
troscopy studies on a sample of 15 ng 147Pm, which was produced by neutron ac-
tivation of enriched 146Nd in a nuclear reactor. In the course of ionization scheme
development for this previously inaccessible element by RIS, several regions in
the atomic spectrum were studied, including high-lying levels close to the IP. The
new ionization schemes pave the way for laser ion sources applications and high-
resolution spectroscopy on atomic Pm, as presented in Publication V.
For the determination of the IP, the approach of Rydberg convergences, as used
for Dy in Publication II, was not applicable due to the high complexity of the
spectrum. Instead, electric field ionization thresholds of weakly bound states were
measured to determine the IP using the classical saddle point model (see Sec.
3.5.2). This technique was used earlier by T. Gottwald [128] in the precursor of
the MABU setup for the study of several lanthanide elements. The results from
these experiments are published in [138]. The study of Pm was deemed not fea-
sible at the time due to low sample availability and comparatively low efficiency
in the required perpendicular ionization geometry. In fact, in the experiment pre-
sented here atom numbers are a factor of 103-104 lower than in earlier experi-
ments on stable species. This challenge was overcome by refining the measure-
ment procedure. Scanning the electric field strength while keeping the ionization
laser wavelength on resonance allows for higher counting statistics, but introduces
some experimental complications, in particular maintaining high ion transmission
through the apparatus. Comparing the IP values for Dy from Publication II of
IPRydDy = 47 901.76(5) cm
−1 with the one of IPSP = 47 901.8(3) cm−1Dy [128] confirms
the excellent agreement of the results obtained from Rydberg analysis and the sad-
dle point model.
Note that this article was published together with supplemental data tables, which
are given in the appendix A.3.
Author contribution
This project was proposed by the author as part of a series of measurements on
the element Pm. The enriched 146Nd sample was provided by C.G. and irradiated
at ILL by U.K. Chemical purification of the sample was performed at PSI by S.H.,
R.D. and D. Schumann. Laser spectroscopy was carried out by the author, R.H.
and P.N. Data evaluation and the manuscript draft were prepared by the author.
This work was supervised by K.W.
71
PHYSICAL REVIEW A 99, 062513 (2019)
Atomic transitions and the first ionization potential of promethium determined by laser spectroscopy
Dominik Studer,1,* Stephan Heinitz,2 Reinhard Heinke,1 Pascal Naubereit,1 Rugard Dressler,3 Carlos Guerrero,4 Ulli Köster,5
Dorothea Schumann,3 and Klaus Wendt1
1Institut für Physik, Johannes Gutenberg-Universität Mainz, 55128 Mainz, Germany
2Belgian Nuclear Research Centre, SCK-CEN, 2400 Mol, Belgium
3Paul-Scherrer Institut, 5232 Villigen, Switzerland
4Departamento de Física Atómica, Molecular y Nuclear, Universidad de Sevilla, 41012 Sevilla, Spain
5Institut Laue-Langevin, 38042 Grenoble, France
(Received 19 March 2019; published 26 June 2019)
The atomic spectrum of neutral promethium has been studied extensively by laser resonance ionization
spectroscopy. We report on more than 1000 atomic transitions in the blue and near infrared spectral ranges, most
of them between high excited energy levels. As Rydberg convergences could not be assigned unambiguously
in the dense spectrum at high excitation energies, the first ionization potential (IP) was determined via field
ionization of weakly bound states within a static electric field. By applying the saddle-point model, a value of
IP(Pm) = 45 020.8(3) cm−1 [5.58188(4) eV] was derived, which confirms previous expectations of 45 027(80)
and 44 985(140) cm−1, which were obtained indirectly from lanthanide IP systematics.
DOI: 10.1103/PhysRevA.99.062513
I. INTRODUCTION First spectroscopy studies of promethium were performed
with milligram samples of 147Pm, corresponding to an activity
The year 2019 has been declared the International Year in the terabecquerel range. These measurements revealed
of the Periodic Table of Chemical Elements for the 150th numerous resonance lines in the spectra of neutral (Pm I)
anniversary of Mendeleev’s discovery, which today comprises and singly charged (Pm II) promethium [7,8], as well as
118 elements. While most stable species are studied thor- hyperfine splittings of 147Pm [9]. The most comprehensive
oughly, for a number of elements, which either have no works on Pm I energy levels and transitions to date are [7,10],
stable isotopes or are produced only artificially, still today which also account for the major part in spectroscopic data
fundamental atomic properties have not been determined with compilations, such as [11,12]. However, one should note that
satisfying precision or are entirely missing. These deficits also only well-assigned atomic transitions from the low-lying 6Ho
include the ionization potential (IP), i.e., the energy required and 6Fo fine-structure multiplets with excitation energies of
to remove one electron from the neutral atom. In this sense we
E < 10 000 cm−11 are given in literature, leaving almost
aim to shed light on the promethium case (Pm, Z = 61), which the upper half of the spectrum unexplored. Moreover, the
is the only exclusively radioactive lanthanide element. The first ionization potential of Pm has never been determined
longest-lived isotope of this element is 145Pm with a 17.7-yr experimentally. Worden et al. [13] and Wendt et al. [14] report
half-life; however, the more commonly used isotope in the few values of 45 027(80) cm−1 and 44 985(140) cm−1, respec-
practical applications of this element is 147Pm with a half-life
147 tively. Both of these results were obtained from a systematicof 2.6 yr. Pm is used in nuclear batteries [1], e.g., for space interpolation of the IPs of all lanthanide elements. A direct
missions and as a β source for thickness gauges [2]. 142Pm
= 142 142 measurement could confirm the underlying assumption of a(T1/2 40.5 s) in a so-called Sm/ Pm in vivo generator linear trend in the IPs of lanthanide atoms above and below
had been used for preclinical positron emission tomography at
149 = the half-filling of the 4 f shell. Considering that the IP hasa Geneva hospital [3]. Pm (T1/2 2.2 days) is a promising recently been measured up to Z = 103 [15,16], it is even more
radiolanthanide for receptor-targeted radiotherapy [4] due to remarkable that this fundamental property of Pm remains
its emission of medium-energy β rays and only a few disturb- unknown. Figure 1 gives an overview of the present situation
ing gamma rays. It can be produced via neutron activation in regarding the experimental uncertainties in the first ionization
non-carrier-added form [5,6]. potential across the Periodic Table. With the exception of
the transactinide elements, Pm marks the last gap where no
experimental result is listed. Apart from the high specific
radioactivity of Pm isotopes, this is a consequence of the
*dstuder@uni-mainz.de
Published by the American Physical Society under the terms of the 1As commonly used in spectroscopy, we give energies (and IP
Creative Commons Attribution 4.0 International license. Further values) in units of cm−1, which can be converted to actual energy
distribution of this work must maintain attribution to the author(s) values by multiplication with hc. Here 1 cm−1 corresponds to 1.24 ×
and the published article’s title, journal citation, and DOI. 10−4 eV.
2469-9926/2019/99(6)/062513(8) 062513-1 Published by the American Physical Society
DOMINIK STUDER et al. PHYSICAL REVIEW A 99, 062513 (2019)
   Uncertainty < 0.1 µeV
   Uncertainty 0.1 - 1.0 µeV
1    Uncertainty 1 - 10 µeV 2
H    Uncertainty 10 - 100 µeV He
3 4    Uncertainty 0.1 - 1 meV 5 6 7 8 9 10
Li Be    Uncertainty 10 - 200 meV B C N O F Ne
11 12    No experimental value 13 14 15 16 17 18
Na Mg Al Si P S Cl Ar
19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36
K Ca Sc Ti V Cr Mn Fe Co Ni Cu Zn Ga Ge As Se Br Kr
37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54
Rb Sr Y Zr Nb Mo Tc Ru Rh Pd Ag Cd In Sn Sb Te I Xe
55 56 57 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86
Cs Ba La Hf Ta W Re Os Ir Pt Au Hg Tl Pb Bi Po At Rn
87 88 89 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118
Fr Ra Ac Rf Db Sg Bh Hs Mt Ds Rg Cp Nh Fl Mc Lv Ts Og
58 59 60 61 62 63 64 65 66 67 68 69 70 71
Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu
90 91 92 93 94 95 96 97 98 99 100 101 102 103
Th Pa U Np Pu Am Cm Bk Cf Es Fm Md No Lr
FIG. 1. Periodic Table of Chemical Elements with a color coded display of the experimental uncertainty in the value of the first ionization
potential for each element. In the case of Pm the upper half of the tile corresponds to the achieved precision in this work. A complete list of all
values, uncertainties, and corresponding references is given in the Supplemental Material [17].
complex atomic spectra of midshell elements, most notably was repurified from the 147Sm decay product using extraction
in the lanthanide and actinide series with an additional open chromatography. The purified 147Pm solution was shipped to
f subshell. Usually the analysis of Rydberg series allows Mainz University for the spectroscopy measurements. The
a determination of the ionization potential with a precision experimental apparatus is shown in Fig. 2. The principle
in the range of 10−5 eV, as demonstrated for a number of of RIS is implemented with a hot cavity laser ion source
radioactive elements, e.g., Tc [18], Ac [19], Po [20,21], At coupled to a compact quadrupole mass spectrometer. The Pm
[22], or No [23]. However, the identification of Rydberg states solution is heated and crystallized on a 3 × 3 mm2 titanium
becomes increasingly difficult with the occurrence of strong carrier foil (also serving as a reduction agent), which is then
configuration mixing in complex atomic systems, up to a folded and introduced into a tubular graphite furnace with
point where an unambiguous level assignment is not possible 37 mm length and 2.2 mm inner diameter. The furnace can
anymore. The spectrum may even exhibit chaotic behavior, be heated resistively with a current of up to 100 A. At a
as recently observed in Pa [24,25]. In this work we apply a temperature of approximately 850 ◦C the Pm is atomized
complementary approach for the IP determination, based on [according to chemical equilibrium simulation (Outotec HSC
dc electric field ionization of highly excited levels, which even Chemistry)] and irradiated by pulsed laser light. Laser-ionized
benefits from high level density. The method was utilized by species are extracted and accelerated by a set of three ex-
Köhler et al. [26] and Erdmann et al. [27] for the measurement traction electrodes (U1, U2, and U3). The ion beam is guided
of IPs of several actinide elements. We refined this approach through a 90◦ electrostatic quadrupole deflector to remove
for applicability at even lower counting statistics without a
loss in precision.
Extraction electrodes
U U U 90° quadrupole1 2 3
II. EXPERIMENTAL SETUP Einzel lens deflector
Atomizer
Our experiment is based on resonance ionization spec- Laser 
troscopy (RIS), which offers an excellent sensitivity for the beams
investigation of minuscule sample amounts. The method relies Sample
on a stepwise photoionization process by pulsed laser radia-
tion, providing an inherent elemental selectivity together with Quadrupole Transversal 
usually high efficiency. mass filterlaser beam
For our measurements we used a sample of approximately
6 × 1013 atoms of 147Pm (corresponding to 15 ng or 500 kBq). Single ion 
It was produced in the high-flux reactor at ILL Grenoble counting
by neutron activation of highly 146Nd-enriched neodymium.
The produced 147Nd decays with a half-life of 11 days to FIG. 2. Sketch of the atomic beam mass spectrometer with ion
147Pm. The irradiated sample was dissolved in 7M HNO3 and flight path (yellow) and laser beams in anticollinear (solid red and
underwent chemical purification via ion exchange chromatog- solid blue) and perpendicular crossed-beam (dashed red) geometry.
raphy at PSI Villigen in order to remove the macroscopic The latter offers a spatially-well-defined laser-atom interaction re-
Nd component, as described in Ref. [28]. Part of this batch gion inside a homogeneous electric field between U1 and U2.
062513-2
ATOMIC TRANSITIONS AND THE FIRST IONIZATION … PHYSICAL REVIEW A 99, 062513 (2019)
FES SESA B0 SESB B1 B2 SESC C1 C2 a search for first excited states (scheme FES) was performed
44 985(140) 4f5(6Ho)6s 7Ho2 by scanning one laser from 408 to 473 nm, along with a
33 352.15 J = 7/2o second laser at a fixed wavelength for nonresonant ionization
33 303.96 J = ?
32 724.72 J = ? from excited states. The spectrum contains 196 lines. In an
32 683.69 J = ? independent scan with a sample of natural Sm we could
22 080.08 J = 5/2 identify 43 of those lines as parasitic resonances from the
21 348.22 J = 7/2 147
21 143.06 J = 7/2 isobaric Sm daughter nuclide of
147Pm, which cannot be
separated in our mass filter. Most of the recorded Pm lines
can be found in [10]. Our data show a systematic deviation
0 4f56s2 6Ho5/2
E (cm-1) A B C of ν̃Pm = (−0.12)sys(4) −1stat cm from Pm literature values
(the statistical error is inferred from the standard deviation).
FIG. 3. Overview of investigated excitation schemes in Pm I. The In the case of the observed Sm lines this deviation is ν̃Sm =
respective scanning excitation step is indicated by a series of arrows. (−0.11)sys(4) −1stat cm when comparing our results to energies
The notation for every scheme is given on top. The letters A, B, and given in the NIST database [11]. This systematic shift is
C below define the schemes in a more general sense, referring to the well understood and arises from an imperfect synchronization
respective first excitation step. The level energies for the first excited in the data acquisition process, depending on the laser scan
states are taken from the NIST database [11]. speed. In independent scans of the ground-state transitions
in schemes B and C we could perfectly reproduce the liter-
unspecific neutral background components and directed into ature values. Therefore, a correction of the shifts mentioned
an rf quadrupole mass filter. Singly charged ions of the desired above was applied to the recorded data. In the Supplemental
mass are finally detected with a channel electron multiplier in Material [17] we list the 32 previously unknown transitions.
single-ion-counting mode. We refrain from giving associated energy levels in this case,
In standard operation all lasers are guided along the ion as we cannot clearly determine the lower level energy. This
beam axis, ionizing the sample directly within the atomizer is due to a thermal population of low-energy states, thus
cavity. The alternative, transversal ionization geometry is observed lines are not necessarily ground-state transitions.
discussed in Sec. IV. The laser system consists of three pulsed In fact, when comparing our spectrum with literature data,
6 o
Ti:sapphire lasers. Each laser is pumped with 13–18 W of a we find that the whole H multiplet of altogether six levels
10-kHz repetition rate Nd:YAG laser at 532 nm (Photonics with 5/2  J  15/2 is considerably populated in the hot
Industries DM100-532). Under optimal conditions the av- atomizer. At an average operating temperature of 1200
◦C,
6 o
erage fundamental output of each Ti:sapphire laser reaches the relative H5/2 ground state population is at approximately
up to 5 W, with a pulse length of 40–60 ns and a spectral 55%. However, one should note that this state maintains
linewidth of 5–8 GHz so that all Doppler classes within the hot leading percentage in the ensemble even at high temperatures◦
atomic vapor are addressed. This type of laser system is also of 2000 C, making it the initial state of choice for efficient
in operation at the majority of on-line radioactive ion beam photoionization. As first excited states we chose the three
facilities worldwide (for details see [29,30]). In our setup odd-parity levels at 21 143.06, 21 348.22, and 22 080.08 cm
−1
we extend the fundamental tuning range of 680–960 nm by for further investigation, because there are strong ground-state
second harmonic generation in an external beta barium borate transitions leading to these levels. Moreover, these transitions
(BBO) single-pass assembly with a conversion efficiency of fulfill the condition 2ν̃ < IP, preventing a one-color, two-
approximately 10%. Wide-range scans are performed with photon ionization process which would induce background in
a dedicated spectroscopy Ti:sapphire laser. It is based on a further spectroscopy measurements.
diffraction grating for frequency selection, allowing mode- Second excitation steps (schemes SESA, SESB, and SESC)
hop-free scanning operation by angle tuning of the grating. were measured in the same manner, i.e., with the first ex-
This laser type has an output power of approximately 2 W citation step fixed on the respective resonance and with the
and a spectral linewidth of 2–5 GHz. A similar laser design addition of a third, nonresonant step. We recorded 157 lines
is described in [31]. Scanning of the second harmonic is per- and 126 associated even-parity energy levels. Possible val-
formed by manual phase-matching adjustment via the BBO ues for the total angular momentum are constrained by the
tilting angle, while spatial beam walk-off is compensated with selection rule J = 0,±1 for dipole transitions and may be
a system of position sensitive detectors and motorized mirrors further restricted whenever a state is visible in more than
(TEM Aligna Beamlock 2D). The fundamental frequency of one excitation scheme. In the case of the excited state at−1
each laser is monitored with a wavelength meter during all 33 352.15 cm the total angular momentum was determined
measurements (High Finesse WS6-600). as J = 7/2 by a measurement of the hyperfine structure of
the 22 080.08 cm−1 → 33 352.15 cm−1 transition. Details on
these measurements are beyond the scope of the present work.
III. BROADBAND LASER SPECTROSCOPY
Some first and second step transitions were also analyzed
Several optical excitation ladders were investigated in or- with respect to their saturation behavior. Figure 4 shows the
der to probe the spectrum of Pm I and for the development laser power influence on the line shape and the ion signal
of resonance ionization schemes. An overview of all schemes in excitation scheme C2. In the region of strong saturation
is given in Fig. 3, where a series of arrows indicates the the ion signal is almost independent of the laser power and
scanned excitation step. In the following these schemes are the line profile is significantly broadened. The saturation
abbreviated with the notation given on top in Fig. 3. Initially, power Psat is defined as the laser power where half of the
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DOMINIK STUDER et al. PHYSICAL REVIEW A 99, 062513 (2019)
TABLE I. Saturation powers Psat for several investigated transi-
tions with lower energy level El and upper level Eu.
Scheme El (cm−1) E (cm−1u ) Psat (mW)
A 0 21 143.06 3(1)
B 0 21 348.22 10(5)
C 0 22 080.08 7(4)
B1 21 348.22 32 683.69 140(50)
C2 22 080.08 33 352.15 200(40)
ionic ground state may not be assigned unambiguously. Low-
lying excited states in Pm II from the NIST databse [11] were
also considered as Rydberg-series limits, most importantly
the 7Ho3 state at 446.45 cm
−1, representing the state in Pm
II with the lowest excitation energy. In this case too, no clear
assignment could be made, rendering the method of Rydberg
convergences inapplicable. On the other hand, many strong
FIG. 4. Shown on the left are line profiles of the first step autoionizing transitions can be observed, which may serve as
(bottom) and second step (top) transitions in excitation scheme C2 final excitation steps for efficient photoionization of Pm, e.g.,
for different laser powers. Ion counts are normalized in order to for high-resolution spectroscopy on the nuclear structure in
emphasize the saturation broadening. Shown on the right is the laser the Pm isotopic chain.
power dependence of the ion signal. All recorded transitions and energy levels are listed in the
Supplemental Material [17]. We included a data table for each
excitation scheme, where all lines are listed by wavelength
maximum ion signal is reached. The saturation curve fit for in descending order. The uncertainties are stated in the ta-
the determination of Psat and the broadened line shape are ble captions. The above-mentioned systematic deviation in
discussed in detail in [32]. All saturation power measurements the measured ground-state transitions was eliminated in the
are summarized in Table I. For reasons of time, only a limited spectra of the second excitation steps by performing scans
number of transitions could be investigated; however, it is in both directions. For the ionizing transitions, comparatively
clear that all these transitions can be easily saturated with the slow scanning speeds were chosen, so the systematic effect is
available laser power, which is favorable with regard to the estimated to be well below the statistical uncertainty.
ionization efficiency. Associated energy levels for the transitions are given when-
Finally, ionizing transitions were measured in the excita- ever possible. We also inferred line intensities from the ion
tion schemes B0, B1, B2, C1, and C2. The high level density count rate on resonance. However, these should be considered
is similar in all spectra and only slightly varies with the signal- as rough guidelines, as intensities in RIS are prone to interfer-
to-background ratio in the different scans. A sample spectrum ence from all involved excitation lasers. In the schemes SESA,
from excitation scheme C2 is shown in Fig. 5, containing 342 SESB, and SESC, where we use an arbitrary-wavelength third
lines in a range of approximately 800 cm−1. An increase in step for ionization, this is particularly striking because the
the overall ion signal can be observed in the regions of the third step may be resonant to an autoionizing transition. In
expected IP [13,14], which suggests that the linear trend in order to counteract this to some extent we repeated each scan
lanthanide IPs is indeed accurate. However, a more precise IP in these schemes with a different ionization laser wavelength
value may not be readily determined from these spectra. The for a more reliable estimation of the transition intensity. In the
nonresonant photoionization threshold is obscured due to the data tables we state the mean value of both intensities. The
high level density and Rydberg states converging to the 7Ho3 second part of the Supplemental Material comprises excited
FIG. 5. Spectrum obtained from scanning the third excitation step in scheme C2. The literature values of the first ionization potential of
44 985(140) cm−1 [14] and 45 027(80) cm−1 [13] are shown by the orange dashed and green dash-dotted vertical lines, respectively. The
shaded regions indicate the uncertainty. The ion counts are linearly scaled with respect to the laser power in the final excitation step (which
varies between 0.5 and 1.3 W over the scan range).
062513-4
ATOMIC TRANSITIONS AND THE FIRST IONIZATION … PHYSICAL REVIEW A 99, 062513 (2019)
levels, sorted by energy in ascending order. The level energies
were derived from the recorded transitions according to the
rules stated in [24]. As discussed above, possible values for
the total angular momentum J are included in the data tables.
IV. IONIZATION POTENTIAL
Our approach for the IP measurement is based on a dc
electric field ionization of highly excited states. The under-
lying concepts, namely, tunneling of the electron through the
potential barrier along the electric field axis and the classical
view of the so-called saddle-point model, are discussed and
compared in detail by Littman et al. [33]. With increasing
field strengths tunneling leads to an exponential increase of
ionization rates of excited atoms and is most notably observed
through a gradual broadening of Stark sublevels into a con-
tinuum. Saddle-point ionization, on the other hand, manifests
as a sharp increase of ionization rates at excitation energies
greater than the saddle-point of the effective Coulomb poten-
tial, which can be written as √ FIG. 6. Determination of ionization thresholds from scans of the
3
= − Zeffe F final laser excitation step in scheme C2. The upper trace shows theWs IP 2 , (1)
4π0 full resonant in-source laser scan (red), the middle trace the in-source
laser scan with detuned second excitation step, revealing parasitic
with the effective charge of the atomic core Zeff and the exter- resonanes (green); and the lower trace the laser ionization scans
nal electric field F . A precise measurement of several electric with external electric field (blue). The ion count offset for each scan
field ionization thresholds allows an extrapolation to zero- is scaled with the corresponding electric field strength. The orange
field strength, thus yielding the ionization potential. From the dashed line illustrates the electric field ionization threshold, with the
experimental point of view, tunneling can be neglected in this shaded region indicating the uncertainty.
case, as ionization rates are very small at moderate electric
fields and do not significantly influence the sharp saddle-point
threshold. After inserting values for the√constants, this law species from the furnace, U1 is set on a positive voltage.
simplifies to Ws = IP − 6.12 (V cm)−1/2 F (assuming Zeff = Because saddle-point ionization is very similar to the mech-
1 for high excited states). At this point one should note that anism of autoionization, states above the threshold ionize
Eq. (1) requires a modification in the form of additional terms almost instantaneously and independently of the absolute field
proportional to |mF |F 3/4 + 3 216 mF F (note that the subscript F strengths (in contrast to tunneling). As a consequence, ions
does not denote the electric field, but the total angular mo- are generated with a relatively small spatial spread around
mentum) for states with nonzero magnetic quantum numbers the laser-atom interaction region, which is advantageous in
[33,34]. A simple explanation is that energy which is stored terms of the ion beam energy spread. Nevertheless, as we tune
in angular momentum perpendicular to the axis of the electric the electric field, the voltages on the extraction electrode U3
field cannot contribute to the escape of the electron over the and the quadrupole deflector have to be adjusted in order to
potential barrier. Consequently, states of high |mF | require guarantee optimal transmission through the apparatus.
significantly stronger electric fields for ionization. Gallagher Initially we recorded the highly excited spectrum by scan-
et al. observed this effect for Rydberg states in sodium [35]. ning the wave number of the laser used in the final excitation
In our experiment all laser beams are polarized perpendicular step in the presence of a constant electric field, similar to the
the direction of the electric field, while the first excitation approach of Köhler et al. [26] and Erdmann et al. [27] in the
step laser is also polarized perpendicular with respect to the actinide series.
second and third excitation step lasers. We do not selectively Figure 6 shows the results for laser scans with excitation
excite certain mF sublevels and thresholds are dominated by scheme C2 over a range of approximately 6 nm in the region
the mF = 0 contribution. slightly below the expected ionization potential. The upper
For this experiment we operate the laser ion source slightly trace shows the relevant region of the spectrum obtained
differently than described in Sec. II. Instead of guiding all from ionization inside the atomizer furnace (see Fig. 5),
lasers along to the ion beam axis, we cross the lasers between i.e., containing all resonances independent of the electric
the two flat electrodes U1 and U2, as depicted in Fig. 2 by a field. The spectra from transversal laser-atom interaction in-
transversal laser beam. In this geometry laser ionization no side the electric field are presented in the lower trace. For
longer takes place inside the atomizer. Neutral Pm atoms ef- the sake of clarity we added an offset proportional to the
fuse from the furnace and the laser-atom interaction region is electric field strength. In comparison to the full spectrum,
spatially well defined within a static electric field generated by one can clearly observe that the spectra are subsequently
U1 and U2. The electrodes are set 1 cm apart and have central cut off towards lower excitation energies. Strong resonances
holes of 2 mm diameter. In order to suppress surface ionized below the threshold (e.g., at approximately 44 930 cm−1) may
062513-5
DOMINIK STUDER et al. PHYSICAL REVIEW A 99, 062513 (2019)
1.0
Data Data
0.5 Sigmoid fit 0.8 Sigmoid fit
Threshold Threshold
0.4
0.6
0.3
0.4
0.2
0.2
0.1 (a) (b)
0.0
22.5 25.0 27.5 30.0 32.5 35.0 195 200 205 210
Electric field F (V/cm) Electric field F (V/cm)
FIG. 7. Electric field ionization threshold for the energy levels at (a) 44 989.3 cm−1 and (b) 44 933.8 cm−1. The threshold corresponds to
the turning point of the sigmoid fit. The shaded region indicates the uncertainty.
remain visible, albeit strongly suppressed, due to nonresonant not trivial as the voltages U1 and U2 significantly influence the
photoionization or collisional ionization of the excited atoms. ion beam transmission through the ion optics downstream. For
One resonance slightly below 44 960 cm−1 is hardly affected this reason we performed reference scans on the energy level
by the electric field. Here the scanned third laser excites at 45 005 cm−1 (which is above threshold for all investigated
the 22 080.08 cm−1 → 33685.3 cm−1 transition, followed by values of F ) for relevant voltage sets. Ionization thresholds
nonresonant ionization (ν1 + ν3 + ν3). These parasitic reso- were measured for 11 energy levels in the range from 44 930
nances can be identified by means of a scan with an off- to 44 990 cm−1 with electric fields between 25 and 205 V/cm.
resonant second step, which in this case corresponds to excita- All data sets were corrected for the ion beam transmission
tion scheme SESC. The relevant region of this scan is plotted loss with the corresponding reference scans. The resulting
in the middle trace of Fig. 6. At this energy scale, all peaks in saddle-point ionization thresholds for the highest and lowest
this spectrum correspond to artifacts in scheme C2 and may investigated level energies are presented in Figs. 7(a) and 7(b),
be ignored with regard to ionization thresholds. respectively. The data can be well described with a sigmoid
Because no clear nonresonant ionization onset can be function
observed, thresholds can only be constrained by the presence A1
or absence of resonances for given electric field strengths. S(F ) = A0 + + − − , (2)1 e k(F FT )
By comparing two data sets, we estimate the photoionization
threshold as the mean value of the energy of a peak which dis- with an offset A0, amplitude A1 and turning point FT . The
appeared and the next higher energy peak, with an error range turning point can be identified as the electric field threshold
spanning to either side. Depending on the local spectral level for the corresponding resonance. For F < FT the high-energy
density, this leads to rather unprecise results, but nonetheless tail of the resonance is gradually ionized and for F > FT
allows a first direct IP determination. With Eq. (1) we derive2 the low-energy tail, respectively. Consequently, for symmetric
− − √ line shapes FT corresponds to an ionization rate of A0 + A1/2.W λs = 45 020.2(6) cm 1 − 6.07(6) (V cm) 1/2 F . The obtained values FT with the associated energies Ws are
The corresponding curve and error range are included in displayed in Fig. 8. A fit with Eq. (1) yields the IP law
Fig. 6. The extr√acted IP law meets the expectation of W √s ∝ W F = 45 020.8(3) cm−1 − 6.08(1) (V cm)−1/2− F . (3)6.12 (V cm) 1/2 F ; however, the achieved precision in the IP s
value is not satisfactory due to the strong dependence on the The extracted value of IP(Pm) = 45 020.8(3) cm−1 is more
spectral level density. This can be improved by turning around than one order of magnitude more precise than the one derived
the measurement procedure: Instead of scanning the final laser from W λs thresholds. The line slopes in the W
λ
s and W
F
s IP
excitation step, we keep the laser on resonance and vary the laws are in perfect agreement with each other; however, at
electric field strength. Naturally this method does not rely on a higher precision we observe a significant deviation from the
nonresonant ionization onset and therefore counting statistics expected value of 6.12 (V cm)−1/2. Moreover, one could argue
benefit from the resonant ionization process. Energy levels can about a minor systematic trend in the fit residuals, which
be precisely assigned to electric field thresholds, determined are presented in the insets of Fig. 8. While this does not
from a sharp increase in the ion count rate. However, the necessarily require a modification to our fitting function (as
improved precision comes at the cost of increased complexity the data are still within a 1σ range), it motivates a careful
in the measurement process, since knowledge of the atomic consideration of possible systematic effects in our measure-
spectrum in the relevant range is a prerequisite for the appli- ments. Merkt et al. report similar deviations (i.e., lower than
cability of this method. Moreover, the scanning procedure is expected slopes) for field ionization of Rydberg states in argon
[36], which become more significant towards lower electric
field strengths. They attribute this observation to electric field
2With W λs we refer to thresholds obtained from scanning the photon inhomogeneities. For our setup we simulated electric fields
energy at a fixed electric field strength, whereas W Fs are fixed in the ion source region for each set of applied voltages, using
energies used for scans of the electric field strength. the IBSIMU C++ library [37]. The simulations yield a constant
062513-6
Ion counts (arb. units)
Ion counts (arb. units)
ATOMIC TRANSITIONS AND THE FIRST IONIZATION … PHYSICAL REVIEW A 99, 062513 (2019)
wavelength lasers and have to consider a convolution of the
approximately Gaussian spectral laser profile and the Stark
manifold as excited states. From our data we do not find a
maximum width limit W of the thresholds, which could be
associated with the laser linewidth (which is on the order of
10 GHz). We expect saturation effects from the high-power
pulsed excitation to extend this beyond the laser linewidth.
In addition to threshold broadening, the Stark effect may
also induce systematic shifts. In the case of a hydrogenic sys-
tem, blueshifted levels ionize at field strengths far beyond the
saddle point, as they are located on the high-energy side of the
potential [38]. Although this restriction is lifted in complex
atomic systems and blueshifted states may autoionize over the
FIG. 8. Overview of all extracted ionization thresholds. The underlying redshifted continuum, they require higher fields
open green circles are the photoionization thresholds obtained from than the classical saddle-point limit for ionization (for details
wavelength scans at a fixed electric field (see Fig. 6), whereas the see [36] and references therein). This results in an offset
closed blue circles are obtained from the electric field scans at a
of field-induced thresholds towards higher fields strengths.
given level energy (see Fig. 7). The linear fit for the extraction of
Note that states which show no splitting may also be affected
the ionization potential (solid orange line) corresponds to the latter.
The insets display the deviation of the fitted curve to the data points by a Stark shift, which is magnified by avoided crossings
(labeled 1–11) with a magnification factor of 27. of strongly interacting neighboring states [38]. A conclusive
analysis of these effects is hampered by the experimental
shift of approximately −0 3% from the nominal field, i.e., resolution in our setup and the lack of knowledge about the.
− −1 configuration of the investigated states. However, as one aims(U1 U2) cm . This shift is already considered in the data to push towards higher precision, all the aspects mentioned
presented above. A displacement of the laser-atom interaction above should be taken into account.
region, e.g., through misalignment of the transversal laser,
would induce an additional field offset due to minor electric
field inhomogeneities. A shift towards the lower field region V. CONCLUSION
would explain the observed deviation. Further effects can be We have presented an extensive study in the spectrum of
recognized in the threshold widths. We included the spectral neutral promethium. The data cover 126 odd energy levels,
widths W in Table II, which were calculated from widths 546 even energy levels, and more than 1000 transitions, which
with respect to the electric field, using Eq. (3). The W add to the knowledge about Pm atomic structure and provide
widths are relatively constant except for the two highest field a considerable contribution to its atomic spectra database. The
thresholds. Three effects play a role in our observation. (i) The data may give valuable input for the study of such phenomena
finite size of the laser-atom interaction region within the field as quantum chaos in the exceptionally dense atomic spectrum,
gradient forces a lower limit on the width of field-induced as recently investigated in Pa [25].
thresholds. (ii) A slightly off-resonant excitation laser will We developed photoionization schemes for Pm, which
cause a broadening and shift the threshold energy towards the pave the way for efficient production of high-purity Pm ion
excitation energy. (iii) The Stark effect causes a level splitting beams. Possible applications include, e.g., fundamental
which broadens the thresholds at high fields. Possibly this nuclear physics research on the Pm isotopic chain or
effect can be observed in the two highest field thresholds. We isobar-free ultratrace analysis via resonance ionization
expect the influence of the Stark effect to be somewhat limited mass spectrometry.
to the laser linewidth, since in our measurement we use fixed The precisely measured value of the first ionization po-
tential serves as a valuable benchmark for ab initio atomic
TABLE II. Electric field ionization thresholds FT for given ex- physics and quantum chemistry calculations. Our findings
citation energies Ws, with corresponding spectral threshold widths confirm the predictions of Worden et al. [13] and Wendt
W . et al. [14], which were assuming a linear trend in the ion-
ization potentials of light lanthanide elements below the
W (cm−1 −1s ) FT (V/cm) W (cm ) half-filling of the 4 f shell. Our measured value of IP(Pm) =
45 020.8(3) cm−1 perfectly fits into this trend (which is tan-
44 989.29(9) 26.94(10) 0.6(2)
44 988 46(9) 28.23(10) 0.5(2) tamount to the good agreement with the interpolation values)..
44 987 40(9) 30.05(9) 0.4(1) The improved precision of a factor of 270 or 470 compared.
44 980.06(9) 44.68(12) 0.5(2) to the previous estimates of Worden et al. and Wendt et al.,
44 970.55(9) 68.22(11) 0.4(1) respectively, could be achieved with the measurement of elec-
44 962.31(9) 92.48(12) 0.4(1) tric field ionization thresholds, which proves to be a powerful
44 960.18(9) 99.24(15) 0.6(2) method for the IP determination in complex spectra. The use
44 951.96(9) 128.85(12) 0.5(2) of narrow linewidth laser systems or dedicated field ionization
44 949.43(9) 138.06(17) 0.6(2) ion sources, allowing for stronger and more homogeneous
44 934.77(10) 199.92(14) 0.8(2) fields, could push the precision even further. In this case
44 933.75(10) 204.03(13) 1.0(3) systematic influences from the Stark effect must be analyzed
and considered carefully.
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DOMINIK STUDER et al. PHYSICAL REVIEW A 99, 062513 (2019)
ACKNOWLEDGMENTS dung und Forschung (BMBF Germany) under Grant No.
05P15UMCIA. The open access fee was covered by
D. Studer gratefully acknowledges financial support from FILL2030, an European Union project within the European
the EU through ENSAR2-RESIST (Grant No. 654002). Commission’s Horizon 2020 Research and Innovation Pro-
R.H. acknowledges financial support from the Bundesmin- gramme under Grant Agreement No. 731096.
isterium für Bildung und Bundesministerium fr Bil-
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[19] J. Roßnagel, S. Raeder, A. Hakimi, R. Ferrer, N. Trautmann, Schmutz, and R. Gunzinger, J. Phys. B 31, 1705 (1998).
and K. Wendt, Phys. Rev. A 85, 012525 (2012). [37] T. Kalvas, O. Tarvainen, T. Ropponen, O. Steczkiewicz, J. Arje,
[20] S. Raeder, H. Heggen, A. Teigelhöfer, and J. Lassen, and H. Clark, Rev. Sci. Instrum. 81, 02B703 (2010).
Spectrochim. Acta B 151, 65 (2019). [38] T. F. Gallagher, Rep. Prog. Phys. 51, 143 (1988).
062513-8

Chapter4
High-resolution spectroscopy as a
probe for nuclear structure
The evolution of nuclear ground state properties across the chart of nuclei is of
high relevance for a basic understanding of nuclear structure and as a test for the-
oretical models. Several observables, i.e. nuclear spin, electromagnetic moments
and mean square charge radii, are directly or indirectly linked to the ground state
configuration, size and deformation of the nucleus and thus offer valuable in-
formation on its many-body character, where simple shell model considerations
fail. The experimental access to these properties through their interaction with the
atomic shell is discussed in Sec. 4.4. As start, basics of the shell model and nuclear
deformation are established and linked to observable nuclear properties.
4.1 The shell model
The discovery of magic numbers, representing proton- or neutron numbers at which
nuclei of particularly high natural abundance or long half-life occur, motivated
the development of a theoretical model capable of explaining this observation.
Introducing a quantum mechanical treatment of the atomic nucleus, it was found
that magic numbers correspond to closed shells in the arrangement of nucleons,
somewhat similar to a noble gas configuration of the electronic shell in an atom
[139, 140]. In analogy to Sec. 3.1, the Schrödinger equation acts as starting point
for the calculation of energy levels. For the atomic nucleus, a common choice of
the binding potential is [ ]
r−R /a −1VWS(r) = −V 1 + e( )0 , (4.1)
which is referred to as Woods-Saxon potential, with V0 ≈ 40 MeV as the depth
of the potential well, R ≈ 1.2 fm · A1/3 as the nuclear radius and a ≈ 0.5 fm as
81
4. High-resolution spectroscopy as a probe for nuclear structure
11/2
11/2
9/2
7i
126
1/2 1/2
4p 3/2 13/2
13/2 3/2
5/2 5/2
5f
7/2 9/2
9/2 7/2
6h
1/2 82 1/23s 3/2 3/2
4d 11/2 11/2
5/2 7/2
7/2 5/2
5g
9/2 50 9/2
3p 1/2
1/2
5/2 5/2
3/2 3/2
4f
7/2 28 7/2
3/2 20 3/2
3d
2s 1/2 1/25/2 5/2
8
2p 1/2 1/23/2 3/2
2
1s 1/2 1/2
protons neutrons
Figure 4.1.: Nuclear energy level diagram of the single particle shell model for pro-
tons (left) and neutrons (right). The left side of each column shows the level
structure without consideration of spin-orbit coupling (nl quantum num-
bers), while the right side includes the spin-orbit term (j quantum numbers).
Magic numbers are indicated by dotted lines. Figure adapted from [143].
the surface diffuseness parameter [141, 142]. Naturally, for protons the Coulomb
repulsion has to be considered, too, and correspondingly different shell structures
are found for protons and neutrons. As solution for single valence nucleons one
obtains the energy level structure depicted on the left side in the two columns of
Fig. 4.1. Additionally, nucleons possess spin of |s| = 1/2 which couples to the
orbital angular momentum l, introducing the total angular momentum j = l + s.
Similar to atomic fine structure, the relative orientation of l and s leads to a level
splitting, as depicted on the right side of each column in Fig. 4.1. However,
unlike the atomic fine structure splitting, which is rather small in most cases, nu-
cleon spin-orbit coupling is a major contribution to the level structure and, at least
82
4.2. Nuclear moments
partly, rearranges the level order. The maximum population of each level is 2j + 1
nucleons. As a result, magic numbers are given by the large gaps between excited
levels, indicated by the dotted lines in Fig. 4.1. The total angular momentum J
of the nucleus results from jj-coupling. Considering the fact that nucleons form
pairs of opposite spin orientation, J and the parity π can have the values
J = |jp − jn|, |jp − j |+ 1, ..., j + j and π = (−1)lp+ln p n n , (4.2)
where the subscripts p and n denote the single proton and neutron quantum num-
bers. In spherical nuclei J directly corresponds to the nuclear spin I. For even-even
nuclei the spin is always equal to zero.
4.2 Nuclear moments
4.2.1 Magnetic dipole
The spin of the charged nucleus induces a magnetic dipole moment
eh̄
µI = gI I = gIµN I, (4.3)2mp
where gI is the Landé g-factor, mp the proton mass and µN = eh̄/2mp the nu-
clear magneton [144]. From a simplistic point of view one can directly derive the
nuclear magnetic moments for even-odd or odd-even nuclei, i.e. featuring an un-
paired single proton or neutron, respectively, from the considerations made so far.
Depending on the spin orientation of the unpaired nucleon, there are only two
possible values of µI . In (units of the n)uclear magneton, they can be calculatedwith
S ± gs − gl 1µI = I gl for I = j = l ± , (4.4)2l + 1 2
where gl and gs are the orbital and spin g-factors of the unpaired nucleon, given
by
gps = +5.586, g
p
l = 1 for protons
n − n (4.5)and gs = 3.826, gl = 0 for neutrons
[144]. These so-called Schmidt moments are rather accurate for ”close-to magic nu-
clei”, which exhibit a spherical shape. Magnetic moments of mid-shell nuclei,
however, might differ significantly from the Schmidt moments. They may even
exhibit a spin which differs from the shell model prediction. This behavior arises
from the effects introduced by nuclear deformations. In sufficiently strong de-
formed nuclei, an axially symmetric harmonic oscillator can be used as nuclear
83
4. High-resolution spectroscopy as a probe for nuclear structure
potential, where the deformation parameter
ω⊥ −ωze = (4.6)
ω0
is defined via the oscillator frequency ω0 of the corresponding spherical potential
and the frequencies ωz and ω⊥ parallel and perpendicular to the symmetry axis,
respectively [145]. Note that sometimes in literature, e is referred to as δ. For large
deformations J, L, S are no good quantum numbers anymore, but rather their
projections on the symmetry axis Ω, Λ, Σ, with Ω = Λ + Σ [145]. Additionally, the
principal quantum number is defined as the sum N = nz + n⊥ of the oscillator
quantum numbers parallel and perpendicular to the symmetry axis. A common
notation for such states is Ω[NnzΣ], often referred to as asymptotic quantum
numbers or Nilsson quantum numbers [145]. The energetic evolution of single
particle shell model states with increasing deformation is shown in the so-called
Nilsson diagram Fig. 4.2. Each shell model states splits into j + 1/2 levels, which
exhibit a two-fold degeneracy for the different signs of Ω [142]. Generally the
nuclear spin of deformed nuclei is given by the sum of total angular momentum
and a collective rotational angular momentum R. However, in the special case of
the nuclear ground state, which is exclusively considered here, I = Ω is expected
[144]. Naturally, the determination of magnetic moments is less conclusive
than in the simple spherical case. The vicinity of several levels of one parity
may lead to level admixtures, which strongly influence µI [144]. Nonetheless,
experimental values close to the Schmidt moment may give hints on the ground
state configuration of the nucleus and thus the deformation parameter. Figure 6 in
Publication V shows the trend of gI = µI/I for several Pm nuclei. As deformation
increases with the neutron number, the nuclear ground state changes from a d5/2
to Nilsson states belonging to the g7/2 shell model state.
4.2.2 Electric quadrupole
Considering a deformed nucleus as an ellipsoid with a charge density ρ(r), the
quadrupole moment Q is defined∫as
Q = d3rρ(r)(3z2 − r2), (4.7)
where z is the symmetry axis [147]. Neglecting higher order terms in e (octupole
e3, hexadecapole e4), the quadrupole moment can be related to the deformation
parameter e via
4
Q = ZR2e, (4.8)
5 0
84
4.2. Nuclear moments
3/2[5 53 /2[2 523]] 3/2[521]1/2[400] 1/2[76
82 02] 1/2[640
1]]
1/2[400]
5/2[4
3s1/2
6.0 2d3/2 9/2[514]5/2[4022] ] 1/2[411]7/ 1[4/024[411] 1/2[411]
2d 1h11/2
7/2[523] 3/2[411]
5/2 5/23[/421[34]11]
1g7/23/2[422] 1/ 52 /[ 24 [2 530 2
5.5 ]
]
50 1/2[301]
1/2[301]
7/2[413] 3/2[301]
1g9/2 3/52/2[ 1/2[301][303] 3/2[301] 1/2[660]5.0 [4314]22] 5/2
-0.3 -0.2 -0.1 0 0.1 ϵ 0.2 0.3 0.4 0.5 0.6
Figure 4.2.: Nilsson diagram for 40 < Z < 82. The single particle energy is plotted
as function of the deformation parameter e. Solid black lines mark even
parity bands and dashed blue lines odd parity bands. The respective single
particle shell model configuration is given in red at the e = 0 line, where also
the magic numbers at Z = 50 and Z = 82 are indicated in circles. Nilsson
quantum numbers are given as Ω[NnzΣ]. Figure adapted from [146].
with R0 ≈ 1.2 fm [142, 147]. From the definitions of Eq. 4.6 and Eq. 4.7 one can
conclude that e > 0 (or Q > 0) corresponds to prolate deformation, i.e. elongation
along the symmetry axis, and e < 0 (or Q < 0) to oblate deformation, i.e. compres-
sion along the symmetry axis. In this sense Q is a more direct probe for nuclear
deformation than the quantity µI . However, in a measurement the quadrupole
moment manifests as the component along the I-axis Qs, rather than the intrinsic
quadrupole moment Q along the symmetry axis. Qs is referred to as spectroscopic
85
Esp (ħω)
9/2[404] 1/2[505]
33//22[[450212]]
73//22[[663432]]
3/2[761]/2[770] 1/2[65
1] 3/2[651] 1/2[420
] 1/2[541]
1 2[660] 3/
2[541]
1/2[651] 5/2[642
] 1/
] 1/2
[530] 3/2[651] 1/2[550]
5/2[642 1/2[660]
[651 [54
1
3/2 1/2][660] 3/2 1/
]2[550]
1/2[541] 1/2[431]
4. High-resolution spectroscopy as a probe for nuclear structure
quadrupole moment and can be related to Q with
3Ω2 − I(I + 1) I 2I − 1
Q I=Ωs = Q = Q (4.9)
(I + 1)(2I + 3) I + 1 2I + 3
[144]. Note that according to Eq. 4.9, Qs(I = 1/2) = 0 even for Q 6= 0.
4.3 Mean square charge radius
A property which is directly linked to the size and deformation of the nucleus is
the nuclear charge radius. Although it is only sensitive to the radius of the proton
distribution, which may differ from the neutron distribution (in the order of 0.1 to
0.2 fm [148]), it is a sensitive probe for relative nuclear sizes and shapes. In the fol-
lowing, only the charge radius is considered and differences to the nuclear matter
radius are neglected. In the liquid drop model, the nuclear radius is described by
Rsph = R0A1/3, with R0 = 1.2 fm and A the number of nucleons [149]. A more
commonly used parameter is the m∫ ean square charge radius
〈 2〉 ∫ρ(r)r2 d3r 3r = ≈ R 2/3sph r d3r 5 0A , (4.10)ρ( )
where the charge density ρ(r) is of the form of Eq. 4.1 [149]. Considering deformed
nuclei, the angle-dependent radius can be expressed as
Rdef(θ) = R0(1 + β2Y20(θ))/N, (4.11)
where β2, as coefficient of the quadrupolar spherical harmonic Y20, describes the
deformation and N acts as a normalization parameter [150]. Similar as in the
previous section, higher order deformations and associated spherical harmonics
are neglected. The corresponding mean sq(uare charge )radius is given by
〈 2〉 2 5r def = 〈r 〉sph 1 + 〈β2〉 (4.12)4π
[150]. A link between β2 and the previously introduced deformation e, as well as
the electric quadrupole moment Q, can b√e established with
≈ 3 5e β2 (4.13)2 4π
3 2
Q = √ZR0 β2 (4.14)
5π
[142, 151]. From Eqs. 4.10 and 4.12 it becomes obvious that a measurement of
′ ′
changes in mean square charge radii δ〈r2〉A,A = 〈r2〉A −〈r2〉A can be used to track
86
4.4. Probing nuclear structure by laser spectroscopy
′
nuclear deformation along a series of isotopes. Discontinuities in δ〈r2〉A,A are
considered as indicators for nuclear sub-shell closures [152]. A phenomenon which
′
is sometimes observed in δ〈r2〉A,A along an isotopic chain is the so-called odd-
even staggering (OES). With few exceptions odd neutron number (odd-N) isotopes
exhibit slightly smaller radii relative to their even-N neighbors. To some extent
this effect has been understood and related to pairing effects, resulting in less
pronounced deformation for odd-N nuclei and correspondingly smaller 〈r2〉 [153–
155]. Just in some exceptional cases an inverted OES is observed, most prominently
reported for neutron deficient Hg isotopes, where it is linked to the coexistence of
prolate and oblate deformed ground states (see e.g. [156]). Inverted OES has
also been interpreted as an indicator for octupole deformation [153, 157, 158].
Quantitatively, OES can be described with the staggering parameter
δ〈r2〉A−1,A
γA =
δ〈r2〉A−1,A 1 (4.15)+
where A is the mass number of an odd-N isotope [149]. For no staggering, γA = 1,
for normal OES γA < 1 and for inverted OES γA > 1.
4.4 Probing nuclear structure by laser spectroscopy
In the previous section the nuclear spin I, the magnetic dipole moment µI , the elec-
tric quadrupole moment Q and changes in mean square charge radii δ〈r2〉 were
introduced as fundamental nuclear properties. Together they form a conclusive
picture of the evolution of nuclear ground states and their deformation across the
chart of nuclei. All these parameters can be probed by laser spectroscopy through
the interactions of the nucleus with the surrounding electronic shell, namely the
hyperfine structure (HFS) and the isotope shift (IS). Since laser spectroscopic ex-
periments usually focus on one or more atomic lines of a given chemical element,
nuclear properties are often studied for extended isotopic chains. The contribution
of HFS and IS to the atomic transition frequency are typically in the order of 0.1
to 10 GHz =̂ 10−5 to 10−7 eV, i.e. much smaller than FS splittings, which are in
the order of 10−1 eV in the medium mass range of Z ≈ 50 (cf. the NIST database
[109]). Correspondingly, the experimental resolution has to be in the order of 107
and beyond for a conclusive analysis of these effects. Radioactive species far off
the valley of β-stability are of highest interest as end points of isotopic chains, of-
ten exhibiting extreme ground state properties. Such experiments are particularly
challenging, since high precision has to be combined with highest sensitivity.
87
4. High-resolution spectroscopy as a probe for nuclear structure
0
Figure 4.3.: Exemplary hyperfine level scheme for J = 1, I = 3/2 and B < 0.
Figure adapted from [144].
4.4.1 Hyperfine structure
Hyperfine structure arises from coupling of the total angular momentum of the
atomic shell J with the nuclear spin I. The resulting angular momentum
F = I + J (4.16)
and its projection on the z-axis F are introduced. The magnetic field induced by
the electronic shell at the location of the nucleus H(0) interacts with the nuclear
magnetic dipole moment µI and leads to a splitting of spectral lines into multiplets.
Depending on the orientation of I and J, this splitting is given by
AC
∆Eµ = with C = F(F + 1)− I(I + 1)− J(J + 1), (4.17)2
where A = µI H(0)/I J is referred to as magnetic hyperfine coupling constant
or simply A-factor [144, 159]. Similarly, the electric field gradient φzz(0) =
〈∂2φ(0)/∂z2〉 interacts with the nuclear electric quadrupole moment, introducing
an energy shift of
B 3/2C(C + 1)− 2I(I + 1)J(J + 1)
∆EQ = , (4.18)4 I(2I − 1)J(2J − 1)
where B = eQsφzz(0) is the electric hyperfine coupling constant or B-factor
[144, 159]. Neglecting higher orders, the total hyperfine splitting is given by
∆EHFS = ∆Eµ + ∆EQ. An example energy level scheme is shown in Fig. 4.3, where
E0 corresponds to the unperturbed atomic level energy. As mentioned above, the
energy difference between two levels F and F′ is often in the order of GHz and
transitions between sublevels of an atomic state can be driven by microwave ra-
88
4.4. Probing nuclear structure by laser spectroscopy
diation. In order to use laser light, one has to consider an atomic transition from
a state |l〉 → |u〉, more specifically between the respective F and F′ levels. The
hyperfine pattern is given by the sum over
EF→F′ = E0 + ∆EHFS(Au,B ′u, F , I, Ju)− ∆EHFS(Al,Bl, F, I, Jl) (4.19)
for all allowed transitions F → F′, where the subscripts denote parameters of
the |l〉 and |u〉 states, respectively. The selection rule for hyperfine transitions is
∆F = 0,±1 with F = 0 9 F′ = 0 [144]. Line intensities follow the coupling of
angular momenta, which can be expressed as  2Ju F′ IIF→F′ ∝ (2F + 1)(2F′ + 1)  , (4.20)F J 1
where the curly bracket denotes the Wigner 6j-symbol [159, 160]. As a rule of
thumb, for transitions between high J-states, the components with ∆F = ∆J have
the highest intensity [144]. However, one should note that in RIS the intensities
predicted from Eq. 4.20 cannot always be reproduced for several reasons. This in-
cludes limited spectral overlap of the secondary laser for further excitation or ion-
ization with the excited state HFS, resulting in reduced intensities for transitions
addressing the outermost F′ states, as well as saturation effects which promote the
relative intensities of weak transitions, or simply depletion of the sample over the
duration of the measurement.
From Eqs. 4.17 and 4.18, it is obvious that HFS patterns contain a great deal of
information on the atomic nucleus, i.e. the spin I and, through the A and B
factors, the magnetic dipole and electric quadrupole moment, respectively. With
known total angular momenta of the involved atomic transitions, I can simply
be derived from the number of observed peaks. Although this method strictly
speaking only allows for an extraction of a lower limit for I, since peaks may be
obscured or unresolved, it usually gives conclusive results since fits only converge
well for a correct spin assignment. With this, A and B are the only parameters
describing the relative energetic positions of all observed resonances and can thus
be extracted with high precision. When fitting HFS patterns, it is convenient to
use the SATLAS python package [121], where Eq. 4.19 and Eq. 4.20, as well as
the constraints through selection rules, are implemented. The intensities are not
necessarily fixed to Eq. 4.20, however, this choice usually provides good starting
parameters. In Publication V fits were performed with the help of this tool, using
Voigt line profiles to account for residual Doppler broadening in the perpendic-
ular laser-atom interaction geometry (see Sec. 3.3). Deriving µI and Qs from the
A and B fit parameters requires knowledge of the magnetic field H(0) and the
electric field gradient φzz(0) at the location of the nucleus, which can be extracted
89
4. High-resolution spectroscopy as a probe for nuclear structure
from sophisticated theoretical calculations. In case nuclear moments are already
known for a reference isotope, A and B ratios can be used for the determination
of previously unknown moments with
A I
µI = A µI I,ref (4.21)ref ref
B
Qs = B Qs,ref (4.22)ref
[7]. Note that Eq. 4.21 is only accurate to a limited precision due to omission
of the so-called hyperfine anomaly. It arises from the Breit-Rosenthal-Crawford-
Schawlow correction eBR for the diffuse nuclear charge distribution, and the Bohr-
Weisskopf effect eBW for magnetism distribution over the nuclear sphere, result-
ing in a modification of the form A = Apoint(1 + eBR)(1 + eBW). The hyperfine
′
anomaly A∆A between two isotopes is specific to an atomic transition and can be
expressed as
AA gA
= I A A
′
AA′ gA′ (1 + ∆ ). (4.23)I
Usually it is in the order of 10−3 to 10−4 and requires very high precision to
be observed or conclusively analyzed [159, 161]. A table of measured hyperfine
anomalies is given in [161].
4.4.2 Isotope shift
Istopes are distinguished by the number of neutrons within the nucleus, which
is accompanied by a change of nuclear mass and volume. Both of these small
changes lead to a shift in atomic transition frequencies δν, which is in the order of
′ ′
the HFS. The effects of mass shift δνA,A and field (or volume) shift δνA,AM F between
two isotopes with mass numbers A and A′ are comprised under the term isotope
shift (IS), which is defined as
δνA,A
′
= νA − νA′ = δνA,A′ ′M + δνA,AF (4.24)
1
= K + Fδ〈r2〉A,A′A,A′ , (4.25)µ
′
where µA,A is the reduced mass and K and F the mass and field shift constant,
respectively [150, 159]. For isotopes exhibiting HFS, the transition frequency νA
is given by the center of gravity of all transitions F → F′. From a measurement
′ ′
of δνA,A for a series of isotopes, changes in mean square charge radii δ〈r2〉A,A
can be determined with Eq. 4.25. Obviously, this requires knowledge of the mass
and field shift constants. A discussion on the separation of mass and field shift
using systematic trends in neighboring elements, as well as the so-called King-plot
90
4.4. Probing nuclear structure by laser spectroscopy
analysis is subject of Publication V. Therefore, a detailed discussion is not given
here to avoid repetition.
91
4. High-resolution spectroscopy as a probe for nuclear structure
4.5 Publication IV: On the reliability of wavelength meters - Part 1: Conse-
quences for medium- to high-resolution laser spectroscopy
The following manuscript was published as a regular article in Applied Physics B:
Lasers and Optics 126, 85 (2020) DOI 10.1007/s00340-020-07425-4. The presented
work focuses on the characterization of the performance of wavelength meters,
specifically in applications of high-resolution laser spectroscopy. Shortcomings in
long-term stability of wavelength meters are a known issue and can be linked to
temperature or pressure fluctuations in the laboratory. Usually such drifts remain
within the specified accuracy of the device, however, in relative frequency mea-
surements, where one aims for higher precision this becomes a limiting factor.
This limitation was already noticed in the isotope shift measurements in Publi-
cation I, where the uncertainty in δνA,A
′
is ultimately dominated by the absolute
accuracy of the wavelength meter, despite the data being of higher quality. Conse-
quently, prior to data taking for Publication V, the laser setup was extended by a
Rb SAS setup as absolute wavelength reference. In combination with relative fre-
quency measurement using a SFPI, the setup allowed for frequent calibration and
characterization of the used WSU-30 wavelength meter (see Sec: 2.2). The author
presented these results on the EMIS conference in 2018 at CERN, where other labo-
ratories reported similar issues. Finally, the submission of a joint publication with
the laboratories at the University of Jyväskylä, KU Leuven, GSI Darmstadt and
the University of Mainz was concluded and resulted in the following manuscript.
Note that this article features a second part ”On the reliability of wavelength meters
– Part 2: Frequency-comb based characterization revealing their relative limitations and
offering opportunities for more accurate absolute wavelength determinations”, submitted
by Kristian König et al. to the same journal. This connected work mainly com-
prises the test of wavelength meters using frequency combs as reference and thus
also allows for a characterization of their absolute accuracy, whereas the work at
hand is mainly focused on the more economic alternative of SFPIs and compact
atomic spectroscopic setups.
Author contribution
The following article has five main authors: M.V., K.D. (KU Leuven), S.G. (Univ. of
Jyväskylä), K.K. (GSI Darmstadt) and D.S. (Mainz Univ.). Each of them contributed
the major part of the measurements performed at the respective institute and pre-
pared a part of the manuscript describing the corresponding setup, measurement
protocol and data evaluation. The final manuscript was then compiled and struc-
tured by the first author, M.V. Specifically for the part of Mainz University, D.S.
installed the SAS setup and data acquisition and performed the wavelength meter
characterization, with support from T.K. Similarly, the corresponding sections and
plots (Fig. 3 and Fig. 8) for the manuscript draft were prepared by D.S.
92
Applied Physics B (2020) 126:85 
https://doi.org/10.1007/s00340-020-07425-4
On the performance of wavelength meters: Part 1—consequences 
for medium‑to‑high‑resolution laser spectroscopy
M. Verlinde1  · K. Dockx1  · S. Geldhof2  · K. König3 · D. Studer4 · T. E. Cocolios1  · R. P. de Groote2 · R. Ferrer1 ·
Yu. Kudryavtsev1 · T. Kieck4  · I. Moore2 · W. Nörtershäuser3  · S. Raeder5,6  · P. Van den Bergh1 · P. Van Duppen1  ·
K. Wendt4
Received: 30 August 2019 / Accepted: 20 March 2020 / Published online: 21 April 2020 
© Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract
Present-day laser-spectroscopy experiments increasingly rely on modern commercial devices to monitor, stabilize, and scan 
the wavelength of their probe laser. Recently, new techniques are capable of achieving unprecedented levels of precision on 
atomic and nuclear observables, pushing these devices to their performance limits. Considering the fact that these observables 
themselves are deduced from the frequency difference between specific atomic resonances, in the order of MHz–GHz, the 
uncertainty on the output of the device measuring the wavelength is often directly related to the final systematic uncertainty 
on the experimental results. Owing to its importance, the performance of several commercial wavelength meters was com-
pared against different reference sources, including a Scanning Fabry–Pérot Interferometer (SFPI) and a frequency comb. 
Reproducible, wavelength- and device-dependent disagreements are observed, potentially skewing the experimental output at 
high precision. In this paper, a practical and relatively inexpensive wavelength meter characterization procedure is presented 
and validated. This method is capable of improving the precision on wavelength differences considerably depending on the 
device, while together with a second investigation that is published separately, (König et al., in Appl Phys B, 2020), it offers 
a full description of the expected wavelength meter performance for users.
1 Introduction variety of optical radiation sources ranging from deep UV 
to infrared in relatively short time scales (> 1 kHz), ideal 
To run modern laser-spectroscopy experiments, the probe for fast correction feedback loops. The performance of these 
laser requires means to monitor, stabilize, and/or scan the wavelength meters has already been the topic of several stud-
wavelength during operation. These tasks are often realized ies, mainly focused on their performance stability (see, e.g., 
using state-of-the-art commercial wavelength meters, which [2–6]).
are capable of performing a wavelength determination for a A specific field of use of these devices is the study of 
exotic radionuclides at radioactive ion beams (RIB) facili-
ties via hyperfine laser spectroscopy. This technique pro-
* M. Verlinde vides information on the electromagnetic structure of the 
Matthias.Verlinde@kuleuven.be nucleus by offering a nuclear-model independent window 
1 to the nuclear spin, nuclear moments, and differences in  KU Leuven, Instituut voor Kern-en Stralingsfysica, 
Celestijnenlaan 200D, 3001 Leuven, Belgium mean-square charge radii, for a range of isotopes [7, 8]. 
2 The hyperfine structure, carrying the nuclear information  Department of Physics, University of Jyväskylä, 
40014 Jyväskylä, Finland imprinted in the form of frequency differences between 
3 specific closely spaced resonances in the atomic spectrum  Institut für Kernphysik, TU Darmstadt, 64289 Darmstadt, 
Germany (MHz–GHz energy scale), can be uncovered with varying 
4 degrees of precision (defined here via the full-width-at-half- Institut für Physik, Johannes Gutenberg-Universität, 
55099 Mainz, Germany maximum (FWHM), ΔfFWHM , of the obtained resonance). 
5 As the production rate of nuclei decreases as one pushes  Helmholtz-Institut Mainz, 55128 Mainz, Germany to more exotic species, resonant ionization spectroscopy 
6 GSI Helmholtzzentrum für Schwerionenforschung GmbH, (RIS), whereby the number of ions produced as a function 
64291 Darmstadt, Germany
Vol.:(012 3456789)
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of laser wavelength is monitored, is the technique of choice differences,  =  −  , in a range of ∼ 10 GHz is inves-
due to the high efficiency of counting ions or detecting the tigated with the aid of a Scanning Fabry–Pérot Interfer-
radioactive decay signal. A number of RIS techniques exist, ometer (SFPI), a frequency comb, and an ionic resonance. 
adapted to the environment in which the atomic species of Section 3 contains a description of the temporal stability of 
interest are probed, which eventually defines the achievable these devices and different solutions on how to improve it. 
precision [9]. These techniques are, for example: RIS in a Several measurement methods are combined to give a com-
hot-cavity source or in a gas cell ( 3 GHz < ΔfFWHM < 10 prehensive overview for a number of devices over a large 
GHz [10, 11]), RIS in a perpendicular geometry, which can spectral range. In Sect. 4, a validation of the results from 
be realized in a gas jet or within the PI-LIST ion source Sect. 2 is done by performing laser spectroscopy on 63,65Cu 
( 0.1 GHz < ΔfFWHM < 1 GHz [11, 12]) and with collinear isotopes in an Atomic-Beam Unit (ABU) and in a gas-jet 
techniques on fast ion/atom beams ( ΔfFWHM ≈ natural environment, confirming the necessity of a proper wave-
linewidth [13]). To reduce the linewidth of the hyperfine length meter characterization.
resonances, and, hence, to provide higher precision data on 
the nuclear observables, the latter two techniques are push-
ing the limits on accurate frequency determination using 2  Determination of 1˛ˇ(WSX)
commercial wavelength meters for monitoring, stabilizing, 
and potentially scanning the probe laser [6].
As the final hyperfine observables of interest are directly 2.1  WSX–SFPI comparison
related to the ill-defined uncertainty of the readout of this 
wavelength meter, it is important to understand its perfor- The first series of tests were performed at the In-Gas Laser 
mance in determining frequency differences  =  −  of and Ionization Spectroscopy (IGLIS) laboratory at KU Leu-
the order ∼ MHz/GHz over the complete operational spectral ven, Belgium. This facility has been built to carry out a full 
range. Additionally, as the isotopes of interest are becoming characterization, validation, and optimization of the in-gas-
increasingly exotic and, thus, only produced in minute quan- jet spectroscopy for its later implementation in a number 
tities, the performance stability over longer periods of time, of online accelerator facilities (S3 LEB, MARA LEB, and 
required to obtain sufficient statistics, is crucial. Moreover, GSI), to study, amongst others, the heavy and super heavy 
RIS most often relies on the measurement of one isotope at elements [11]. In the in-gas-jet method, the atoms of inter-
a time, so that the accurate determination of isotope shifts est are embedded in a low-density and low-temperature gas 
strongly depends on the comparability of the data and, thus, jet environment, minimizing the spectral pressure and tem-
the reproducibility of the frequency determination. In this perature broadening mechanisms, while still offering high 
paper, we report on a reliability study performed in differ- selectivity, short extraction time (< 0.5 s), high efficiency, 
ent laboratories using different wavelength ranges, different and an independence to the chemical nature of the species of 
wavelength meters, and different measuring protocols with interest [14]. To probe the hyperfine structure of the atoms 
the goal to provide an easy, cost-friendly, widely applicable embedded in the gas jet, high-repetition rate, high-power 
and potentially performance-increasing, wavelength meter dye lasers are available, supported by a pulsed dye amplifier 
characterization procedure. The wavelength meters of inter- system seeded with a cw single-mode diode laser for high-
est in this paper and [1] belong to the WS series from HighF- resolution laser operation [15].
inesse GmbH. These devices consist of beam optics coupling A second set of characterization tests were performed in 
the laser light, entering the device via an optical fiber, into the RISIKO laboratory at Johannes Gutenberg-University 
Fizeau interferometers. The induced interference pattern is (JGU) Mainz, Germany. This facility is in use for studies 
imaged on a CCD photodiode array. The obtained spectrum on beams of stable or long-lived radioactive ions, in com-
is fitted and compared to the calibration pattern resulting in bination with related development on hot cavity laser ion 
a wavelength determination. Here, we will concentrate on sources, dedicated laser systems, and spectroscopic tech-
the accuracy of relative frequency measurements, while in a niques. The laser ion source here is based on high-repeti-
second study, the focus will lie on the accuracy of absolute tion rate pulsed Ti:sapphire lasers specifically developed 
frequency determinations [1]. for this application [16]. While these lasers provide high 
To determine the precision on  , Δ , for different output power required for efficient ionization, a comple-
wavelength meters in different wavelength ranges, the read- mentary cw laser system provides the stability and narrow 
out of these devices was compared to another reference. To linewidth necessary for ultra-trace analysis applications [17, 
summarize the tests, the paper is structured as follows. In 18] and high-resolution spectroscopy [19–21]. The benefits
Sect. 2, the capabilities of several wavelength meters (WS of both systems can be combined using a cw external cavity
series HighFinesse GmbH, when no specific type is specified diode laser (ECDL) as master laser for seeding of a pulsed
the notation WSX is used) to accurately measure frequency injection-locked Ti:sapphire laser (slave). This combination
1 3
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provides both, high-power pulsed laser radiation and a nar-
row spectral linewidth of ≈ 20 MHz with appropriate stabil-
ity [22, 23], well suited for sensitive RIS studies.
2.1.1  Measurement protocol
The tests at the IGLIS laboratory were done by studying, 
simultaneously, the readout of a wavelength meter (WS7-60, 
acquired in 2012), which has a quoted accuracy of 60 MHz (a)
(according to the 3 criterion) in the range 420–1100 nm, 
and a Scanning Fabry–Pérot Interferometer (SFPI, Top-
tica FPI-100-0500-1) with a Free Spectral Range (FSR) 
of 4 GHz. A schematic overview of the setup is given in 
Fig. 1a. The IGLIS control software performs a stepwise 
frequency scan of a diode laser (TA:pro, TOPTICA Photon-
ics AG) by applying a DC voltage to the DC 110 diode laser 
driver, a component of the Diode Laser Driver Electronics 
(Sys DC 110, TOPTICA Photonics AG), via a pulse gen-
erator (PicoScope 5000a, Pico Technology). This voltage 
is amplified in the DC110 diode laser driver and applied (b)
to a piezo actuator in the diode laser for accurate control 
of the laser wavelength. The TA:pro laser, lasing around 
654.9 nm, is stabilized relative to the WS7-60’s readout of 
either a 770.108796 nm diode reference laser (DL pro 780, 
TOPTICA Photonics AG), frequency locked to a potassium 
cell (CoSy, TEM Messtechnik GmbH), or a 632.991026 nm 
frequency-stabilized HeNe laser (Model 32734, Research 
Electro-Optics, Inc.) during a laser scan, see [15]. For the 
wavelength determination via the SFPI, both TA:pro and 
HeNe laser beams are overlapped in the SFPI. In this way, 
both wavelength measuring devices contain a reference 
source for calibration and stabilization purposes. A finesse, (c)
F ≈ 300 , is obtained in the SFPI for both TA:pro and HeNe 
laser light. To provide optimal working conditions for the Fig. 1  Experimental techniques used in this work. (a) Simplified 
SFPI, a scanning range of its piezo actuator is chosen, such schematic layout of a general setup used to compare the output of 
that a previously optimized number of fringes ( ≈ 10 ) of an SFPI with that of a specific wavelength meter. The probe laser is 
both lasers is visible in one single voltage ramp. At each measured by a specific WSX wavelength meter together with a ref-
wavelength step of the TA:pro, one or more traces of the erence laser. The wavelength scan of the probe laser is controlled externally by a feedback loop, based on the readout of the WSX. One 
SFPI’s diode sensor are recorded. Off-line, all data are ana- reference laser is also overlapped with the probe laser and directed 
lyzed with a Python-based algorithm. This program uses to the SFPI. For details, see text. (b) Simplified schematic layout of 
peak finder and peak tracker algorithms to identify HeNe the continuous wave (cw) laser setup at TU Darmstadt. The Matisse 
and TA:pro fringes, fitting each with Gaussian profiles. The 2 TS laser frequency, locked to both reference cavity and FC1500 fre-quency comb, is monitored during a wavelength scan by the WS7-60 
fringe positions of the HeNe laser are used as a ruler to wavelength meters and by the comb itself via a Beat Detection Unit 
accurately transform the time positions of each fringe into (BDU). For details, see text. (c) Schematic view of the light collec-
a frequency value via the known FSR. After this procedure, tion region and laser systems of the collinear beamline at IGISOL for 
the average position of the TA:pro fringes of each trace in the measurements on 89Y. The ion beam enters the beamline from the right side. The laser interaction region is monitored by a seg-
the frequency domain is saved together with their stand- mented Photo-Multiplier Tube (PMT) for resonance fluorescence 
ard deviation. In case higher precision is required, multiple detection
traces can be extracted at each wavelength, providing a final 
value as the weighted average with corresponding uncer-
tainty, taking into account the reduced 2. 2003) and a home-made SFPI. The WSU-30(UV) wavelength 
At the RISIKO laboratory, a similar comparison was per- meter has an accuracy of 30 MHz in the range 248–1180 nm. 
formed between a wavelength meter (WSU-30, acquired in The scanning ECDL consists of a custom-built mount with 
1 3
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a piezo-actuated grating for external feedback, and a Peltier In Eq. (1), WSX represents the frequency readout at a certain 
element for temperature stabilization, supplied by commer- moment during a laser scan, while 0,WSX represents a refer-
cial laser driver electronics (LDC202, Thorlabs Inc.). In total, ence point within the scan.
two different laser diodes were used in this setup (RWE-920, 
RWE-980, Eagleyard Photonics GmbH). Fast stabilization and 2.1.2  Results
scanning operation are performed with a quadrature interfer-
ometer, (iScan, TEM Messtechnik GmbH). The long-term and The procedure described for the IGLIS laboratory, using the 
accurate stabilization of the ECDL set frequency is obtained setup in Fig. 1a, was applied to a number of scan ranges. 
from an SFPI via a fringe off-set locking (FOL) technique The results for ΔSFPI−WS7() , defined in Eq.  (1), in the 
[24]. More information on the laser setup can be found in [25]. 654.9570–654.9969 nm range (spanning roughly 28 GHz 
Here, the light from the probe ECDL and from a stabilized in total) are shown in Fig. 2. These results show that the 
HeNe laser (SL-03, SIOS Messtechnik GmbH) is overlapped WS7-60 and SFPI disagree reproducibly on the step size 
in a custom-built confocal SFPI, with a piezo-actuated mirror. taken by the TA:pro laser with a maximum of 8 MHz, with 
The SFPI has a free spectral range of FSR = 298.721 MHz an additional degree of periodicity. To map this periodic-
and a Finesse of F ≈ 400 . Depending on the wavelength, the ity, a triangular wave form was fitted to the data of Fig. 2 
piezo ramp covers 2–3 fringes. The transmission of the probe without any prior knowledge on the underlying mechanism:
ECDL and the HeNe fringes are separated by a dichroic mirror � � ��
and detected with separate photodiodes. The time difference 4A T 2( + S) 1Δtriangle() = ( + S) − +
of the first ECDL fringe after the start of the voltage ramp is T 2 T 2 (2)
measured with respect to the fringe from the reference HeNe ⌊ 2(+S) 1(−1) + ⌋⋅ T 2 .
laser via a counter card and the frequency change is evaluated 
using an Arduino MCU, via the precisely known FSR and This function of the frequency  has three parameters; the 
HeNe wavelengths. To ensure proper single-mode operation amplitude, A, period, T and shift, S, of the triangular wave. 
of the ECDL, the time between the first and the second fringe The fitting procedure reveals a peak-to-peak amplitude 
is in addition evaluated. Values of the mean relative frequency AWS7 = 8.2(2) MHz and a period TWS7 = 3.871(10) GHz 655 655
and frequency jitter within a time of ≈ 50 ms (matched to the for Eq. (2). The period matches closely to the FSR of the 
data acquisition cycle of the wavelength meter) are sent to most precise interferometer of the WS7-60 wavelength meter 
a LabVIEW interface, used for controlling, monitoring, and ( ≈ 4 GHz). To understand the behavior of the WS7-60 in 
recording. An absolute frequency measurement is provided more detail, the wavelength range 654.973–654.985 nm was 
by the WSU-30, where both the probe ECDL and the stable scanned with higher resolution (≈ 10 traces per wavelength 
HeNe output are measured through a multichannel switch step were combined). The results of this measurement are 
(HighFinesse GmbH). The absolute reference and calibration shown in yellow in Fig. 2 with a magnified region shown in 
source for the wavelength meter is an additional ECDL (DL Sect. 4, Fig. 10. The finer details observed in Fig. 10 show 
pro 780, Toptica Photonics AG), coupled to a compact rubid-
ium saturated absorption spectroscopy setup (SAS) (CoSy 4.0, 
TEM Messtechnik GmbH). Using a dither-lock stabilization 
(LaseLock 3.0, TEM Messtechnik GmbH), it is locked to the 
F = 2 → F = 3 transition in the D2 line of 87Rb at 780.24602 
nm. A schematic overview of this setup is shown in Fig. 1a.
To compare the relative performance of both SFPI and 
wavelength meter during a frequency scan, the magnitude of 
each laser step with respect to the starting point of the scan is 
monitored for both devices. Finally, the difference in the step 
size as measured by the SFPI and wavelength meter, respec-
tively, is subtracted to obtain a relative result. Mathematically, 
the final output ΔSFPI−WSX() for a random wavelength meter 
WSX, reads as follows:
ΔSFPI−WSX() = Δ( SFPI
() − ΔWS)X
()
( ) (1)
= SFPI − 0,SFPI − WSX − 0,WSX .
Fig. 2  Results for ΔSFPI−WS7() , defined in Eq.  (1), recorded at the 
IGLIS laboratory. The results presented here combine multiple scans 
taken at different times to prove the reproducibility of the data. For 
details, see text. c represents the speed of light in m/s
1 3
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that the underlying mechanism, causing the disagreement middle and lower graph, respectively ( 0,SFPI = 0 ). In both 
between the WS7-60 and SFPI, is of a more complex nature measurements, a calibration of the wavelength meter was 
than a simple triangular waveform. However, the general performed after each data point, to exclude any time-depend-
features of the disagreement between both devices are clear. ent drifts of the wavelength meter performance, as discussed 
The data of Fig. 2 present multiple measurements confirm- in the next section. The rather large scatter in the scan at 
ing the reproducibility of the results. Additionally, the struc- 905 nm arises from stability issues of the probe ECDL, 
ture obtained for Fig. 2 is independent of the calibration which may be caused by internal feedback in the laser diode, 
laser. The specific calibration tool only causes an absolute owing to an inferior anti-reflection coating of the front win-
offset, not visible in these measurements. dow. The different colors represent measurements performed 
The comparison between the WSU-30 wavelength meter on different days over the same frequency range and under-
and the home-made SFPI at the RISIKO laboratory is pre- line the reproducibility of the periodic pattern. Minor shifts 
sented in Fig. 3 (middle and bottom panel). The data in Fig. 3 may be caused by drifts of the HeNe laser (i.e., the SFPI ref-
show also a periodic deviation of the WSU-30 readout with erence), but still lie within the specified stability. Fitting all 
respect to the SFPI, calculated according to Eq. (1), with datapoints of one frequency range with the triangular pattern 
0,WSU30 = c∕905.795 nm and 0,WSU30 = c∕938.853 nm for from Eq. (2) yields a period of TWSU30 = 1.923(14) GHz and 905
TWSU30 = 1.912(12) GHz, close to the FSR of the final WSU-
938
30 interferometer of ≈ 2 GHz. The peak-to-peak deviation 
is AWSU30 = 5.1(3) MHz and AWSU30 = 5.3(2) MHz, respec-
905 938
tively. To confirm both the IGLIS and RISIKO data acquisi-
tion and, in general, the SFPI measurement procedure, the 
WSU-30 wavelength meter was remeasured at the IGLIS 
laboratory in the wavelength range around 654.980 nm. The 
results are shown in Fig. 3 (top panel) and they confirm both 
the ≈ 2 GHz period for this WSU-30 and the smaller ampli-
tude compared to the WS7-60 ( AWSU30 ≈ 5 MHz). While 
655
the ’global’ periodicity of the signal is easily distinguished, 
extra structures are clearly visible. The obtained results for 
ΔSFPI−WSU30 , also, clearly show both a wavelength range 
and device-specific dependence of the wavelength meter 
response, as was confirmed in the next measurements.
2.2  WSX‑frequency comb comparison
A third series of wavelength meter tests was performed at 
the COllinear Apparatus for Laser spectroscopy and Applied 
physics (COALA) at TU Darmstadt, Germany. This labora-
tory was originally designed for accurate high-voltage evalu-
ations based on Collinear Laser Spectroscopy (CLS) opera-
tion. Nowadays, precise measurements of absolute transition 
frequencies and isotope shifts in ions are also performed to 
Fig. 3  Results for ΔSFPI−WSU30 , measured for three different laser benchmark atomic theory and to support on-line investiga-
wavelength ranges. The upper panel at 654.980 nm was obtained at tions of short-lived isotopes. For this purpose, a cw laser 
the IGLIS laboratory. Each data point of the upper panel is taken 
as the weighted average with corresponding uncertainty of the system based on Ti:sapphire lasers combined with Wavetrain 
results from 10 SFPI traces, obtained via Eq.  (1), at a distinct fre- frequency doublers is available alongside a GPS-referenced 
quency. Around ten consistent measurements were taken, from frequency comb to determine and stabilize its frequency [1, 
which three are shown in the upper panel. The other panels, scanned 26, 27].
at 905.795  nm and 938.853  nm, respectively, were measured at the 
RISIKO laboratory in Mainz. The results are obtained with a similar 
analysis to the one in the IGLIS laboratory, and the final data points 2.2.1  Measurement protocol
represent the average and standard deviation of all SFPI results taken 
within one wavelength bin. 11 and 8 consistent measurements were At the COALA laboratory, the output of both the IGLIS 
taken for the 905  nm and 938  nm cases, respectively, from which 
again three full range results are shown in both panels. All three WS7-60 wavelength meter and the in-house WS7-60-IR 
measurements for Δ  show the same period in their structure (630–1750 nm, acquired in 2007) device was compared to SFPI−WSU30
the frequency comb (FC1500-250-WG, Menlo Systems) 
1 3
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and the accuracy of the wavelength meter’s absolute readout 
could be tested. The setup is shown in Fig. 1b. A Ti:sapphire 
laser (Matisse 2 TS, Sirah) is stabilized to its reference cav-
ity to avoid short-term frequency fluctuations. Additionally, 
a slower stabilization feedback loop for long-term stabiliza-
tion is realized using the frequency comb. To achieve this, 
the beat frequency between the nearest comb mode and the 
Ti:sapphire beam is measured in a fiber-coupled beat detec-
tion unit (BDU) and digitally communicated to the Matisse 
commander software, which adapts the length of the refer-
ence cavity to keep the beat frequency constant. In this way, 
an accurate and stable absolute reference is available with a 
precision of better than 100 kHz, limited by the linewidth of 
the Matisse. For the measurements performed here, the laser 
is scanned across a similar frequency range as in the IGLIS/
RISIKO measurements, locked to the frequency comb at 
every wavelength step. The customized data acquisition sys-
tem records the readout from both the frequency comb and 
the two WS7-60 wavelength meters. With this setup, both 
relative and absolute performance of the WS7-60 can be 
mapped across a large wavelength range.
As the combination of the frequency comb and the Mat-
isse laser at the COALA laboratory offers a reference with a 
well-known frequency, one can go a step further than Eq. (1) Fig. 4  Benchmarking the performance of two different WS7-60 
and compare directly the frequency output of both devices: devices, in the vicinity of 805.56  nm, 856.45  nm, and 795.56  nm against a frequency-comb measurement of the laser frequency result-
ing in Δ
Δ Comb−WS7
()
Comb−WSX() = Comb − WSX. (3)
In this case, the wavelength meters are not only tested in 
their ability to determine   but also in measuring   itself. an additional device-dependent effect on the results of  
ΔComb−WS7() . Finally, it should be mentioned that the struc-
ture in the results of Fig. 4 also does not depend on the spe-
2.2.2  Results cific calibration point of the laser. Only the absolute offset 
to the real wavelength determined with the frequency comb 
The results for the comparison between the WS7-60 and might change, which is strongly wavelength-dependent 
WS7-60-IR wavelength meters and the FC-1500 frequency itself. This, as well as, a full description of the frequency-
comb, performed at the COALA laboratory, are shown comb-based specification of various high-precision wave-
in Fig. 4. They are obtained from a scan of the Matisse length meters is presented in [1].
laser across ≈ 16GHz around 805.56 nm and 795.56 nm, 
and across ≈ 8 GHz around 856.45 nm, respectively. The 2.3  WSX‑ionic resonance comparison
wavelength meters are calibrated at 812.77 nm using the 
frequency-comb stabilized Matisse, for the measurements A final series of measurements was done at the IGISOL 
at 805 nm and 856 nm and at 632.99 nm with a frequency- facility of the Accelerator Laboratory in the University of 
stabilized HeNe laser (SIOS SL 03, Meßtechnik GmbH) for Jyväskylä, Finland. This facility uses the ion guide tech-
the measurement at 795.56 nm. To identify device-depend- nique for the production and study of low-energy beams of 
ent effects, a WS7-60-IR was included in the measurements. exotic radioactive nuclei [28]. Fundamental nuclear ground 
From Fig. 4, it follows that similar periodic patterns arise and isomeric state properties and mass are probed using a 
at different wavelength ranges, with similar peak-to-peak variety of ion (and atom) manipulation devices including ion 
discrepancies for both wavelength meters. The structure is traps, radiofrequency (rf) cooler-bunchers, as well as meth-
found to be highly reproducible over months in the previous ods of optical spectroscopy. Over the years, an expanding 
measurements performed at COALA [1]. Inspecting both program of optical spectroscopy at the facility has resulted 
Figs. 2 and 4 indicates a wavelength dependence of the dis- in a variety of improvements to methods including collinear 
crepancy between the reference and the WS7-60. Addition- laser spectroscopy as well as resonance ionization spectros-
ally, both devices do not react in the same way, indicating copy. The former technique is applied for high-resolution 
1 3
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spectroscopy on fast ionic and atomic beams, routinely line at IGISOL, are depicted in Fig. 5. A triangular-wave 
providing measurements of optical frequency splittings to pattern applied to the data, following Eq. (2), resulted in 
1–10 MHz precision. For these applications, a high-resolu- a peak-to-peak amplitude of AWSU10 = 1.3(3)MHz , which 
727
tion laser spectroscopy setup based on a Matisse 2 TS laser is almost an order of magnitude smaller than for the WS7-
and a Wavetrain frequency doubler is available. Additional 60. The period TWSU10 = 1.99(12)GHz , is consistent with 
727
infrastructure includes an injection-locked Ti:sapphire laser, the ≈ 2 GHz FSR of the most precise interferometer in the 
seeded by the Matisse cw light, and several wavelength ref- wavelength meter.
erence options.
2.4  Summary
2.3.1  Measurement protocol
In summary, the results indicate that each wavelength meter 
At the IGISOL facility beam line for collinear laser spec- has its characteristic Δ that is unique for every instru-
troscopy, a wavelength meter (WSU-10, acquired in 2017), ment separately. It can be extracted from ΔSFPI−WSX() , 
with a specified 10 MHz accuracy, was investigated. A ΔComb−WSX() and ΔCentroid() , depends on the wavelength 
schematic of the laser system and light collection region of range of interest and is characterized by a periodic structure 
the collinear beam line can be seen in Fig. 1c. More details which follows the FSR of the most precise interferometer in 
on the beamline and data acquisition system can be found the device. To obtain a value for Δ , one should perform 
in [29]. Stable 89 Y, produced by a spark discharge source, a characterization procedure as presented here and further 
was measured on the 363.4157 nm transition from the ionic elaborated in Sect. 4, or otherwise remain with the conserva-
ground state using the Matisse TS laser, pumped by a cw fre- tive absolute accuracy mentioned by the manufacturer. To 
quency-doubled YAG-laser (Millenia eV, Spectra Physics) assess the potential systematic uncertainty to be expected, 
and stabilized to a fixed setpoint in the wavelength meter. our data are summarized in  Table 1, which contains the 
Resonant interaction between the anti-collinear laser beam AWSX alongside the outer boundaries of the Δ
 SFPI−WSX
() , 
and ions is measured by monitoring the optical deexcitation ΔComb−WSX() and ΔCentroid() distributions covering 95% or 
of the excited state with a segmented Photo Multiplier Tube 99.7% of all measurements.
(PMT). The hyperfine structure can be mapped by tuning the 
acceleration voltage of the ion beam. To probe systematic 
discrepancies between the WSU-10 and the centroid of the 3  Temporal stability of ˛(WSX)
363.4157 nm transition used as a reference, the stabilization 
setpoint was changed in steps of 600 MHz, and for each Following a comparison of the performance of different 
setpoint, a spectrum with sufficient statistics (> 1000 counts wavelength meters in determining  in a range of ∼ 10 GHz 
on the resonance peak) was collected. with that of an SFPI and a frequency comb, its stability over 
For the IGISOL wavelength meter tests, the centroid of time is mapped. A well-known feature of these wavelength 
89 Y presents an absolute reference while it is assumed that 
the voltage scan is identical for every measurement. This 
results in:
( ) 
ΔCentroid() = VCentroid, − VCentroid, . (4)0 V
Here, VCentroid, is the voltage at which the centroid of the 
transition is obtained for a random measurement at fixed 
setpoint  and VCentroid,  is the same for a reference measure-0
ment. ∕V  converts the acceleration voltage difference 
to a frequency difference via the Doppler shift. In this way, 
similar results are obtained as for Eqs. (1) and (3).
2.3.2  Results
The resulting 89Y hyperfine spectrum consists of an unre-
solved doublet, which was fitted by fixing the hyperfine 
89
parameter of the upper state to the literature value of Fig. 5  Fitted centroid of the  Y hyperfine structure at changing laser stabilization setpoints using the WSU-10 wavelength meter (blue). 
32.6(1) MHz [30]. The fitted centroid frequencies of the The resulting data have been fitted using a triangular-wave function 
363.4157 nm transition, obtained from the collinear beam according to Eq. (2) (red solid line)
1 3
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Table 1  Peak-to-peak amplitude Wavelength meter Wavelength probe (nm) WSX Q  (MHz) Q  (MHz)
WSX
A and outer boundaries of A (MHz) 95 99.7
 [±5 − 20GHz]
the ΔSFPI−WSX() , ΔComb−WSX() 
and ΔCentroid() distributions, WS7-60 655.0 8.2(2) 11.7 18.0
covering 95% or 99.7% of all 
measurements performed,  WS7-60 856.5 ≈ 3.5 5.0 5.9Q95
and Q WS7-60 805.6 ≈ 5 5.1 6.199.7
WS7-60-IR 856.5 ≈ 4 5.7 6.2
WS7-60-IR 805.6 ≈ 3.5 4.7 5.8
WS7-60-IR 795.6 ≈ 5 4.5 5.4
WSU-30 655.0 ≈ 5 6.4 7.3
WSU-30 905.8 5.1(3) 8.8 13.7
WSU-30 938.9 5.3(2) 7.2 11.6
WSU-10 726.8 1.3(3) 7.2 9.2
When no explicit correction to the wavelength meter output is applied, see Sect. 4, Q95 and Q99.7 should be 
taken into account to determine the systematic uncertainty on a determination of Δ in a specific wave-
length range. The Q values are not only influenced by the wavelength meter but also by the uncertainty of 
the analysis procedure. The values of WSXA  are approximated, in case the discrepancy of the wavelength 

meter shows a significant deviation from Eq. (2)
meters is their tendency to drift over longer periods of time, side-of-fringe locking method. In this manner, the absolute 
strongly correlated to external temperature and/or pressure frequency stability is now directly related to the frequency 
instabilities. The magnitude of these drifts is most often in stability of the HeNe laser, eliminating the need for the 
the range of a few MHz/hour dependent on the magnitude of wavelength meter. Collinear laser spectroscopy on stable 
the time derivative of the external conditions. During longer even–even ytterbium isotopes was performed using either 
measurement times, these drifts will have a profound impact the wavelength meter or the transfer cavity for frequency 
on the results obtained. Two options exist to compensate stabilization to verify proper functioning of the transfer 
for the time-dependent readout of the wavelength. First of cavity. The scatter on the fitted centroids for each isotope, 
all, one can correct for the drift of the scanning laser by measured in the course of a few hours, was reduced when 
monitoring the wavelength of an externally locked reference stabilized to the transfer cavity compared to the wavelength 
laser at the same time, which will be discussed in Sect. 3.1. meter, confirming the wavelength meter as a possible source 
Second, a periodical calibration of the wavelength meter can of systematic uncertainty, see Fig. 6.
be included in the control software of the laser, see Sect. 3.2.
To exemplify the importance of a well-controlled external 3.1  Drift correction
environment on the wavelength meter’s long-term perfor-
mance, the Matisse 2 TS laser at IGISOL was stabilized The most general correction to drifts in the wavelength 
to a Rb hyperfine peak using a side-of-fringe stabilization meter output, in the presence of a reference laser, can be 
method implemented in LabVIEW while being monitored written as follows:
by the WSU-10. Any wavelength meter drifts are then trans-
�
ferred to the device’s readout. The largest variation seen is  =  + ( ,  , t)( −  ).corr,WSX set set ref ref ref,WSX (5)
approximately 4 MHz over 24 h. This stability is in part 
due to the stable laboratory environment, with laboratory set is the originally defined setpoint at which the laser should 
temperature control and minimal disturbance. To account for be stabilized, ref represents the absolute frequency of the 
larger drifts in less stable conditions, they can be corrected reference laser, and ref,WSX is the reference’s wavelength 
for by (auto-)calibrating the device to a frequency-stabilized meter readout. The parameter (set, ref, t) takes into account 
HeNe laser at certain times suitable to the ongoing meas- any kind of frequency and/or time-dependent differences 
urements, see Sect. 3.2. Because the high-resolution work between the drift of the reference laser and the probe laser. 
at the collinear beam line of IGISOL is performed with a As outlined in [15], the IGLIS control software stabilizes the 
′
fixed laser frequency setpoint, the Matisse transfer cavity can scanning TA:pro’s frequency at a wavelength   in the set,WS7
be used to bypass the wavelength meter in general. In this WS7-60, with (set, ref, t) = 1 . Doing so, wavelength meter-
case, a digital plugin of the Matisse control software uses the dependent drifts in time, which can be as large as 5 MHz/h 
intensity of the HeNe (HRS015B, Thorlabs Inc.) measured for the WS7-60 of interest, are corrected. To identify higher 
behind the reference cell with a photodiode (PDA36A-EC, order (wavelength and/or time-dependent) corrections to � −
′ set,WS7 set
Thorlabs Inc.) to stabilize the reference cell length with the   in the form of (set,WS7 set, ref, t) =  , three inde-ref−ref,WS7
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time (this would be the case (set, ref, t) = 0 ). For the 
TA:pro at 654.98 nm, (set, ref, t) = 1 is sufficiently accu-
rate to keep the laser stable to within 1 MHz. This 1 MHz 
limit was chosen arbitrarily as it is similar to other uncertain-
ties contributing to the laser stability, as will be discussed in 
Sect.  4. For both infrared lasers, the inclusion of the 
(set, ref) factor is required to ensure a similar stability over
this time domain. Through these measurements, it can be
concluded that a correction to the WS7-60 output with
(set, ref, t) = 1 is sufficient up to scan times of ≈ 30 min.
For longer scans, either the (set, ref) factor has to be deter-
mined and applied, or a recalibration is required with a rep-
etition rate higher than once every ≈ 30 min, as will be dis-
cussed next.
Scatter of the 168  , 170  , 172  , 174  and 176 Yb centroids, 3.2  Periodical calibrationFig. 6  Yb Yb Yb Yb
obtained through collinear laser spectroscopy for different measure-
ments stabilizing the probe laser to either the WSU-10 wavelength The stability of the WSU-30 wavelength meter readout at 
meter or the Matisse 2 TS transfer cavity. All centroids of a specific the RISIKO laboratory was tested over a period of ≈ 1 day 
isotope, which were measured with a total of six different laser set-
points, are compared to their average. The  confidence level was by monitoring the measured frequencies of the Rb-locked 1
reduced from 4.6 to 3.8 MHz when stabilization to the transfer cavity ECDL and the HeNe after one initial calibration to the Rb 
was done D2 line. In a second measurement, 1 day later, the wave-
length meter was auto-calibrated to the Rb-locked ECDL 
with a cycle of 10 min. The results are presented in Fig. 8.
pendent measurements were done both at the IGLIS labora- It can be clearly seen that without auto-calibration (AC), 
tory, a temperature-controlled (±0.5 ◦ C) ISO8 clean room, the wavelength meter readout drifts over a few tens of MHz, 
and the COALA laboratory (see Fig. 7a–c). In all three strongly correlated to the temperature. Moreover, at large 
cases, a HeNe laser was used both to calibrate the wave- deviations from the nominal frequency, the HeNe readout 
length meter and as reference for the correction applied as it seems to drift further than the Rb-locked ECDL, indicating 
is the most common reference source. In addition to the also here (set, ref, t) ≠ 1.
HeNe, another externally stabilized laser, a proxy for the Auto-calibration resolves the long-term stability issues of 
laser to be monitored during the experiment, was read out the wavelength meter readout almost completely. The devia-
by the WS7-60 to search for any frequency dependence in tion  − cal to the calibration frequency is < 2 MHz over 
(set, ref, t) . First, the IGLIS TA:pro, stabilized to the wave- the measurement duration and can be further reduced by a 
length meter readout at 654.97538 nm was included. Second, shorter calibration interval. As a consequence, an AC routine 
a potassium-locked diode was used at 770.10878 nm, also was added to the data acquisition cycle, so that the wave-
at the IGLIS laboratory. Finally, a Matisse 2 TS Ti:sapphire length meter can be calibrated (taking less than 1 s) before 
laser, locked to the FC1500 frequency comb at the COALA moving to the next frequency setpoint. Alternatively, a stable 
laboratory, was monitored at a wavelength of 787.82884 nm. temperature environment for the wavelength meter should 
The drift of the TA:pro was measured by supplying the laser, provide superior frequency stability than in our test without 
stabilized to set in the WS7-60, also to the SFPI. The data AC. In this case, one should also consider the air pressure 
analysis of these results remains the same as described in in the room, which could not be measured with our device. 
Sect. 2.2. For all three measurements, the full drift of the Newer devices usually have an integrated pressure sensor.
WS7-60’s response in ≈ 6 h is mapped together with the
results of available corrections. These corrections include
(set, ref, t) = 0, (set, ref, t) = 1 a n d 4  Validation
(set, ref, t) = (set, ref) . The factor (set, ref) is a repro-
ducible, wavelength-dependent constant, which is obtained The reliability of the laser system in general and the WS7-
after longer periods of drift as can be seen in Fig. 7a–c. This 60 wavelength meter in particular was tested by performing 
number is reproducible for different measurements, inde- hyperfine spectroscopy on the 4s 2S1∕2 ground-state (g.s.) 
pendent of the drift rate, showing only a dependence on the to the 4p 2P1∕2 excited-state (e.s.) transition in 63,65Cu , in 
device, set and ref . From the data, one can see that the WS7- an Atomic-Beam Unit (ABU) and in a gas jet, and com-
60 does not provide a stable read out of the wavelength over paring the results with the literature. The resulting data as 
1 3
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well as the excitation and ionization scheme are presented multitude of scans are performed in high-resolution mode 
in Fig. 10. To achieve the excitation at 327.49 nm, light in the ABU. For each scan, a delay of around 6 ns between 
from the scanning TA:pro laser is amplified in a Pulsed Dye excitation and ionization laser pulses was implemented to 
Amplifier (PDA, Sirah Lasertechnik GmbH) and frequency find the optimal compromise between linewidth reduction 
doubled in a BBO nonlinear crystal. The ionization step of and scan time [32]. The obtained FWHM of the reso-
287.98 nm is provided by a broadband tunable dye laser nances was between 110 and 130 MHz, including the 
(CREDO, Sirah Lasertechnik GmbH) with also an integrated natural linewidth, the Fourier-limited amplified TA:pro 
frequency conversion unit. Both PDA and broadband dye laser linewidth (≈ 70 MHz) , and some residual power 
lasers are pumped by Nd:YAG lasers (INNOSLAB, Edge- broadening from the ionization laser. In addition, for the 
wave GmbH) at 1 kHz with a pulse length of ≈ 7 ns. The in-gas-jet data, a resolution of ≈ 400 MHz was achieved, 
ABU provides a copper atom plume by resistively heating consisting of the components already mentioned added to 
a graphite tube filled with copper. After ionization, these a T ≈ 22 K Doppler ensemble in a Mach 7.5 jet. The final 
atoms experience a two-stage acceleration region before a results for the hyperfine parameters of 63,65Cu are sum-
field-free drift towards a Multi Channel Plate (MCP) detec- marized in Table 2. These values are obtained after evalu-
tor. At the MCP, the time-of-flight of copper ions is recorded ation with the Statistical Analysis Toolbox for Laser 
to provide a mass-resolving power of R ≈ 150 for 63Cu. Spectroscopy (SATLAS) module in python [33]. This 
For the gas jet, copper atoms are produced by resistively software is designed specifically to analyze the data of 
heating a copper filament inside a buffer gas cell filled with laser spectroscopy experiments and allows for both 2 and 
argon. After laser ionization in the jet formed by a de Laval maximum-likelihood fitting procedures. A model for the 
nozzle, placed at the gas-cell exit, these ions are transported hyperfine structure of the element of interest is fitted 
through a set of Radio-Frequency Quadrupoles (RFQ’s) directly to the experimental spectrum, providing both 
and ion optical elements to a dipole magnet mass separa- hyperfine parameters and resonance characteristics. From 
tor ( R ≈ 300 ) on high voltage. The mass-separated ions are Table  2, a consistent and reproducible disagreement 
finally detected by an MCP. More details on the setup sys- > 10𝜎 with the literature on the value a(63Cu,g.s.) is found.
tem are available in [15, 31]. A schematic overview of the The WS7-60-to-SFPI comparison in Fig. 10 shows, how-
laser setup for an ABU measurement is shown in Fig. 9. ever, an overestimation of the relative distances, defining,
The scheme for in-gas-jet measurements is similar with the for example, the 63Cu ground-state splitting, as indicated
exception that the laser beams are sent to the adjacent sepa- by the relative difference in position on the ΔSFPI−WS7()
rator laboratory for overlap in the gas jet. An example of the function of the particular resonances in the figure. There-
resulting hyperfine structure, obtained from an ABU meas- fore, to improve the WS7-60’s precision, the wavelength
urement, is visualized in the bottom part of Fig. 10. array in the hyperfine spectra is corrected by a fit of the
The measuring protocol, automatized in the IGLIS waveform in Fig.  10. Because the fine structure of
Control Software and outlined in [15], provides, together ΔSFPI−WS7() as a function of wavelength is much more
with additional systematic checks, all data required to complex than a triangular waveform, a spline generated
specify the expected uncertainties on both the ion rate and by the splrep function of the scipy python library,
wavelength determination. The uncertainty on the ion weighted by the errors on each measurement point, was
arrival rate, I, is deduced from the standard√ deviation of used to describe its behavior by finding the B-spline rep-
a number of measurements, I ± ΔI = ⟨I⟩ ± ⟨I2⟩ − ⟨I⟩2  , resentation of the curve. The distribution of residuals
at a specific wavelength,. The uncertainty on the wave- from this spline was used to define Δcorr ≈ 1 MHz. The
l e n g t h    c o m p r i s e s  s e v e r a l  c o m p o n e n t s resulting hyperfine parameters, obtained after correcting
Δstat,Δstab,Δdri√ft,Δcorr  ,  c o m b i n i n g  t o the wavelength array of each scan by the spline function,
 ± Δ = ⟨⟩ ± (Δ )2 + (Δ )2  stat stab + (Δ 2drift) + (Δc.o  )2rr are shown in Table 2. This correction procedure alters the
Here, Δstat represents the standard deviation of all wave- readout of the WS7-60, such that it would match that of
length values read out by the WS7-60 in a specific wave- the SFPI reference. Agreement with the literature is
length step, typically Δstat ≈ 1 MHz, see [15]. Δ 63,65 63stab cov- obtained for Cu within 1  = 0.5( Cu), 0.8(65Cu) MHz
ers the stability of the frequency reference, ≈ 1 MHz in 1 for the ABU, and 1.5 =  3 MHz for the gas jet, respec-
h for the HeNe and < 1 MHz for the potassium-locked tively, taking into account only statistical errors. This cor-
diode laser. Third, Δdrift describes the uncertainty on the respondence means that with the correction applied to the
WS7-60’s drift correction. For the IGLIS control soft- WS7-60 output, an uncertainty Δ654.98 = 3  MHz is
,total
ware, (set, ref, t) = 1 . In this case, Δdrift remains achieved in this specific wavelength region. Combining
< 1 MHz for a scan at 654.98 nm, see Fig. 7a. Finally, the results for both hyperfine a parameters of 63,65Cu
Δcorr can be added to account for any applied corrections r e v e a l s  a(63Cu,g.s.)∕a(63Cu,e.s.) = 1.600(11)  a n d
to the WS7-60 output. Within these specifications, a 
1 3
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On the performance of wavelength meters: Part 1—consequences for medium-to-high-resolution… Page 11 of 14 85
(a) (b)
(c)
Fig. 7  Time dependence of the WS7-60’s response to an exter- (set, ref, t) = 1 and red for (set, ref, t) = (set, ref) ), see text for
nally locked laser at 654.97538  nm (a), 770.10878  nm (b), details. The measured correction factor (set, ref, t) , with its stable
and 787.82884  nm (c), respectively. The drift is defined as value, (set, ref) , fitted to the data, is added to the top panel of each
ΔX = WS7(t) − WS7(t0) , with t0 being the time of calibration and figure. The different drift amplitudes originate from differences in the
X the specific laser used. The uncorrected readout (right axis, external conditions during the measurement
blue) is plotted alongside possible corrections (left axis, yellow for 
a(65Cu,g.s.)∕a(65Cu,e.s.) = 11.620(17)  ,  r e s p e c t i ve ly, from  Table1. When no information is available on the 
excluding any hyperfine anomaly within this precision. wavelength meter response in the required range, the con-
An isotope shift 63−65 of 573.7(18) MHz can also be servative absolute uncertainty of the device (60 MHz for 
extracted from the data, also in agreement with the litera- WS7-60) should be taken into account.  
ture [34, 35].
In case no spline correction were applied, an additional 
non-stochastic systematic error would have to be intro-
duced to the resulting observables, aCu,g.s. , aCu,e.s. and 
63−65 , such that Δ654.98  is bound by a specific condition 
,total
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Fig. 8  Long-term frequency drifts in the readout of the WSU-30 tion (AC) in a 10 min interval to the Rb-locked ECDL. For a better 
for the HeNe laser (orange) and the Rb-locked ECDL (blue). Lower readability, the HeNe frequency has an offset of +5 MHz in the meas-
panel: deviation of the frequency readout  to the frequency readout urement with AC. Upper panel: temperature readout of the WSU-30 
at the time of calibration cal . The measurement was performed two for the measurement without AC (black) and with AC (green)
times: first with one initial calibration and second with auto-calibra-
directly related to the final physical observables of interest, 
is determined by a comparison to both an SFPI and a GPS-
referenced frequency comb. For these frequency differences, 
induced by the hyperfine interaction, it was observed that 
the wavelength meters, which were all performing within 
specifications of the manufacturer, exhibit reproducible, 
quasi-periodic wavelength and device-dependent discrep-
ancies with other reference sources, with the period lying 
close to the free spectral range of the device’s most precise 
interferometer. This rather inexpensive, practical, and sim-
ple characterization allows for a firm determination of the 
Δ in the wavelength range of interest. Either Δ can be 
Fig. 9  Schematic overview of the setup used to determine the hyper- reduced to the measurement uncertainty of the comparison, 
fine parameters of the 4s 2S 21∕2 to 4p P1∕2 transition. For the in-gas- by correcting the observed periodic behavior or, the peak-
jet measurements, the UV laser beams were guided to the adjacent 
offline beam separator laboratory, see [15, 31] to-peak discrepancy of the observed pattern is used to define 
an additional systematic uncertainty Δ . In case no com-
parison is performed, the absolute uncertainty, quoted by 
5  Conclusion the manufacturer, remains the only trustworthy source for 
Δ . This procedure was validated by laser spectroscopy 
In this paper, two performance aspects of several com- on 63−65Cu isotopes in an Atomic Beam Unit (ABU) and in 
mercial wavelength meters (HighFinesse GmbH), which a gas jet. Finally, to ensure stable performance when probing 
are commonly used to monitor, stabilize and scan a laser’s rare exotic isotopes over longer times, two different solutions 
wavelength in medium/high-resolution laser hyperfine are validated, both taking advantage of an external refer-
spectroscopy experiments, are investigated in a number ence source’s wavelength stability. In conclusion, the quoted 
of laboratories. First, the measurement uncertainty of fre- absolute measurement uncertainty of the specific wavelength 
quency differences in the order of  10 GHz, Δ  , which is meter should coincide with the expected attainable precision 
on the physical observables of the experimental laser-spec-
troscopy technique. In case the former significantly exceeds 
the latter, an extra characterization of the wavelength meter, 
as described here, should be performed in the specific wave-
length range of interest to provide a trustworthy estimate 
of the measurement uncertainty. This statement, alongside 
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On the performance of wavelength meters: Part 1—consequences for medium-to-high-resolution… Page 13 of 14 85
Table 2  Literature values for the hyperfine parameters of the 4s 2S1∕2 
to 4p 2P1∕2 transition in 63Cu and 65Cu compared to results obtained 
for the measurements in the ABU and in a gas jet
Literature a(63Cu,g.s.) (MHz) a(63Cu,e.s.) (MHz)
5866.90871(2) 505.2 (8)
Experiment a(63Cu,g.s.) (MHz) a(63Cu,e.s.) (MHz)
ABU 5874.4(5) 505.0(5)
ABU 5866.9(5) 505.8(5)
Gas jet 5873(2) 506(2)
Gas jet 5870(2) 506(2)
Literature a(65Cu,g.s.) (MHz) a(65Cu,e.s.) (MHz)
6284.38997(6) 542.9(16)
Experiment a(65Cu,g.s.) (MHz) a(65Cu,e.s.) (MHz)
ABU 6290.9(8) 539.9(8)
ABU 6284.0(8) 541.0(8)
The correction to the WS7-60 wavelength meter output, discussed in 
the text, was applied to the data with the X mark [34–37]
The authors would like to thank both F. Karlewski (HighFinesse) for 
his efforts and the fruitful discussions and P. Imgram (TU Darmstadt) 
for his support with the transfer cavity setup at JYFL.
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Copyright 2020 by Springer Nature. https://doi.org/10.1007/s00340-020-07425-4
4.6. High-resolution laser resonance ionization spectroscopy of 143−147Pm
4.6 Publication V: High-resolution laser resonance ionization spectroscopy of
143−147Pm
The following manuscript was published as a regular article in the European Phys-
ical Journal A: Hadrons and Nuclei 56, 69 (2020) DOI 10.1140/epja/s10050-020-
00061-8. Based on the laser ionization schemes developed in the scope of Publica-
tion III, more challenging high-resolution spectroscopic experiments on Pm were
prepared at the RISIKO mass separator, using the novel PI-LIST ion source module
[41]. First, the feasibility was demonstrated using the remains of the 147Pm sample
from the previous broadband spectroscopic measurements. Afterwards, a num-
ber of long-lived Pm isotopes were produced by proton irradiation of natural Nd
at the Bern medical cyclotron, followed by chemical purification at PSI Villigen.
The sample solution delivered to Mainz contained about 1012 atoms per isotope of
143−147Pm, which is a factor of ≈ 100 lower than the previously used 147Pm sam-
ple, and included an isobaric contamination of Pm : Nd ≈ 1 : 100 after chemical
separation. Under these challenging conditions, i.e. low sample amounts and high
isobaric contamination, the experiment was a perfect test case for the PI-LIST per-
formance. Additionally, it marks the first precision laser spectroscopy of neutral
Pm. The measured hyperfine spectra and isotope shifts could be used to deter-
mine electromagnetic moments and changes in mean square charge radii for the
investigated isotopes. Some of these properties were measured for the first time,
while others improved existing literature values. Altogether the experiment set
an important stepping stone towards on-line laser spectroscopy on Pm isotopes,
most probably using the PI-LIST, which is currently tested and adapted for on-line
application after the long shutdown at CERN in 2021.
Author contribution
The author performed the major part of the experimental set-up and spectroscopic
measurements, which are the central topic of this publication, with support of R.H.
and S.R. during the ion source and laser setup, respectively. The 147Pm sample
production was performed by U.K. at ILL. J.U. coordinated the production of the
cyclotron samples in collaboration with S.B. and T.S.C. (AEC-LHEP Bern), and
afterwards performed the chemical separation at PSI. The author evaluated the
spectroscopic data and prepared the manuscript draft. This project was supervised
by R.D. and K.W. Note that this article features an authors contributions section,
where individual tasks are summarized.
107
Eur. Phys. J. A           (2020) 56:69 
https://doi.org/10.1140/epja/s10050-020-00061-8
Regular Article - Experimental Physics
High-resolution laser resonance ionization spectroscopy
of 143−147Pm
Dominik Studer1,a , Jiri Ulrich2, Saverio Braccini3, Tommaso Stefano Carzaniga3, Rugard Dressler2,
Klaus Eberhardt4, Reinhard Heinke1 , Ulli Köster5, Sebastian Raeder6,7, Klaus Wendt1
1 Institut für Physik, Johannes Gutenberg-Universität Mainz, 55099 Mainz, Germany
2 Paul-Scherrer Institut, 5232 Villigen, Switzerland
3 Albert Einstein Center for Fundamental Physics, Laboratory for High Energy Physics, University of Bern, 3012 Bern, Switzerland
4 Institut für Kernchemie, Johannes Gutenberg-Universität Mainz, 55099 Mainz, Germany
5 Institut Laue-Langevin, 38042 Grenoble, France
6 Helmholtz-Institut Mainz, 55099 Mainz, Germany
7 GSI Helmholtzzentrum für Schwerionenforschung, 64291 Darmstadt, Germany
Received: 9 October 2019 / Accepted: 7 January 2020
© The Author(s) 2020
Communicated by Ari Jokinen
Abstract We present the results of high-resolution laser (Pm, Z = 61), however, marks a gap in the map of inves-
spectroscopy of the long-lived radioactive isotopes 143−147Pm. tigated nuclei [1], which can be attributed to its exclusively
The hyperfine structures and isotope shifts in two different radioactive nature and its complex atomic spectrum, render-
atomic ground-state transitions at 452 nm and 468 nm were ing preparatory experiments difficult.
probed by in-source laser spectroscopy at the RISIKO mass Precision spectroscopy in the Pm isotopic chain is of high
separator in Mainz, using the PI-LIST ion source. From the relevance to gain information on nuclear moments and for
hyperfine coupling constants the nuclear magnetic dipole and the study of nuclear shape transition phenomena. Leander
electric quadrupole moments for 143−147Pm were derived, et al. expect a transition from spherical nuclei to a regime
and the measured isotope shifts allowed the extraction of of strong deformation towards neutron deficient isotopes in
changes in nuclear mean square charge radii. the light lanthanide region, which is predicted to be best
accessible (at N < 75) and particularly sharp in the case
of Pm [4]. On the neutron-rich side, the shape transition to
1 Introduction deformed nuclei for N > 88 can be studied. The influence
of 146Gd, which shows certain features typical for a doubly
High-resolution laser spectroscopy of atomic transitions magic nucleus [5], has been related to the abrupt change in
can be used as a high precision, model-independent probe charge radii in this region. Budick et al. observe a remark-
for a number of fundamental properties of nuclear ground able degree of deformation in 151Pm compared to 147Pm,
states or long-lived isomers. The analysis of hyperfine split- measured via atomic beam magnetic resonance (ABMR) [6],
tings allows the extraction of nuclear spin, magnetic dipole similar to what has been observed for the corresponding iso-
moment and electric quadrupole moment, while isotope tones of Eu [7]. Although we cannot access these neutron
shifts are linked to changes in mean square charge radii along numbers in our off-line experiment, a valuable basis for on-
a series of isotopes [1–3]. During the last decades, with the line studies can be established.1
use of radioactive ion beam facilities based on the Isotope Modern cyclotrons are capable of producing a number of
Separation On-Line (ISOL) technique in combination with long-lived Pm isotopes in relevant quantities and with suit-
sensitive laser spectroscopy methods, such studies contin- able specific activity, rendering laser spectroscopic exper-
ued to push further away from the valley of beta-stability, iments feasible. In the historical context Pm spectroscopy
towards very exotic short-lived radioisotopes. In this regard is not entirely new, however, experiments were most often
the region of lanthanide elements is one of the most thor- limited to the easiest accessible isotope, 147Pm. First hyper-
oughly studied along the entire chart of nuclei. Promethium
1 In this context, on-line means the experiment is coupled to the isotope
a e-mail: dstuder@uni-mainz.de (corresponding author) production site, enabling experiments on short-lived nuclei.
0123456789().: V,-vol 123
   69 Page 2 of 13 Eur. Phys. J. A            (2020) 56:69 
fine patterns were measured in the 1960s by Klinkenberg cal purification and shipping. To complement the isotopes
et al. [8] and Reader et al. [9]. In these experiments, mil- accessible by neutron irradiation we opted for proton irradi-
ligram amounts of 147Pm were used in both, electrodeless ation of a natural neodymium target, which was performed
discharge or hollow cathode light sources and studied using at the 18 MeV proton cyclotron at Bern University Hospi-
grating-based and Fabry–Pérot spectrographs. Although sev- tal [16]. A target pellet with 1 cm diameter and thickness of
eral hundred lines were measured, the assignment of the 0.65 mm was pressed from a mixture of natural Nd2O3 and
associated energy levels was not possible in most cases, and graphite powder with a total weight of 113 mg. The addi-
sometimes even the information was lacking whether a spe- tion of approx. 25 wt% graphite as binding agent was neces-
cific line belongs to the spectrum of neutral (Pm I) or singly sary to increase the mechanical stability of the pressed pellet,
ionized (Pm II) promethium. Nonetheless, a nuclear spin which was then encapsulated in an aluminum sample holder
of I = +7/2 and nuclear moments of μI = 2.58(7) μN and irradiated with an integrated current of approximately
and Q = 0.74(20) eb for 147s Pm could be extracted, which 12µAh. After irradiation, the pellet was removed from the
are the most precise values until today (together with values aluminum holder, the Nd2O3 was dissolved in 7M HNO3
obtained from complementary measurement methods). First and the graphite was removed by filtration. The radiochemi-
direct excitation spectroscopy was performed in the 1990s by cal separation of the produced Pm isotopes from the Nd bulk
Alkhazov et al. [10] and Otto et al. [11] by means of collinear material was performed by ion exchange chromatography on
fast beam laser spectroscopy using dye lasers. In both exper- the SYKAM cation exchange resin, following the procedure
iments transitions in the spectrum of Pm II were studied. described in [15]. As a tracer of the Nd-fraction during the
Alkhazov et al. also had 145Pm at their disposal, which was chemical separation, 1 MBq of 147Nd was produced by neu-
produced in the reaction 144Sm(n, γ )145Sm(EC)145Pm, and tron activation of a natural Nd2O3 solution in the TRIGA
accordingly also extracted nuclear moments for this nuclide, research reactor at the Department of Nuclear Chemistry at
with the precision limited by the reference nuclear moments Mainz University, and afterwards shipped to PSI Villigen,
in 147Pm [12]. where the radiochemical separation took place. An ICP-MS
Other than these laser spectroscopic studies on Pm II tran- analysis of the Pm fraction was performed after separation.
sitions, our work is dedicated to the study of Pm I. In the A Nd:Pm ratio of approx. 100:1 indicates a decontamination
scope of our recent work on the atomic structure of neu- factor of Pm from Nd of around 6·105. A separate publication
tral Pm, we identified several laser ionization schemes and with detailed information on the production and separation
determined the first ionization potential of Pm [13]. Utiliz- is in preparation, in which also half-life measurements of
ing these schemes, two atomic ground state transitions at 143,144Pm will be presented [17].
452 nm and 468 nm are investigated here. In contrast to many Table 1 comprises all Pm nuclides which were produced
state-of-the-art spectroscopy experiments based on collinear in relevant quantities. Half-lives are taken from the Evaluated
laser spectroscopy of fast atom- or ion beams, we performed Nuclear Structure Data File (ENSDF, [18]). The activity was
in-source spectroscopy directly in the atomic beam effusing measured via γ -spectroscopy at PSI Villigen, and the atom
from a hot atom source. This concept is implemented in the number of each nuclide n was derived from the γ -activity.
PI-LIST (perpendicularly illuminated laser ion source and No γ -lines for 145Pm and 147Pm could be observed in the
trap), which presents a complementary technique to collinear
laser spectroscopy and has undergone various performance
tests on stable and radioactive species lately [14].
Table 1 Composition of the Pm sample produced by irradiation of a
Nd2O3 target with 12µAh of 18 MeV protons. Half-lives were taken
from [18]. The activity and atom number n were determined by γ -
2 Experimental setup spectroscopy. The mass ratio was measured via RIMS (see Fig. 1) 19
days after production
2.1 Sample production and purification Nuclide T1/2 Activity (kBq) n/1012 Mass ratio (%)
143Pm 265(7) d 60.7(7) 2.00(6) 17.2(15)
The samples for our experiment originate from two different
144
production routes. One sample, containing some 1014
Pm 363(14) d 84.9(8) 3.8(2) 35.2(24)
atoms
of 147
145
Pm, was produced by neutron activation of enriched Pm 17.7(4) y 17.6(15)
146 146Nd at the high-flux reactor at ILL Grenoble and purified Pm 5.53(5) y 6.9(2) 1.74(6) 18.7(16)
147
at PSI Villigen. For details on the production we refer to [15]. Pm 2.6234(2) y 9.9(11)
Part of this sample was already used for our studies of the 148Pm 5.368(7) d 116(2) 0.077(1) 1.1(3)∗
atomic structure of Pm [13]. Other suitable isotopes for off- 148mPm 41.29(11) d 18.1(2) 0.093(1)
line experiments are 143,144,145,146,148mPm, with half-lives The value of 1.1(3)% marked with an asterisk gives the combined mass
of at least some 10 of days, which is required for chemi- ratio for 148Pm and 148mPm
123
Eur. Phys. J. A            (2020) 56:69 Page 3 of 13    69 
γ -spectra and thus no activity and atom numbers could be with a Fourier-limited linewidth of ≈ 20 MHz for the spec-
determined by means of γ -spectroscopy for these isotopes. troscopy transition [21,22], seeded by an external cavity
This is expected as both isotopes have significantly longer diode laser (master ECDL). In this case the second harmonic
half-lives, resulting in lower emission rates of their decay was generated outside the cavity by focusing the laser into
radiation in the sample. Furthermore, the γ -ray emission a BBO crystal in simple single-pass transmission. For the
probabilities during the decay of both isotopes are low in master ECDL we used two different laser diodes: Eagleyard
general (especially for 147Pm they are well below 10−4). The RWE-920 and RWE-980 for scheme (A) and (B), respec-
possibly detectable line of 145Pm at 72.5 keV is obscured tively. It was stabilized with an iScan unit (TEM Messtech-
in the measured spectrum with the much more prominent nik GmbH). For a relative laser frequency measurement we
Kα2 line of lead at 72.8 keV, originating from X-ray fluo- simultaneously recorded the output of the master ECDL and
rescence of the detector shielding. For an additional analy- a stabilized HeNe laser (SIOS SL-03) in a home-built scan-
sis of the sample composition, mass spectra were recorded ning Fabry–Pérot-interferometer (S-FPI) with a free spectral
via resonance ionization mass spectrometry (RIMS). The range of 299.721 MHz and a finesse of F ≈ 400. The fre-
RIMS measurements were performed 19 days after the γ - quency offset to an arbitrary anchor point can be deduced
spectroscopy (details on this measurement are discussed in from the distance of the transmission fringes of the master
Sect. 2.3). While RIMS itself does not give information about ECDL laser when using the transmission fringes of the HeNe
absolute atom numbers, the isotope ratios can be compared as a ruler. For a complementary, absolute frequency mea-
with the ones from γ -spectroscopy. The ratios match within surement we used a wavelength meter (High Finesse WSU-
the uncertainties (with consideration of the decay time), so 30). An additional ECDL (Toptica DL pro 780), locked to
we can conclude that atom numbers of 145Pm and 147Pm are a Rb saturation absorption spectroscopy unit (TEM CoSy
also in the order of 1012 atoms, similar to the other long-lived 4.0) served as a calibration source for the wavelength meter.
isotopes 143,144,146Pm. Note that in a comparative study of the wavelength meter
and the S-FPI readout, performed at different laboratories,
2.2 Laser setup we observed periodic deviation patterns which necessitate a
correction to recorded spectra [23]. The data presented here
Our Pm laser ion source relies on two different laser ion- was corrected for this periodic behavior by subtracting a fre-
ization schemes, which we developed in our previous work quency deviation term, according to Eq. 1 in [23], from the
[13]. Both schemes use three laser steps λ1, λ2, λ3 to con- wavelength meter data. A drift correction was not applied to
secutively excite sample atoms to higher lying atomic states, the data, but rather a frequent calibration of the wavelength
with the final state having an excitation energy above the first meter to the reference laser (see section IIIB in [23]). The
ionization potential and thus undergoing auto-ionization. reference also provides a more detailed description of the
cw-laser setup.
452 nm 887 nm 849 nm
0 −−−−→ 22 080.06 −−−−→ 33 352.2 −−−−→ 45 135.8 (A) 2.3 Ion source setup
λ1 λ2 λ3
468 nm 882 nm 804 nm The laser spectroscopy was performed at the RISIKO mass
0 −−−−→ 21 348.21 −−−−→ 32 683.7 −−−−→ 45 128.4 (B) separator at JGU Mainz, using the resonance ionization spec-
troscopy technique. The used setup, i.e. its standard configu-
All level energies are given in units of cm−1. ration, is described in [24]. The sample solution was dried on
By measuring the number of produced ions as a function a titanium carrier foil, folded and put into a tubular tantalum
of the laser wavelength, spectroscopy can be performed. The atomizer, which can be resistively heated up to 2000 ◦C.
ionization schemes will be abbreviated in the following by For the experiment we used a refined version of the well-
(A) and (B), respectively, where λ1 is the spectroscopy tran- proven Laser Ion Source and Trap (LIST) [25–27]. It fea-
sition in both schemes. Each step was driven by a 10 kHz tures a dual repeller electrode on the side facing the atomizer
repetition rate pulsed Ti:sapphire laser, with pulse lengths of oven, a rf quadrupole for radial confinement of ions, and an
40–60 ns, an average output power of 3–4 W, and a spec- exit electrode to prevent field leakage of the strong extraction
tral linewidth of 5–10 GHz. For a detailed description of potential in the LIST volume. It has two modes of operation.
these home-built “Z-cavity” lasers, which are in use at on-line When operated in ion-guide (IG) mode both repellers are
radioactive ion beam facilities worldwide, see e.g. [19,20]. set on a negative voltage, so that positive ions are extracted
Since λ1 is in the blue wavelength regime, we generated from the source. The ions are guided towards the exit elec-
the second harmonic intra-cavity, using a beta barium borate trode by the rf field. Upon passing the exit electrode, they
(BBO) crystal. For measuring hyperfine spectra we can alter- are accelerated to 30 keV (from the source potential at + 30
natively produce λ1 by an injection-locked Ti:sapphire laser kV towards the grounded extraction electrode). The IG mode
123
   69 Page 4 of 13 Eur. Phys. J. A            (2020) 56:69 
a ≈ 4.2 GHz spacing. We therefore presume a molecular
species (possibly in a higher charge state) where a vibra-
tional band was excited by the laser light, and which was
subsequently ionized non-resonantly by a second photon.
When switching to LIST-mode, these contaminants were
suppressed and the ion beam composition was similar to the
one of the cold ion source. Isotope ratios were measured
with both, a cold source in IG-mode and with the hot source
in LIST-mode in good agreement, mean values are given
in Table 1. In the following, for the high-resolution spec-
troscopy application, the ion source was exclusively oper-
Fig. 1 Mass spectra of the cyclotron-produced Pm samples. Left
≈ ◦ ated in LIST-mode, introducing the injection seeded probepanel: Cold ion source. Right panel: Hot ion source at 1500 C.
For details see text laser for the spectroscopy transition in perpendicular geome-
try [14]. The probe laser beam was horizontally widened with
a profile of approximately 40 mm×2 mm for a large overlap
resembles the standard laser ion source operation without a area with the ionizing lasers. A sketch of the experimental
LIST unit, with an efficiency loss factor of < 2 [25]. In the arrangement is given in Fig. 2.
second mode of operation (LIST mode) one repeller is set
on a positive voltage, so that ionized species from the source
region (e.g. via surface ionization) are suppressed. The nega- 3 Hyperfine spectroscopy
tive repeller electrode deflects electrons emitted from the hot
oven, preventing electron impact ionization within the LIST The hyperfine splittings of both spectroscopy transitions, at
volume. The LIST mode thus offers a suppression of ions 452 nm and 468 nm, are schematically illustrated in Fig. 3.
which are produced independently of the laser, in particu- The positions and spacings of the arrows indicating individ-
lar isobaric contaminants which cannot be mass-separated. ual hyperfine transitions are chosen in such a way that they
Since laser-ionized species from the source region are lost, depict the position of the respective line in the spectrum, as
this gain in ion beam purity comes at the cost of ionization plotted exemplarily for the case of 147Pm. In order to achieve
efficiency. Despite this trade-off this technique offers unique a sufficiently narrow experimental linewidth to resolve the
opportunities whenever the ion beam composition is dom- hyperfine patterns, several parameters which are specific to
inated by isobars of the nuclides of interest, which cause the ionization scheme were characterized. Firstly, the power
strong background. In the present experiment this was the of the spectroscopy laser has to be properly chosen to prevent
case for e.g. Nd isotopes from the cyclotron target. Figure. 1 saturation broadening of the spectral lines. The laser power
shows mass scans in the Pm region for different ion source influence on the two spectroscopy transitions of interest was
conditions. For these scans we used the broadband laser sys- measured, and is shown in the left panels of Fig. 4. In scheme
tem tuned to scheme (A), so that full hyperfine splittings and (A) we chose the F = 6 → F ′ = 5 transition and in scheme
isotope shifts were covered by the laser linewidth and all Pm (B) the F = 5 → F ′ = 6 transition between the ground
isotopes were equally ionized. In the left panel, no heating state and the respective first excited state. A fit according
current is applied to the atomizer and the LIST is operated to the procedure described in [28] yields saturation powers
in IG-mode. The release of sample atoms was caused by (defined as the power at which half of the maximum ion sig-
heating of the atomizer by the incident laser beams. In this nal is reached) of P452s = 8(2)mW and P468s = 0.6(2)mW
situation the influence of the laser ionization scheme could for the transitions at 452 nm and 468 nm, respectively. As not
be well tested, as the contribution of surface ionization was all components of the hyperfine spectrum were investigated
negligible. We observe the isotope ratio as expected from and the values are specific to the individual hyperfine transi-
the γ -spectroscopy measurements given in Table 1, with a tions, these values are used as guide figures to estimate the
slight interference of about 3 % intensity at mass 146, occur- power threshold upon which saturation broadening occurs. In
ring when the lasers were detuned from the Pm ionization the earlier broadband spectroscopy experiment [13] we mea-
scheme. In the right panel, at a temperature of approximately sured a comparable saturation power of P452
◦ s,ref
= 7(4)mW
1500 C, the measured isotope ratios in IG-mode are sig- in the first step of scheme (A). In scheme (B), however, the
nificantly different. The dominant components of the surface earlier measured value of P468s,ref = 10(5)mW deviates by
ionized pattern are expected to be atomic neodymium from an order of magnitude from the value in this work, which is
the cyclotron target and a so-far unidentified species on mass ascribed to different operation conditions, i.e. a change of the
146. The latter was weakly influenced by the 452 nm laser laser power density by a variation in the laser beam profile, as
radiation and shows a pattern of equidistant resonances with well as the relatively high intensity of the F = 5 → F ′ = 6
123
Eur. Phys. J. A            (2020) 56:69 Page 5 of 13    69 
PI-LIST ion source Broadband laser system PBS: polarizing beam-splitter
Quadrupole
E: Fabry-Pérot etalon
rods
Repeller
PBS SHG: second harmonic generation
electrodes
PD: fast photodiode
Ionizing lasers Ti:sa: Ti:sapphire crystal
Atomizer
Exit SF: single-mode fiber
electrode
FI: Faraday isolator
Pm sample
E
Probe laser BRF: Birefringent filter
PM: Piezo-mounted mirror
cw laser system Injection-seeded Ti:sa
lock-in ECDL: external cavity diode laser
lock-in
PD
ECDL Ti:sa Rb SAS: rubidium saturated 
Rb SAS
780 nm
S-FPI SHG absorption spectroscopy
HeNe S-FPI: scanning Fabry-PérotFI
633 nm interferometer
ECDL iScan: frequency control and 
SF BRF
904/938 nm PM stabilization
Pulsed output
iScan PC PC: Personal Computer
Fig. 2 Sketch of the experimental setup. Top left: vertical cross sec- lasers for ionizing transitions. Bottom left: cw laser system with seed-
tion of the PI-LIST ion source unit with indicated incident laser beams. ing diode laser and frequency measurement references. Bottom right:
For the sake of clarity the mounting and heat shielding of the resistively pulsed, injection-seeded Ti:sapphire ring cavity for spectroscopy tran-
heated atomizer is not shown. Top right: broadband pulsed Ti:sapphire sition. A legend for the used abbreviations is given on the right
A B
Fig. 3 Excitation schemes (A) (left) and (B) (right) illustrating the positions chosen in relation to the example spectrum presented above.
hyperfine splitting of the atomic ground state and respective first excited For the spectrum we chose the fit function to our 147Pm data. IP: Ion-
state. The blue arrows indicate allowed hyperfine transitions, with the ization potential; AIS: Auto-ionizing state
transition in the pattern of the 468 nm transition. For hyper- In order to avoid this effect, the ionization laser has to be
fine spectroscopy in the 452 nm and 468 nm transitions, the decoupled from the excitation step by temporal delay. How-
first excitation laser were correspondingly operated at 5 mW ever, depending on the excited state lifetime, the population
and 0.5 mW, respectively. decay causes a certain loss in efficiency. The loss factor was
Another spectral line broadening effect is caused by the measured for the transitions of interest by simultaneous and
high-power ionization lasers, which couple the excited state stepwise shifting the second- and third laser (λ2, λ3) pulse
to the ionization continuum. When the probe and the ion- delays relative to the spectroscopy excitation. Since the probe
ization lasers are synchronized, the lifetime of the excited laser is pumped by a separate pump laser, the second- and
state is effectively shortened, causing a line broadening [29]. third laser pulses can be delayed simultaneously by adjust-
123
2 Nd:YAG 2 Nd:YAG
532 nm 532 nm
Wavelength meter
   69 Page 6 of 13 Eur. Phys. J. A            (2020) 56:69 
one spectrum took approximately 1–2 h to record. The wave-
length meter was calibrated to the Rb-locked ECDL every 10
steps in order to keep drifts of the wavelength readout at min-
imum. This is particularly important since one isotope at a
time is measured, and the accuracy of extracted isotope shifts
relies on the reproducibility of the data. The recorded spectra
are shown in Fig. 5. For all isotopes, with the exception of
143Pm, at least two datasets could be recorded per isotope
and transition. In the 452 nm transition the spectral resolu-
tion varies between 100 and 170 MHz FWHM, whereas the
468 nm spectra are somewhat inferior with regard to count-
ing statistics and linewidths lying between 150 and 250 MHz
FWHM. The spectra were fitted with a sum of Voigt profiles,
using the SATLAS python package [31], which is tailored
to the evaluation of hyperfine spectra. The nuclear spins of
each isotope could be fixed to literature values (143Pm: [32],
Fig. 4 Laser power (left) and ionization pulse delay (right) influence 144Pm: [33], 145Pm: [10], 146Pm: [34], 147Pm: [10,35], with
on the ion signal for the transitions at 468 nm and 452 nm. Saturation the values comprised in Table 3). In order to estimate the
curves (orange) are fitted according to [28]. The lifetime is fitted with statistical uncertainties, all datasets were fitted with both, the
a convolution of a Gaussian distribution with an exponential decay law
(green). The zero-point of the ionization pulse delay is arbitrary wavelength meter and the S-FPI laser frequency data, and
for three different binning sizes. The resulting fit parameters
were averaged and the standard deviation taken as uncer-
ing the pump laser triggers relative to each other. The probe tainty. Afterwards, for different datasets of one isotope, a
laser was tuned to the same hyperfine transitions as used in the weighted average was determined. For the isotope shifts we
measurement of saturation powers, with a power of 70 mW added a systematic error of 4 MHz, based on the stability of
in the 452 nm transition and 5 mW in the 468 nm transition. the 87Rb saturated absorption spectroscopy, which serves as
The response of the ion signal is shown in the right panels reference for the wavelength meter. In both transitions, the
of Fig. 4. It can be fitted with a convolution of the approxi- data for the 147Pm isotope has the highest quality in terms
mately Gaussian laser pulse shape with an exponential decay of linewidth and counting statistics, since the scan was per-
contribution for the lifetime of the excited state [30]. In the formed with a dedicated sample with larger atom numbers
case of the 452 nm transition, a lifetime of τ452 = 19(2) ns (≈ 3×1012 atoms), whereas the cyclotron-produced samples
is extracted for the upper state. For the 468 nm transition, were comparatively small (few 1011 atoms) and suffered a
however, the signal shape is completely dominated by the larger Nd contamination. Additionally, 147Pm has the highest
Gaussian contribution. The larger Gaussian standard devia- nuclear quadruple moment Qs among the studied isotopes.
tion compared to the measurement in the 452 nm transition is For these reasons it was used as a reference for the ratio of
caused by the laser operation near the edge of the Ti:sapphire the electric quadrupole hyperfine coupling constant of lower
gain profile, leading to an extended laser pulse length. As a and upper level, i.e. Bl/Bu , which is expected to be constant
consequence the lifetime of the excited state of the 468 nm over the series of isotopes [1]. Correspondingly, in the fits
transition can only be constrained to be significantly shorter of both transitions, this ratio was fixed to the result of 147Pm
than the laser pulse length. This finding is consistent with in the SATLAS fit of the other isotopes. Also, for reasons of
the much lower saturation power compared to the 452 nm superior data quality in the 452 nm transition, Bl468 was fixed
transition. For the spectroscopy experiment a delay between to Bl452, since both transitions couple to the atomic ground
30 and 50 ns was chosen for both transitions, as a reason- state. The magnetic dipole hyperfine coupling constants Al
able compromise between linewidth and efficiency. In the and Au , on the other hand, remained a free parameter in all
452 nm transition, we measured an efficiency loss factor of fits.
≈ 6 for a delay of 30 ns and a laser power of 5 mW, while The final values for isotope shifts δν, as well as A- and B-
the linewidth improved to a value of ≈ 150 MHz full width parameters are given in Table 2. The resulting Al/Au ratios
at half maximum (FWHM), down from ≈ 250 MHz FWHM for both transitions remained within the statistical uncertainty
as determined without delay and with ≈ 70 mW laser power. (Al /Au = 1.2401(2), Al /Au452 452 468 468 = 1.455(10)). From
Scans of the hyperfine spectra were performed by tuning the two independent parameters Al l452 and A468, which are
the ECDL master laser in steps of 10 MHz while recording also expected to be identical as both transitions couple to the
the ion signal. Depending on the counting statistics for the atomic ground state, we estimate an additional error of 1 MHz
measured isotope, data was taken for 3–5 s per step, so that for all A hyperfine coupling constants (which is included in
123
Eur. Phys. J. A            (2020) 56:69 Page 7 of 13    69 
Fig. 5 Measured hyperfine spectra in the ground state transitions of ence for the frequency offset ν − ν147, which is indicated by the green
scheme (A) at 452 nm (left) and of scheme (B) at 468 nm (right). The dashed line. Fit parameters are given in Table 2
centroid frequency of the 147Pm hyperfine structure is taken as refer-
Table 2 Extracted parameters from the hyperfine spectra of the 452 nm δν are given with respect to the reference isotope 147Pm. For details on
and the 468 nm transitions. The superscripts l and u denote the asso- fixed and dependent parameters see text. All values are given in units
ciated lower and upper level of the respective transition. Isotope shifts of MHz
′
Isotope 147,Aδν Al Bl Au u 147,A
′ l l u u
452 452 452 452 B452 δν468 A468 B468 A468 B468
147Pm 0 620.3(14) −407(18) 500.0(14) −119(15) 0 619.4(17) −407∗ 438.2(15) −48(13)
146Pm 226(12) 429.8(22) 8(19) 347.1(22) 2† −164(16) 429.7(40) 8∗ 302.6(24) 1†
145Pm 344(10) 1255.7(11) −135(17) 1011.7(15) −40† −216(11) 1254.8(15) −135∗ 886.8(13) −16†
144Pm 594(10) 329.0(12) 131(13) 265.2(11) 39† −384(13) 322.0(56) 131∗ 227.6(46) 15†
143Pm 737(11) 1368.9(25) −47(18) 1104.0(28) −14† −495(14) 1363.9(29) −47∗ 964.8(23) −6†
∗Fixed parameter; Bl l468 set to the value of B452
†Dependent parameter; Bl/Bu set to the result for 147Pm
Table 2). Similarly, for the B hyperfine coupling constants, an 4 Results and discussion
additional error of 10 MHz was added, based upon fit devi-
ations in the 468 nm transition with free Bl468-parameters. 4.1 Nuclear moments
Note that in these fits the Al468 changed by much less than
1 MHz compared to the fits with Bl468 fixed to Bl452. We did Magnetic dipole moments and electric quadrupole moments
not include the results for Bl468 in Table 2, since we deem for Pm isotopes are given in Table 3. Earlier values reported
Bl452 parameters to be much more accurate. Looking at the in literature are included. The most precise values are avail-
values in Table 2, we observe a perfect agreement of Al 147452 able for Pm, which were measured with different com-
with Al for the isotopes 145,146,147 143,144468 Pm. In Pm, on plementary methods, i.e. paramagnetic resonance of Pm IV
the other hand, there is a deviation of few MHz. Considering [41], ABMR of Pm I [6] and optical spectroscopy of Pm II
the rather large uncertainty in Al (144468 Pm), this deviation [12], all with similar precision. The result of μlit 147I ( Pm) =
is covered within 1.3 σ . In 143Pm, the error margins of Al452 2.58(7)μN given in the work of Reader et al. is based
and Al468 barely overlap. The significance of these deviations on the evaluation of the Gouldsmit–Fermi–Segré formula
is therefore rather low, but should be noted. [42]. The authors used a magnetic splitting factor of A =
123
   69 Page 8 of 13 Eur. Phys. J. A            (2020) 56:69 
Table 3 Nuclear spins Iπ , magnetic dipole moments μI and electric 147Pm were re-evaluated in this work, for details see text. The values for
quadrupole moments Q for several Pm nuclei. Values with no leading 145Pm and 149ms Pm are based on the new reference value of 147Pm. The
sign indicate that only an absolute value is known. The results forμI and Schmidt limits for a g S7/2 and a d5/2 proton are μI (g7/2) = 1.72μN
Q are calculated according to Eq. 1, with the reference isotope 147s Pm. and μSI (d5/2) = 4.79μN , respectively. All literature values of Qlits are
References for literature values of μlitI are given in the last column for taken from [36]
the individual isotopes. The values from the reference for 144Pm and
Isotope N Iπ μ (μ ) Q (eb) μlitI N s I (μ
lit
N) Qs (eb) References
This work This work Literature Literature
151Pm 90 5/2+ 1.8(2) 2.2(9) [6]
149mPm 88 5/2+ 2.0(2) [37]
149Pm 88 7/2+ 3.3(5) [38]
148Pm 87 1− +2.1(2) +0.2(2) [38]
147mPm 86 5/2+ 3.53(6)∗ [39]
147Pm 86 7/2+ +2.57(4)∗ +0.74(20) [12]
146Pm 85 3− +1.53(3) −0.01(4)
145Pm 84 5/2+ +3.72(5) +0.25(7) +3.71(5)∗ +0.23(8) [10]
144Pm 83 5− +1.95(4) −0.24(7) 1.71(14)∗ [40]
143Pm 82 5/2+ +4.05(6) +0.08(4) 3.8(5) [38]
*Re-evaluated results. For details see text
647(13)MHz for the 4 f 56s2 6H5/2 atomic ground state, ture nuclear orientation measured via anisotropy of the γ -
which is not a direct experimental result, but was estimated radiation of oriented 144Pm nuclei [40]. If we re-evaluate
on the basis of experimental data for the 4 f 56s2 6H7/2 state their experimental result using the same value for 〈r−3〉 as
from the ABMR measurements in [6]. When we re-evaluate was used in [12], we obtain |μlitI |(144Pm) = 1.71(14) μN
the Gouldsmit–Fermi–Segré formula in Reader’s work, but (assuming an unchanged uncertainty), which approaches
with our experimental value of A = 619.9(7)MHz (the the result from our work, but still lies outside its uncer-
weighted average of A452l and A468l ) for the atomic ground tainty. One might consider a hyperfine anomaly iΔ j in this
state splitting, the result for the magnetic moment changes to case, which specifies a relative deviation from Eq. 1, i.e.
μlit(147I Pm) = 2.51(5)μN . The other values forμI from [41] Ai/A j = gi /g j (1 − i jI I Δ ), with gI = −μI /I the gyro-
and [6] were re-evaluated in the scope of [12], based on more magnetic ratio for the respective isotopes i, j . However, the
recent theoretical results of 〈r−3〉. Since there is no reason hyperfine anomaly is usually in the order of < 1% [45],
to prefer one of these experimental values over the other, we and should thus be covered within the given uncertainty of
calculate the weighted average μlitI (
147Pm) = 2.57(4)μN . μI (in order to explain this deviation a hyperfine anomaly
For the electric quadrupole moment, we take the value of of 147Δ144 = 0.12(7) would be required). Also note that
Qlits (
147Pm) = 0.74(20) eb from [36] as reference. It is based the difference of the Al and Al452 468 hyperfine coupling con-
on the laser spectroscopy measurements of Alkhazov et al. stants in 144Pm, as mentioned in Sect. 3, is covered by the
[43], but takes into account more recent results for the electric uncertainty of μI and therefore not sufficient to explain
field gradient at the location of the nucleus of Pyykkö [44], this large discrepancy with literature. Since our results for
which no longer rely on Sternheimer corrections. In order to μ (145I Pm) are in perfect agreement with laser spectroscopy
determine nuclear moments μI and Q for 143−146s Pm, we measurements of Alkhazov et al. [10] (both for μI and Qs),
use the relations who studied a different transition in singly ionized Pm, we
A are confident with our results and expect an inconsistency
μI = I μI,ref (1) between the literature values of μlit(147Pm) and μlit(144A I I Pm),ref Iref with the former being used as reference for the values in
= BQ Q (2) our work. Looking at the even-neutron-number isotopes, ones B s,refref clearly observes the expected trend of increasing deforma-
tion from a rather spherical nucleus at the magic neutron
with 147Pm as reference isotope. The results are given in number N = 82 towards more neutron rich isotopes. The
Table 3. With the exception of μ (144I Pm), the obtained val- trend in gI factors is plotted in Fig. 6. Due to their small
ues agree with the ones previously reported in literature. In deformation, 143Pm and 145Pm can be represented by the
the case of 144Pm, the magnetic dipole moment was deter- d5/2 shell model state. They lie close to the Schmidt limit
mined from the temperature dependence of low tempera-
123
Eur. Phys. J. A            (2020) 56:69 Page 9 of 13    69 
A,A′ ′
δν A Ai = νi − νi . (3)
Our measured results for 143−147Pm are included in Table 2,
extracted from the center of gravity of the individual hyper-
fine structures relative to the center frequency of 147Pm. The
data shows a different sign for isotope shifts in the 452 nm
′ ′
and the 468 nm transition, i.e. A,Aδν452 > 0 and
A,A
δν468 < 0
for A > A′. The sign of the isotope shift gives hints on the
configuration of the upper levels in the respective transition.
For the 468 nm transition, we expect a 4 f 56s2 → 4 f 56s6p,
since the involved s electron requires a higher transition fre-
quency for lighter (i.e. smaller) nuclei. From the positive
isotope shifts in the 452 nm transition we conclude that no s
Fig. 6 g factors for the even-neutron-number Pm isotopes. The electron is involved and expect a 4 f
56s2 → 4 f 45d6s tran-
I
dashed lines mark the Schmidt limits of the d5/2 and g7/2 shell model sition. However these assignments are based on the expected
configurations. The cross markers indicate the isomers 147mPm and change in electron density at the nucleus and should be used
149mPm at excitation energies of 91 keV and 114 keV, respectively. They with care.
are connected to the 145Pm ground state by the dash-dotted line to guide
the eye In order to analyze the data with regard to changes in mean
square charge radii, one can express the isotope shift as
of gS ′ ′I (d5/2) = 1.92μN/h̄. Adding more neutrons changes A,A = A,A + A,A′ 1 ′143 δνi δνi,M δνi,F = Ki ′ + Fiδ〈r2〉A,A (4)this situation. After a small decrease of gI from Pm to μA,A
145Pm, a sudden drop is observed towards 147Pm. As can
be seen in Fig. 6, 147,149,151Pm lie closer to the Schmidt ′ ′where A,Aδνi,M denotes the mass shift and
A,A
δνi,F the field
limit of gSI (g7/2) = 0.49μN/h̄. This can be explained by shift, accounting for the change of mass and volume of the
a positive (prolate) quadrupole deformation, leading to the nucleus, respectively. They depend on the mass shift constant
population of the 7/2[404] Nilsson orbital in 147,149Pm and ′Ki , the reduced massμA,A = mAmA′/(mA−mA′), the field
the 5/2[413] orbital in 151Pm [46], both belonging to the g7/2 shift constant Fi and the change in the mean square charge
shell model state. The same transition can be observed in the ′radius δ〈r2〉A,A between two isotopes with mass numbers A
isomeric states 147mPm at 91 keV and 149mPm at 114 keV and A′. Both, Ki and Fi depend on the atomic transition and
excitation energy, but shifted by two N , indicating that the have to be carefully analyzed in order to quantitatively extract
d5/2 states are located at increasingly high excitation energy. δ〈r2〉A,A′ . In our case this analysis is hampered by an uncer-
In the quadrupole moments, the increasing deformation is tain assignment of the excited atomic levels and the lack of
even more clearly visible. The unpaired proton induces a pro- theory input. Still, from the data of well-studied neighboring
late (Qs > 0) deformation as neutrons are added, with the elements and the fact that we have measured isotope shifts
trend becoming very steep towards 151Pm [6]. For the odd- in two atomic transitions, an evaluation may be attempted.
neutron-number isotopes, on the other hand, the unpaired The mass shift can be further separated to the so-called
neutron induces an oblate (Qs < 0) deformation, which to normal mass shift (NMS) and the specific mass shift (SMS),
some degree compensates the one from the unpaired proton, accounting for the change in the center of motion and
but is much less pronounced. Consequently, 144Pm exhibits a electron-electron correlations, respectively. While the former
negative quadrupole moment of Qs = −0.24(7) eb, increas- can be exactly calculated via NMSi = νi/1836.1 [42], esti-
ing to Q 146s = −0.01(4) eb for Pm, where the deformation mations about the SMS require theory input. However, the
induced by the single proton and neutron states compen- SMS is often in the order of the NMS, and we thus assume
sate, and continues to larger positive quadrupole moments for SMSi = 0±NMSi , as often done in cases where SMSi is not147,151Pm, where the influence of the valence proton becomes known [1]. With Eq. 4 we can then calculate the field shift
dominant. A,A′
δνi,F , which usually dominates the isotope shift in heavy′
atoms. In order to extract values for Fi and δ〈r2〉A,A , we
4.2 Isotope shifts rely on data of neighboring elements, as compiled in [47].
In the reference, data from K X-ray shifts, elastic electron
The isotope shift defines the frequency difference δν in an scattering, muonic atoms and optical isotope shifts is eval-
atomic transition i for two isotopes with mass numbers A uated for the extraction of root mean square charge radii.
′
and A′, However, the listed changes in rms charge radii δ〈r2〉A,A
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   69 Page 10 of 13 Eur. Phys. J. A            (2020) 56:69 
Table 4 Change in mean square charge radius per two neutrons for
different light lanthanide elements, evaluated for neutron numbers N =
82, 84, 86. Nuclear charge radii data is taken from [47]
Z Element δ〈r2〉N ,N+2 (fm2)
64 Gd 0.282(8)
63 Eu 0.272(12)
62 Sm 0.274(22)
60 Nd 0.296(20)
59 Ce 0.256(14)
only take optical isotope shifts into account. The following
analysis is based on the latter. Starting from the neutron shell
closures at N = 28, 50, 82 and 126, the increase in nuclear
charge radii is approximately linear towards neutron-rich iso-
topes and neighboring elements exhibit similar slopes, with
few exceptions. Assuming this trend holds valid for Pm, we
can use this regularity to extract the field shift constant Fi .
The mean square charge radii of the Pm neighbors Ce, Nd,
Sm, Eu and Gd over the even neutron number isotopes, i.e. Fig. 7 Changes in mean square charge radii in the promethium region.
= Data for the neighboring elements is taken from [47]. Arbitrary offsetsN 82, 84, 86 is given in Table 4. As a weighted average of multiples of 0.2 fm2 are added to the different isotopic chains for
we obtain δ〈r2〉N ,N+2 = 0.276(13) fm2. The field shift con- visual separation. For details see text
stant Fi of the two investigated transitions is varied until the
change in mean square charge radii, related to Fi with Eq. 4,
matches this value. We obtain F468/F452 with just the isotope shifts as underlying data,
i.e. independent of the assumptions made above. The rela-
′
F = −1210(60)MHz/fm2 tion between the modified isotope shifts μδνA,A in different452
= + 2 atomic transitions i, j is expected to be linear up to highF468 1015(55)MHz/fm precision, and can be expressed as
in the 452 nm and 468 nm transition, respectively, where ( )′ F ′ F
the uncertainty is derived from the standard deviation of A,A i A,A iμδν = μδν + Ki − K j . (5)
δ〈 i jr2〉N ,N+2 in Table 4. The results, together with the data of Fj Fj
the neighboring elements from [47], are displayed in Fig. 7.
The trend in charge radii exhibits several interesting fea- The ratio of the respective field shift constants is given by
tures. Most noticeable is the kink in the curve of all elements the line slope. The King–Plot of the modified 452 nm and
at the magic neutron number N = 82, followed by a similar 468 nm isotope shifts is presented in Fig. 8. The best fit to the
slope in 〈r2〉A,A′ for all displayed elements with increasing data yields a slope of F468/F452 = −0.82(24), in excellentδ
neutron number. Below N = 82, a Z -dependence in the slope agreement with the value of F468/F452 = −0.84(6) from the
can be observed. While Ce and Nd charge radii are rather neighboring element analysis. Note that using this ratio from
constant, Sm and Gd show increasing charge radii towards the King–Plot, the Fi values would be shifted apart from
neutron deficient isotopes. Pm lies exactly in between these each other by ≈ 30 MHz, well within the stated uncertainty
two trends, which highly motivates further measurements in from the neighboring element analysis. For the mass shift
this region. Note that an even more distinct Z -dependence is constants Ki , on the other hand, the King–Plot analysis is
observed around the N = 28 shell closure, which is discussed less conclusive, since the uncertainty of the offset is in the
e.g. in [48]. Lastly, one should note the sudden increase in order of 150 % of the value itself and consistent with zero.
the charge radius of Eu from N = 88 to N = 89, which From the best fit we can extract
has been related to the influence of the almost-doubly magic
146Gd [5]. K468 + 0.82(24) · K452 = 620(940)GHz/u
In order to verify the results of the neighboring elements
analysis and to obtain a reasonable error estimate on Fi , and which agrees with our assumption of
accordingly on δ〈r2〉A,A′ , a complementary King-plot anal-
ysis was performed. A King–Plot can be used to determine NMS468 + 0.84(6) · NMS452 = 640(14)GHz/u (6)
123
Eur. Phys. J. A            (2020) 56:69 Page 11 of 13    69 
induced by the single proton and the single neutron orbitals,
whereas in particular the neighboring 147Pm has a rather high
quadrupole moment, resulting in a staggering parameter sig-
nificantly different from 1.
5 Summary
We measured hyperfine spectra of the five long-lived prome-
thium isotopes 143−147Pm in two different atomic ground
state transitions, allowing the precise extraction of hyperfine
coupling constants and isotope shifts. From this data, refined
values for the magnetic moments of 143,144,145Pm were
146
Fig. 8 King–Plot analysis of the investigated optical ground-state tran- extracted. The magnetic moment of Pm and quadrupole
sitions at 452 nm and 468 nm. The modified isotope shifts are plotted moments of 143,144,146Pm were determined for the first
with respect to the reference isotope 147Pm. The solid orange line dis- time. Since the excited state configuration in the transi-
plays the best fit to the data and the green dashed line has a fixed slope tions under investigation is unknown, a precise analysis
of F468/F452 = 0.84, as obtained from the analysis of neighboring
elements of the isotope shifts was hampered. However, a compari-
son with neighboring elements allowed good estimate on
Table 5 Changes in mean square charge radii with respect to 147Pm. the transitions’ field shift constants and changes in mean
The values derived from isotope shifts in the 452 nm and the 468 nm square charge radii. The results indicate that the specific
transitions are averaged, with uncertainties in brackets. The last col- mass shift in both transitions is small compared to the field
umn contains the staggering parameter γA for the odd-neutron-number
isotopes shift. A King–Plot analysis confirmed the consistency of
our results and allowed an estimate of systematic uncertain-
A 〈r2〉147,Aδ 2avg (fm ) γA ties.
146 −0.17(2) 0.60(17) For a better understanding of the evolution of deforma-
145 −0.24(3) tion, visible in nuclear moments and changes in mean square
144 −0.42(5) 0.77(15) charge radii, it is of high relevance to continue laser spec-
143 −0.53(6) troscopy studies of Pm, both towards
151Pm, but also of light
Pm nuclei below N = 82. With this work we established a
basis for future experiments aiming for more exotic nuclei
at radioactive ion beam facilities, possibly by using the PI-
but prevents any reasonable conclusions about the individual LIST ion source, which has recently been adapted for on-line
components. Note that the uncertainty in (6) would increase application.
to 460 GHz/u when the assumption SMSi = 0 ± NMSi
would have been considered. Acknowledgements Open Access funding provided by Projekt DEAL.
Finally, we extract values for the changes in nuclear mean The authors thank Stephan Fritzsche, Randolf Beerwerth and Dorothea
square charge radii, as given in Table 5. From the values Schumann for their ideas and stimulating discussions. We would also
〈 2〉147,A 〈 2〉147,A like to thank Nick van der Meulen for support with the target pelletof δ r 452 and δ r 468 , individually derived from the preparation. D. Studer acknowledges financial support from the EU
isotope shifts in the transitions under investigation, we calcu- through ENSAR2-RESIST (Grant No. 654002) and from the Bun-
lated an average 〈r2〉147,Aδ avg . The results indicate an odd-even desministerium für Bildung und Forschung (BMBF, Germany) under
staggering in mean square charge radii, which is defined via grant No. 02NUK044B. R. Heinke acknowledges financial support
from the BMBF Germany under Grant No. 05P15UMCIA. S. Brac-
〈 〉 − cini and T.S. Carzaniga acknowledge the support of the Swiss National= 2δ r
2 A 1,A Science Foundation (SNSF) (Grants: 200021-175749, CRSII5-180352,
γA
δ〈r2〉A−1,A+1 (7) CR23I2-156852).
for odd-neutron-number isotopes, with the staggering param- Author contributions Irradiation of the Nd-target at the Bern med-
ical cyclotron by T.S. Carzaniga and S. Braccini. Target production,
eter γA [49]. For γA < 1, this is referred to as normal odd- post-irradiation radiochemical separation and γ -spectroscopic mea-
even staggering. It is qualitatively related to the quadrupole surements by J. Ulrich. 147Nd tracer production by K. Eberhardt. 147Pm
deformation, as given in Table 3. In 144Pm, γA is closer to sample production by U. Köster. Laser spectroscopic measurements
1 (little staggering), since the deformation in 144,145Pm is by D. Studer, R. Heinke and S. Raeder. Data analysis, figures and
146 manuscript draft by D. Studer. All authors contributed to the finalsimilar, despite the different sign in Qs . Pm, however, manuscript. The supervisors of this project were R. Dressler (PSI) and
is almost spherical due to the compensating deformation K. Wendt (U. Mainz).
123
   69 Page 12 of 13 Eur. Phys. J. A            (2020) 56:69 
Data Availability Statement This manuscript has no associated data or 18. ENSDF database as of December 2019. http://www.nndc.bnl.gov/
the data will not be deposited. [Author’s comment: comment: The spec- ensarchivals/
troscopic data of all laser scans which were performed within the scope 19. C. Mattolat, S. Rothe, F. Schwellnus, T. Gottwald, S. Raeder, K.
of this work are available upon request to the corresponding author. All Wendt, T. Iguchi, K. Watanabe, A.I.P. Conf, Proc. 1104, 114 (2009).
other relevant data is included in the presented manuscript.] https://doi.org/10.1063/1.3115586
20. S. Rothe, B.A. Marsh, C. Mattolat, V.N. Fedosseev, K. Wendt,
Open Access This article is licensed under a Creative Commons Attri- J. Phys. Conf. Ser. 312, 052020 (2011). https://doi.org/10.1088/
bution 4.0 International License, which permits use, sharing, adaptation, 1742-6596/312/5/052020
distribution and reproduction in any medium or format, as long as you 21. T. Kessler, H. Tomita, C. Mattolat, S. Raeder, K. Wendt, Laser Phys.
give appropriate credit to the original author(s) and the source, pro- 18(7), 842 (2008). https://doi.org/10.1134/S1054660X08070074
vide a link to the Creative Commons licence, and indicate if changes 22. V. Sonnenschein, I.D. Moore, S. Raeder, M. Reponen, H. Tomita,
were made. The images or other third party material in this article K. Wendt, Laser Phys. 27, 085701 (2017). https://doi.org/10.1088/
are included in the article’s Creative Commons licence, unless indi- 1555-6611/aa7834
cated otherwise in a credit line to the material. If material is not 23. M. Verlinde, K. Dockx, S. Geldhof, K. König, D. Studer, T.E. Coco-
included in the article’s Creative Commons licence and your intended lios, R. de Groote, R. Ferrer, T. Kieck, I.D. Moore, W. Nörter-
use is not permitted by statutory regulation or exceeds the permit- shäuser, S. Raeder, P. van den Bergh, P. van Duppen, K. Wendt,
ted use, you will need to obtain permission directly from the copy- submitted to Appl. Phys. B (2019)
right holder. To view a copy of this licence, visit http://creativecomm 24. T. Kieck, S. Biebricher, C.E. Düllmann, K. Wendt, Rev. Sci.
ons.org/licenses/by/4.0/. Instrum. 90, 053304 (2019). https://doi.org/10.1063/1.5081094
25. D.A. Fink, S.D. Richter, K. Blaum, R. Catherall, B. Crepieux,
V.N. Fedosseev, A. Gottberg, T. Kron, B.A. Marsh, C. Mattolat,
S. Raeder, R.E. Rossel, S. Rothe, F. Schwellnus, M.D. Seliverstov,
M. Sjödin, T. Stora, P. Suominen, K. Wendt, Nucl. Instrum. Meth-
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123
Chapter5
Summary and outlook
The scope of this dissertation spans over various applications of laser resonance
ionization, specifically covering sensitive spectroscopy for atomic and nuclear
structure research. Several publications emerged from this work, five of which
were presented within this thesis. Development efforts concerned technical aspects
of narrowband lasers, accurate wavelength measurements and performance tests
of the novel PI-LIST ion source. On top of that specific spectroscopic techniques,
i.e. resonant de-excitation, a refined approach in saddle-point ionization and new
laser excitation schemes for Dy and Pm were addressed. Nonetheless, the included
publications primarily focus on measurements of fundamental atomic and nuclear
properties, significantly refining and extending existing literature data. In this
context, the outstanding capabilities of RIS, covering both atomic and structure
research, were demonstrated.
Publication I focused on the search for a specific atomic ground-state transition
in Dy. Its characteristics, being both extremely weak and with its wavelength of
λ ≈ 1001 nm close to the infrared edge of the Ti:sapphire gain profile, rendered this
experiment extremely challenging and called for an unconventional spectroscopic
approach. Rather than direct excitation spectroscopy, a full three-step ionization
scheme was established based on a stronger ground-state transition with a similar
configuration in the upper energy level. The searched upper level of the 1001 nm
transition could then be localized by resonant de-excitation of the second excited
state, competing with the resonant ionization process, thus causing a dip in the
ion signal. Direct excitation spectroscopy became feasible through this previously
established ionization scheme. Isotope shifts in both investigated ground-state
transitions, at 741 nm and 1001 nm, were measured for all stable isotopes, includ-
ing the least abundant ones, 156Dy (0.0056 %) and 158Dy (0.095 %). The obtained
data served as an important stepping stone towards precision spectroscopy of the
1001 nm transition on cold atoms trapped in a MOT, which was afterwards suc-
cessfully performed [115].
121
5. Summary and outlook
Publication II, also dealing with Dy atomic structure, represents an exemplary case
for the measurement of the IP in a rare-earth atomic system through Rydberg-
spectroscopy. Spectroscopic data obtained in different excitation schemes was
evaluated and Rydberg-convergences could be identified. Although they were
partly subject to strong perturbations, a precise value of IPRydDy = 47 901.76(5) cm
−1
could be determined. Note that this is in perfect agreement with the result of
IPSPDy = 47 901.8(3) cm
−1, obtained from saddle-point ionization [128, 138], i.e. the
technique which was used in Publication III for the determination of IPPm. Addi-
tionally, the efficiency of the investigated ionization schemes was assessed. For a
three-step scheme, where all transitions could be saturated, an efficiency of 25(4)%
was demonstrated in a series of dedicated measurements on calibrated samples. It
serves as an alternative to previously used schemes relying on dye lasers or non-
resonant ionization (cf. [37]), and was later used for measurements on Dy isotope
ratios in a 163Ho sample used for the ECHo project [137].
Moving on to the scarcely studied atomic system of Pm, Publication III represents
one of the most comprehensive spectroscopic investigations of this element so far.
Over 1000 atomic transitions were measured in different RIS schemes, and are tab-
ulated in appendix A.3. This extraordinarily rich atomic spectrum prevented an
unambiguous identification of Rydberg states, as carried out successfully in Dy.
Consequently, the approach of saddle-point ionization was applied for the deter-
mination of the IP. In order to overcome limitations through the efficiency of this
method, the measurement process was turned around: rather than scanning the
laser frequency across ionization thresholds for a number of given field strengths,
the electric field strength was varied to effectively scan the threshold itself across
several weakly bound atomic levels, while keeping the laser on resonance. While
this introduced some operational complications, the sensitivity was increased by
at least two orders of magnitude, rendering the experiment feasible in the first
place. The precision of the extracted value of IPPm = 45 020.8(3) cm−1 is compa-
rable to that of most stable elements and closes the last gap for an experimental
value of this fundamental property in the Periodic Table below Z = 100 (cf. Fig.
1 in Publication III). Although the efficiency of the newly developed ionization
schemes could not be quantified due to the limited sample amounts, two promis-
ing schemes were added to the RILIS database [37]. They form the basis of the
high-resolution spectroscopy studies of Publication V.
Publication IV presents a characterization of laser frequency measurement in high-
resolution spectroscopy. Several commercial wavelength meters were tested with
respect to their long-term stability and relative accuracy by a collaboration of Euro-
pean RIS teams. Long-term drifts could be effectively suppressed by frequent cal-
ibration or data post-processing, using an absolute frequency reference. In Mainz,
a Rb saturated absorption spectroscopy setup was installed for this purpose. More
importantly, device-specific systematic deviations in relative frequency measure-
122
ment were discovered using complementary measurement methods, i.e. frequency
combs and scanning Fabry-Pérot interferometers. The latter is a cost-efficient addi-
tion to any narrow-linewidth laser setup and may be used to eliminate systematic
effects introduced by wavelength meters. As a result, a long-term relative accuracy
in the range of 2 MHz can be achieved.
Finally, Publication V deals with high-resolution spectroscopy on a chain of long-
lived Pm isotopes, which were produced in a cyclotron. This work marks the
first high-precision laser spectroscopic study on neutral Pm. Additionally, the
experiment is an important performance test for the PI-LIST ion source, demon-
strating its capabilities with regard to isobaric background suppression, effi-
ciency and spectroscopic linewidth. Even with high isobaric contamination of
Pm/Nd ≈ 1/100 and low sample amounts in the order of 1011 atoms, experi-
mental linewidths between 100 and 200 MHz were achieved. The two investigated
atomic ground-state transitions were characterized and the obtained spectra deliv-
ered valuable data for the extraction of nuclear moments and mean square charge
radii. For the majority of investigated nuclides these quantities were previously
unknown. Furthermore, the results serve as starting point for high-resolution in-
source spectroscopy studies at on-line RIB facilities and pave the way for the ex-
traction of nuclear properties of short-lived Pm isotopes. An on-line experiment
at CERN-ISOLDE will be assessed after the long shutdown in 2021 the RILIS team
using the PI-LIST ion source, which is currently prepared for on-line application.
In conclusion, goals of the EU RTN project RESIST could be well addressed, at the
same time providing fundamental atomic and nuclear structure data. The PI-LIST
was proven to be a valuable tool for high-resolution spectroscopic studies under
challenging conditions, which served as further step towards routine operation of
this novel instrument. Under the aspect of laser development, the accuracy of pre-
cision frequency measurement was characterized, ensuring the reliability of future
spectroscopy results. Additionally, two laser prototypes were developed as part of
this thesis (see appendix A.1). The compact-footprint injection-seeded laser was
used successfully for Doppler-free two-photon spectroscopy at ISOLDE [59] and
has now become a permanent part of the RILIS laser setup. The concept of the un-
seeded bowtie-resonator laser, on the other hand, was abandoned due to spectral
stability problems, which could not be overcome. As a future prospect, this laser
concept is now being adapted for cw operation, offering superior stability [60, 61].
With recently upcoming high-power laser diodes, which are suitable as Ti:sapphire
laser pump source, it is a cost-efficient alternative to expensive commercial laser
systems. It will be used as seed for a pulsed amplifier, i.e. an injection-seeded
Ti:sapphire laser. Compared to ECDL master lasers, the spectral coverage naturally
matches the Ti:sapphire amplifier emission range and eliminates the need for fre-
quent modification of the laser setup. Lastly, the applied spectroscopic techniques
will be highly beneficial in the upcoming LISA (Laser Ionization and Spectroscopy
of Actinides) project, which acts as a follow-up to RESIST. Specifically, resonant
123
5. Summary and outlook
de-excitation is now considered in search of the lowest-lying odd-parity states in
Ac, which were not observed so far. Recent atomic structure calculations [162]
serve as a starting point for this experiment, and the experimental results can later
be used to benchmark the theoretical predictions. Another objective of LISA is the
determination of precision values for electron affinities and ionization potentials
of actinide elements. In context of the latter, saddle-point ionization may play an
important role. As demonstrated in Pm, it is perfectly suited for application in
the actinide series, where similarly low sample amounts and complex spectra are
expected.
124
ChapterA
Appendix
A.1 Laser prototypes
The following section briefly introduces two laser prototypes, that were developed
in the framework of this dissertation. The development was based on a Wolfram
Mathematica script implementing Gaussian ray transfer matrix calculations, more
specifically the so-called ABCD formalism. In simple terms, an incident Gaussian
beam with position vector ri = (ri, φi), where ri and φi are the distance and angle
to the z-axis, respectively, is transformed to r f = (r f , φ f ) through a 4× 4 matrix
M representing an optical element. The beam transport along a laser resonator
can thus be calculated through composition of all optical elements and free beam
paths. In order to obtain a stable resonator, the beam should be transferred to its
original position vector after one round trip. Moreover, the difference in tangential
and sagittal beam waist, i.e. parallel and perpendicular to the resonator plane,
should be minimized for an optimal beam profile. For details on the ABCD for-
malism, which shall not be further discussed here, the reader is referred to [58] or
to [62], where the latter gives a compact summary of the most important concepts
and equations.
The script that was used here directly generates beam waist plots for the chosen
resonator geometry, as well as a printable 2D layout, which can be fixed to an
optical breadboard and allows for fast setup and testing. All calculations were
performed for a wavelength of 800 nm, near the gain maximum of the Ti:sapphire
laser medium. Calculated Brewster angles should thus be close to optimum over
the whole Ti:sapphire output range.
Printable layouts of both laser types are attached at the end of this section. Note
that the radius of curvature for curved mirrors is rcurv = 75 mm. Unlabeled optical
mounts serve as alignment help. All length units are given in mm.
125
A. Appendix
CM2 CM1
L Ti:sa
pump
seed
PAM OC
output
Figure A.1.: Photograph of the compact-footprint injection-seeded Ti:sapphire laser
prototype at the ISOLDE-RILIS. L: plano-convex lens; CM: curved mirror;
Ti:sa: Ti:sapphire crystal; PAM: piezo-actuated mirror; OC: output-coupler.
A.1.1 Compact-footprint injection-seeded laser
As the name suggests, the compact-footprint injection-seeded laser is based on the
injection-seeded laser presented in Sec. 2.1.3. It was designed and successfully
used for Doppler-free two-photon in-source spectroscopy at the ISOLDE-RILIS
[59]. Considering the operation purpose, the resonator was designed as small
as possible. A photograph and the calculated 1/e beam waist of the resonator are
shown in Figs. A.1 and A.2, respectively. Apart from the practical advantage of
taking up less valuable space on the laser table (which is particularly important
at ISOLDE-RILIS), the shorter resonator exhibits a larger FSR and shorter pulse
length compared to the ”standard” injection-seeded laser. The large FSR close to
900 MHz greatly suppresses side-modes and thus allows for higher dither ampli-
tudes in the resonator lock, if needed. The short pulse length increases the power
density of the output radiation, which is particularly important in the non-linear
process of two-photon excitation. Moreover, it facilitates temporal de-coupling of
subsequent excitation steps, which is sometimes necessary to avoid power broad-
ening (see Sec. 3.3.4). On the other hand, shorter pulses lead to an increase in the
Fourier-limited linewidth, which was measured as 21 MHz in [59]. With a Gaus-
sian time-to-bandwidth product of TDP = 0.44, this corresponds to a pulse length
of 21 ns.
This laser was installed at ISOLDE-RILIS by the author in March 2017, where las-
ing could be achieved within several days. Further optimization and locking was
then performed by the local PhD student Katerina Chrysalidis.
The printable layout attached to the end of this section uses top-adjustable LIOP-
TEC 1” Star mounts, with round 1” diameter posts.
126
A.1. Laser prototypes
0.03
0.25 0.02
0.20 0.01
0.15 0.00
0.10 -0.01
0.05
Tangential -0.02
Sagittal
0.00 -0.03
0 50 100 150 20[0 ] 250 300 0 50 100 150 200 250 300resonator position mm resonator position [mm]
3000 Figure A.2.: Left: Calculated 1/e beam wais0.t10for the compact-footprint injection-
Tangential Tangential
Sagittal seeded laser in the sagittal and tangenti l resonator planes. The piezo-2000 Sagittal
actuated mirror marks the zero positi0o.0n5 of the resonator. Right: 1/e beam
1000 waist difference (tangential−sagittal).
0 0.00
-1000 A.1.2 Unseeded bowtie-resonator laser
- -0.052000
- The unseeded bowtie-resonator laser is based on a previous design by T. Kron,3000
0whic50h is 1d00escr1i5b0ed i2n0[0 []742]50and
-0.10
30w0 as already us0ed fo5r0 hig1h00-res1o5l0utio2n00 spe25c0tros3c0o0 py
resonator position mm resonator position [mm]
on stable copper isotopes [91] and long-lived Tc isotopes [163]. It is designed to
achieve single-mode operation without the use of a cw master laser, hence the
name unseeded laser. The bowtie-shaped geometry, which is necessary to avoid
spatial hole burning, is adapted from the injection-seeded laser. Single-mode op-
eration is achieved by combination of several frequency-selective elements, i.e. a
LF and a 0.3 mm FPE, similar to the standard Ti:sapphire laser (see Sec. 2.1.1),
with an additional air-spaced etalon (ASE). The latter is composed of two wedged
mirrors with a partially reflective coating on one side and an anti-reflection coat-
ing on the other side. Frequency scanning can be performed by piezo-actuators on
one cavity mirror and one of the mirrors of the ASE.
The novel design presented here was developed to improve the stability of single-
mode operation by minimizing the resonator length, thus increasing the FSR, as
well as by improving the mechanical damping of the cavity base plate through sor-
bothane isolators. Additionally, the R = 0.3 mirrors used in the ASE were replaced
by R = 0.4 mirrors for increased finesse. The resulting geometry is shown in Fig.
A.3, with the corresponding beam waist calculations in Fig. A.4. This laser type
was used for spectroscopy in the 741 nm transition of Dy, presented in Publication
I. Although single-mode operation could be achieved, it was difficult to maintain
while scanning the laser frequency, which resulted in visible side-modes in the
recorded spectrum, similar to what has been observed in Cu [91]. Consequently,
it was concluded that this design did not offer major advantages over its prede-
cessor. However, one should note that as an alternative mode of operation, it is
possible to set a fast voltage ramp on the piezo-actuated cavity mirror, resulting in
a ”scrambled” frequency output with an average linewidth of ≈ 600 MHz, which
127
wavefront radius [mm]
beam waist [mm]
CM1
CM1
Ti:sa
CM2
Ti:sa
CM2
M1
OC
1/wavefront radius [mm] beam waist difference [mm]
CM1 CM1
Ti:sa Ti:sa
CM2 CM2
M1 OC
A. Appendix
L CM2 CM1
pump Ti:sa
SE
PAM output
LF OC
ASE
Figure A.3.: Photograph of the unseeded bowtie-resonator Ti:sapphire laser pro-
totype. L: plano-convex lens; CM: curved mirror; Ti:sa: Ti:sapphire crystal;
SE: solid thin etalon; PAM: piezo-actuated mirror; LF: Lyot filter; ASE: air-
spaced etalon; OC: output-coupler.
is superior to the standard dual-etalon laser [50]. A comparison between normal
and ”scrambled” scanning operation is shown in Fig. A.5. The left panel corre-
sponds to Fig. 4 in Publication I, whereas the right panel shows the same spectra
in ”scramble” mode. While this does not offer superior data quality in the present
case, laser operation is strongly simplified and may be considered for in-source
spectroscopy of actinide elements, where the expected Doppler-broadening is in
the order of ≈ 1 GHz due to their high mass (cf. Fig. 3.2).
The printable layout as given at the end of this section uses Thorlabs VM1-M
mounts with custom-build rectangular posts for easy alignment. Etalons are not
included in the layout, since their position does not notably influence the resonator
geometry√. Note that this layout is designed to fit on A3 paper size and was scaled
down by 2 to fit on an A4 paper. For printing it needs to be re-scaled accordingly.
128
A.1. Laser prototypes
0.03
0.5 Tangential
Sagittal 0.02
0.4
0.01
0.3
0.00
0.2 -0.01
0.1 -0.02
0.0 -0.03
0 100 200 300 400 500 0 100 200 300 400 500
resonator position [mm] resonator position [mm]
3000 Figure A.4.: Left: Calculated 1/e beam wa0i.1s0t for the unseeded bowtie-resonator
Tangential
Sagittal laser in the sagittal and tangential resona
TtaongrenptialSagittal lanes. The piezo-actuated mir-2000
ror marks the zero position of the reson0.0a5tor. Right: 1/e beam waist difference
1000 (tangential−sagittal).
0 0.00
-1000
- -0.052000
-3000 -0.10
0 100 200 300 400 500 0 100 200 300 400 500
resonator position [mm] resonator position [mm]
104
104
1000
1000
100
100
10
10
1 1
0.1 0.1
0 1000 2000 3000 4000 5000 6000 0 1000 2000 3000 4000 5000 6000
ν164-ν [MHz] ν164-ν [MHz]
Figure A.5.: Spectrum of the 741 nm line in Dy for all stable even-even isotopes
(no HFS) using the unseeded bowtie-resonator laser. Left: normal operation,
corresponding to Fig. 4 in Publication I. Right: ”scramble” mode, with a
fast piezo ramp on the piezo-actuated cavity mirror, resulting in an average
linewidth of ≈ 600 MHz.
129
wavefront radius [mm]
beam waist [mm]
ion counts [1/s]
CM1
Ti:sa
CM1
CM2
Ti:sa
CM2
M1
OC
LF
LF
1/wavefront radius [mm] beam waist difference [mm]
CM1 CM1
Ti:sa Ti:sa
CM2 CM2
M1 OC
LF LF
200 mm
Compact-footprint injection-seeded laser
Print on A4 paper.
Make sure to select "actual size" CM1
in printer settings.
CM2
Ti:sa
51
20
20 29.6°
34.9°
34.9° 82.7 10
0
OC
PAM 34.9° 34.9°
61.5
Total resonator length: 335 mm
Free spectral range:     894 MHz
290 mm
285 mm
CM1
CM2
Ti:sa
29.6°
50
0
20 2
35.1°
35.1°
1
5 56 81 .0
PAM 35.1° OC
30
141.1
57.0° 35.1°
LF
Unseeded bowtie-resonator laser
Total resonator length: 593 mm
Print on A3 paper. Free spectral range:     506 MHz
Make sure to use 141.4 % (=√2) scaling
in the printer settings.
395 mm
A. Appendix
A.2 Supplemental Material for ”Laser spectroscopy of the 1001-nm ground-state
transition in dysprosium”
The following table contains atomic transition data in dysprosium, that was pub-
lished as supplemental material to Publication I: Phys. Rev. A 98, 042504 (2018)
DOI 10.1103/PhysRevA.98.042504. The data was obtained by scanning a laser
from 401 nm to 437 nm, with a fixed first excitation step at 740.962 nm and a non-
resonant ionization laser near 780 nm. The corresponding spectrum is given in Fig.
A.6.
Step 2 wavenumber (cm 1)
25000 24500 24000 23500 23000
105
104
103
102
400 405 410 415 420 425 430 435 440
Step 2 wavelength (nm)
Figure A.6.: Spectrum of the second excitation step in Dy, starting from the
13 495.96 cm−1 excited state. For details see text.
132
Ion count rate (1/s)
Supplemental material for "Laser spectroscopy of the 1000 nm ground state transition
in dysprosium"
D. Studer, L. Maske, P. Windpassinger, and K. Wendt
Institut für Physik, Johannes Gutenberg-Universität Mainz, 55128 Mainz, Germany
(Dated: July 20, 2018)
TABLE I. Complete list of second excitation steps starting from the level at 13495.96 cm−1(J = 9). The transition wavelength
error is 0.0015 nm. If within the error range, corresponding upper energy levels and J-values, as listed in the NIST database
[1], are included.
λ [nm] E −1 −1 −1up [cm ] J λ [nm] Eup [cm ] J λ [nm] Eup [cm ] J
439.9536 continued continued
439.1222 421.2404 413.1506 ∗ 24204.19 8
436.7539 36392.11 8 421.2120 413.0479 37706.12 10
434.9479 36487.20 9 420.1685 37295.97 7† 412.7220 ∗ 24229.22 9
434.8932 36490.07 10 420.0148 412.2835 37751.03 9
433.6905 36553.84 8 419.9625 411.1571
433.5572 419.8388 411.1114 37820.22 8
432.8343 36599.44 8 419.7614 411.0837
431.3647 419.6717 410.7457 37841.84 8
430.6329 36717.57 9 419.6589 410.6156 ∗ 24353.58 7
430.4753 419.5268 410.1022
429.8364 36760.64 8 419.4721 410.0151
429.3162 419.4336 409.6383
428.9732 36807.39 8 419.3938 37339.89 8 409.2031 37933.63 9
428.6989 36822.27 9 419.3034 408.6275
428.4753 419.2812 408.2147 37992.78 8
427.7745 419.2463 407.2033
427.1762 36905.44 10 419.1803 406.7968 38078.12 8
426.2856 36954.32 9 418.9332 37366.09 7† 408.0718
426.1049 36964.32 9 418.8958 406.2176
425.3207 37007.58 10 418.8343 405.6035 38150.52 8
423.8807 37087.47 8 418.8091 405.4961
424.0865 418.7886 405.2414
423.6245 418.7574 405.0809
423.5194 418.7415 405.0487
422.3842 418.7256 404.7105
422.3642 418.6708 404.5512
422.2508 418.6350 404.3931
422.2356 418.3647 37398.46 8 404.3583
422.2243 417.7956 403.9844
422.2075 416.1240 37527.15 8 403.8934 38254.97 8
422.1893 415.9216 403.3975 38285.36 9
422.0029 415.0086 37591.83 9 402.6736 38329.91 10
421.9295 414.0714 37646.28 8o 402.2465 38356.27 8
421.7075 413.5472 37676.89 8
421.6332 413.5864
∗ ground state transition
†∆J > ±1
o odd parity
[1] A. Kramida, Y. Ralchenko, J. Reader, and the NIST ASD Team, “NIST Atomic Spectra Database,” (2018).
A. Appendix
A.3 Supplemental Material for ”Atomic transitions and the first ionization po-
tential of promethium determined by laser spectroscopy”
The following tables contain atomic transition and energy level data for neutral
promethium, that was published as supplemental material in Publication III: Phys.
Rev. A 99, 062513 (2019) DOI 10.1103/PhysRevA.99.062513.
Table I to Table VII list observed atomic lines. For an overview of the used exci-
tation schemes and the respective abbreviations see Fig. 3 in the article. Since the
tables also include relative intensities for most observed lines, plots of the spectra
are not included here.
Table VIII and Table IX list odd and even energy levels, respectively. The assign-
ments are inferred according to the rules presented in [164].
Table X comprises values of the first ionization potential for all elements up to
Z = 103 and the respective uncertainties, which were used for Fig. 1 in the arti-
cle.
134
Supplemental material for "Atomic transitions and the rst ionization potential of
promethium determined by laser spectroscopy"
Dominik Studer,1, ∗ Stephan Heinitz,2 Reinhard Heinke,1 Pascal Naubereit,1 Rugard
Dressler,2 Carlos Guerrero,3 Ulli Köster,4 Dorothea Schumann,2 and Klaus Wendt1
1Institut für Physik, Johannes Gutenberg-Universität Mainz, 55128 Mainz, Germany
2Paul-Scherrer Institut, 5232 Villigen, Switzerland
3Dpto. de Física Atómica, Molecular y Nuclear, Universidad de Sevilla, 41012 Sevilla, Spain
4Institut Laue-Langevin, 38042 Grenoble, France
(Dated: May 29, 2019)
I. ATOMIC TRANSITIONS IN PM I BY WAVELENGTH
TABLE I. Wavelengths and transition wavenumbers of new Pm I transitions, as observed in the excitation scheme FES, starting
from the 4f56s2 5Ho ground state ne structure multiplet (J = 5/2, ..., 13J /2) in the range from 415 nm to 472 nm. Lines that
can be found in [1] are not given. A transition wavenumber error of 0.09 cm−1 is estimated from deviations of observed lines to
corresponding literature values in [1].
λ (nm) ν̃ (cm−1) λ (nm) ν̃ (cm−1)
467.1271 21 407.45 432.9483 23 097.44
464.5078 21 528.16 431.7275 23 162.76
461.2212 21 681.57 430.3682 23 235.92
459.2919 21 772.65 429.6406 23 275.27
456.8613 21 888.48 427.2667 23 404.58
454.9335 21 981.24 427.1864 23 408.98
452.8707 22 081.36 426.1191 23 467.62
452.3198 22 108.25 425.7047 23 490.46
451.9271 22 127.46 423.1948 23 629.78
450.2230 22 211.22 422.4935 23 669.00
445.6781 22 437.72 421.9184 23 701.26
435.4264 22 965.99 420.7243 23 768.53
435.3269 22 971.24 417.9427 23 926.73
433.8384 23 050.06 417.1122 23 974.37
433.7817 23 053.07 416.5837 24 004.78
433.6554 23 059.79 416.4680 24 011.45
2
TABLE II. Second excitation steps, as observed in the excitation schemes SESA, SESB and SESC. The transition wavenumber
uncertainty is 0.06 cm−1. Corresponding to the excitation scheme, lower level energies El and total angular momenta Jl are
given. The upper energy levels have odd parity for all schemes. Relative intensities are given, but should be treated carefully
as the third excitation step has an arbitrary wavelength and may be resonant to an auto-ionizing transition.
λ (nm) E (cm−1) J E (cm−1l l u ) Irel λ (nm) El(cm
−1) Jl E
−1
u(cm ) Irel
909.1162 22 080.08 5/2 33 079.8 57 878.5937 22 080.08 5/2 33 461.9 644
907.8514 21 348.22 7/2 32 363.2 25 878.5307 21 348.22 7/2 32 730.9 119
907.6267 21 348.22 7/2 32 366.0 161 877.7962 21 348.22 7/2 32 740.4 304
907.2064 22 080.08 5/2 33 102.9 44 877.6647 21 348.22 7/2 32 742.1 76
905.6460 21 348.22 7/2 32 390.1 33 877.2443 22 080.08 5/2 33 479.4 85
904.3576 22 080.08 5/2 33 137.7 85 877.0358 22 080.08 5/2 33 482.1 616
903.9762 22 080.08 5/2 33 142.3 96 876.9105 21 143.06 7/2 32 546.7 8
901.8636 22 080.08 5/2 33 168.2 24 876.0522 21 348.22 7/2 32 763.1 131
900.8337 21 348.22 7/2 32 449.0 259 875.9097 21 143.06 7/2 32 559.7 8
900.0311 22 080.08 5/2 33 190.8 341 875.8704 22 080.08 5/2 33 497.3 441
898.7373 21 348.22 7/2 32 474.9 105 875.7395 21 348.22 7/2 32 767.1 90
898.4834 22 080.08 5/2 33 209.9 98 874.8512 22 080.08 5/2 33 510.6 870
897.2069 21 348.22 7/2 32 493.9 65 874.4846 21 143.06 7/2 32 578.4 67
897.1827 22 080.08 5/2 33 226.1 93 874.1081 22 080.08 5/2 33 520.3 2285
897.0471 22 080.08 5/2 33 227.8 321 873.7907 21 143.06 7/2 32 587.5 4
895.8691 21 348.22 7/2 32 510.6 38 873.2634 22 080.08 5/2 33 531.4 457
895.1104 21 348.22 7/2 32 520.0 20 871.8625 21 348.22 7/2 32 817.9 526
891.9396 21 348.22 7/2 32 559.7 374 871.5657 21 143.06 7/2 32 616.6 23
891.0338 21 143.06 7/2 32 366.0 46 870.9198 22 080.08 5/2 33 562.2 429
890.9575 22 080.08 5/2 33 304.0 89 870.5816 22 080.08 5/2 33 566.7 454
890.4639 21 348.22 7/2 32 578.4 56 868.6450 21 348.22 7/2 32 860.4 63
889.7613 22 080.08 5/2 33 319.0 152 868.1676 21 348.22 7/2 32 866.8 77
889.7364 21 348.22 7/2 32 587.5 115 867.2384 22 080.08 5/2 33 610.9 53
888.3754 21 348.22 7/2 32 604.7 107 866.9691 21 348.22 7/2 32 882.7 29
888.2549 22 080.08 5/2 33 338.1 271 866.5053 21 143.06 7/2 32 683.7 6
887.4418 21 348.22 7/2 32 616.6 148 865.6487 22 080.08 5/2 33 632.2 124
887.1423 22 080.08 5/2 33 352.3 218 865.2606 21 348.22 7/2 32 905.4 34
886.8169 21 348.22 7/2 32 624.5 22 864.8667 22 080.08 5/2 33 642.6 468
886.3874 22 080.08 5/2 33 361.9 426 864.4839 22 080.08 5/2 33 647.7 81
885.3811 22 080.08 5/2 33 374.7 628 864.0721 22 080.08 5/2 33 653.2 232
884.5260 21 348.22 7/2 32 653.7 6 863.4338 21 143.06 7/2 32 724.7 13
883.3989 21 348.22 7/2 32 668.1 292 862.4271 21 348.22 7/2 32 943.4 77
882.6909 22 080.08 5/2 33 409.1 280 861.7821 21 348.22 7/2 32 952.1 142
882.4663 21 143.06 7/2 32 474.9 259 861.6819 22 080.08 5/2 33 685.3 222
882.1863 21 348.22 7/2 32 683.7 451 861.6411 22 080.08 5/2 33 685.8 22
881.9959 21 348.22 7/2 32 686.1 172 860.5925 21 143.06 7/2 32 763.1 10
881.3313 21 143.06 7/2 32 489.5 5 860.3704 22 080.08 5/2 33 703.0 10
879.6942 21 143.06 7/2 32 510.6 12 860.2220 21 348.22 7/2 32 973.1 30
879.2967 22 080.08 5/2 33 452.8 21 859.7980 22 080.08 5/2 33 710.7 9
879.0109 21 348.22 7/2 32 724.7 293 859.7276 22 080.08 5/2 33 711.7 63
878.9688 21 143.06 7/2 32 520.0 11 859.6579 21 348.22 7/2 32 980.8 18
(Continued on next page.)
3
TABLE II: (Continued.)
λ (nm) E (cm−1l ) Jl Eu(cm
−1) I −1rel λ (nm) El(cm ) Jl Eu(cm
−1) Irel
858.5175 22 080.08 5/2 33 728.1 50 834.0306 21 348.22 7/2 33 338.1 27
857.9137 22 080.08 5/2 33 736.3 68 833.0502 21 348.22 7/2 33 352.3 40
856.6005 21 348.22 7/2 33 022.3 293 832.5344 21 348.22 7/2 33 359.7 252
856.5406 21 143.06 7/2 32 817.9 31 832.3808 21 348.22 7/2 33 361.9 29
856.3304 22 080.08 5/2 33 757.8 351 831.4941 21 348.22 7/2 33 374.7 65
856.1504 22 080.08 5/2 33 760.3 82 830.6553 21 348.22 7/2 33 386.9 257
855.1672 22 080.08 5/2 33 773.7 107 829.1234 21 348.22 7/2 33 409.1 208
854.5395 22 080.08 5/2 33 782.3 595 827.1163 21 348.22 7/2 33 438.4 142
853.4363 21 143.06 7/2 32 860.4 11 826.1281 21 348.22 7/2 33 452.8 6
852.9640 21 143.06 7/2 32 866.8 22 825.4299 21 348.22 7/2 33 463.1 247
851.8174 21 143.06 7/2 32 882.7 38 824.1364 21 348.22 7/2 33 482.1 178
850.9522 22 080.08 5/2 33 831.6 237 822.2062 21 348.22 7/2 33 510.6 95
850.7232 21 348.22 7/2 33 102.9 56 821.5500 21 348.22 7/2 33 520.3 82
850.1717 21 143.06 7/2 32 905.4 15 820.7988 21 348.22 7/2 33 531.4 84
848.8406 22 080.08 5/2 33 860.9 465 820.5950 21 348.22 7/2 33 534.5 122
848.7463 22 080.08 5/2 33 862.2 213 818.7294 21 348.22 7/2 33 562.2 39
848.2634 21 348.22 7/2 33 137.0 310 818.4347 21 348.22 7/2 33 566.7 52
848.2169 21 348.22 7/2 33 137.7 42 814.0621 21 348.22 7/2 33 632.2 176
847.8814 21 348.22 7/2 33 142.3 69 813.0423 21 348.22 7/2 33 647.7 167
846.0866 22 080.08 5/2 33 899.2 827 812.6791 21 348.22 7/2 33 653.2 186
844.5634 22 080.08 5/2 33 920.5 807 811.5166 21 348.22 7/2 33 670.8 136
844.4525 22 080.08 5/2 33 922.1 1031 810.5625 21 348.22 7/2 33 685.3 431
843.9424 22 080.08 5/2 33 929.2 205 810.1528 21 348.22 7/2 33 691.6 496
842.9201 22 080.08 5/2 33 943.6 199 808.8326 21 348.22 7/2 33 711.7 49
841.7066 22 080.08 5/2 33 960.7 33 808.2331 21 348.22 7/2 33 720.9 201
840.4995 22 080.08 5/2 33 977.8 87 807.7634 21 348.22 7/2 33 728.1 65
839.5658 22 080.08 5/2 33 991.0 29 805.8254 21 348.22 7/2 33 757.8 84
838.9859 21 348.22 7/2 33 267.4 160 804.7952 21 348.22 7/2 33 773.7 53
838.8404 22 080.08 5/2 34 001.3 258 804.2384 21348.22 7/2 33 782.3 945
837.9388 22 080.08 5/2 34 014.1 24 803.5399 21 348.22 7/2 33 793.2 215
837.4111 22 080.08 5/2 34 021.6 28 801.0632 21 348.22 7/2 33 831.6 866
836.4164 21 348.22 7/2 33 304.0 22 800.9863 21 348.22 7/2 33 832.8 681
835.3611 21 348.22 7/2 33 319.1 97 800.4523 21 348.22 7/2 33 841.2 449
835.3536 22 080.08 5/2 34 051.1 38 799.1909 21 348.22 7/2 33 860.9 140
834.9238 22 080.08 5/2 34 057.2 50
4
TABLE III. Ionizing transitions obtained in the two-step excitation scheme B0. Upper energy levels have odd parity and possible
total angular momenta of J = 5/2,7/2,9/2. The transition wavenumber uncertainty is 0.06 cm−1. Resonances with a gaussian
width of > 0.5 cm−1 are marked with w. Relative line intensities are given.
λ (nm) Eu(cm
−1) Irel λ (nm) Eu(cm
−1) Irel λ (nm) Eu(cm
−1) Irel
432.4560 44 472.0 1 426.7000 44 783.9 25 424.1209w 44 926.4 83
431.7280 44 510.9 47 426.6425 44 787.0 18 424.0939 44 927.9 33
431.4429 44 526.3 17 426.6085 44 787.6 15 424.0836 44 928.5 41
431.4288 44 527.0 14 426.6323 44 788.9 28 424.0719 44 929.1 21
431.2497 44 536.6 93 426.5533 44 791.9 70 424.0427w 44 930.8 64
430.8989 44 555.5 29 426.5326 44 793.1 36 424.0223 44 931.9 42
430.4517 44 565.6 22 426.2568 44 808.3 30 424.0129 44 932.4 136
430.7114 44 567.0 11 426.2085 44 810.9 31 423.9839 44 934.0 37
430.6857 44 579.6 15 426.1398 44 814.7 21 423.9534w 44 935.7 29
430.3098 44 587.3 9 426.0186 44 821.4 47 423.8910 44 939.2 91
430.0654 44 600.5 48 425.9810 44 823.4 17 423.8611 44 940.9 32
430.0378 44 602.0 18 425.8371 44 831.4 32 423.8329 44 942.4 101
429.9929 44 604.4 13 425.7625 44 835.5 20 423.8172 44 943.3 49
429.9521 44 606.6 15 425.7053 44 838.7 46 423.7780 44 945.5 78
429.9103 44 608.9 36 425.6616 44 841.1 81 423.7170w 44 948.9 80
429.8640 44 611.4 23 425.6313 44 842.7 17 423.6585w 44 952.1 93
429.8503 44 612.1 22 425.5579 44 846.8 50 423.6291 44 953.8 88
429.7917 44 615.3 136 425.5409 44 847.7 115 423.6136 44 954.6 57
429.7423 44 618.0 50 425.5053 44 849.7 27 423.5807 44 956.5 20
429.5372 44 629.1 19 425.4869 44 850.7 18 423.5659 44 957.3 22
429.5161 44 630.2 45 425.3641 44 857.5 11 423.5497 44 958.2 39
429.4196 44 635.5 27 425.3456 44 858.5 18 423.5148 44 960.1 17
429.0687 44 654.5 11 425.3067 44 860.7 15 423.4687 44 962.7 107
428.9895 44 658.8 19 425.1762 44 867.9 25 423.4586 44 963.3 299
428.7328 44 672.8 30 425.1185 44 871.1 31 423.4466 44 963.9 84
428.5846 44 680.8 13 425.0373 44 875.6 12 423.4059 44 966.2 216
428.5600 44 682.2 33 424.9829 44 878.6 12 423.3767w 44 967.9 171
428.4969 44 685.6 84 424.9479 44 880.5 16 423.3540 44 969.1 81
428.2358 44 699.8 7 424.9036w 44 883.0 16 423.3187 44 971.1 30
428.1675 44 703.6 57 424.8233 44 887.4 83 423.2207 44 976.6 19
428.0749 44 705.7 17 424.7822 44 889.7 123 423.1885 44 978.3 9
428.1292 44 708.6 10 424.7242 44 892.9 57 423.1635 44 979.7 51
427.8505 44 720.9 22 424.7119 44 893.6 46 423.1512 44 980.4 83
427.5124 44 739.4 30 424.6452 44 897.3 10 423.1300 44 981.6 37
427.4327 44 743.7 58 424.5665 44 901.7 21 423.1074 44 982.9 38
427.3429 44 748.6 41 424.4490 44 908.2 20 423.0971 44 983.5 149
427.2668 44 752.8 35 424.3063 44 916.1 43 423.0861 44 984.1 79
427.1720 44 758.0 27 424.2277 44 920.5 18 423.0707 44 984.9 46
427.0975 44 762.1 12 424.2089 44 921.5 182 423.0385w 44 986.7 256
427.0885 44 762.6 16 424.1758 44 923.4 175 423.0176 44 987.9 19
427.0697 44 763.6 26 424.1681 44 923.8 65 422.9589w 44 991.2 58
426.7537 44 780.9 72 424.1563 44 924.4 162 422.9336 44 992.6 308
(Continued on next page.)
5
TABLE III: (Continued.)
λ (nm) E (cm−1u ) Irel λ (nm) Eu(cm
−1) Irel λ (nm) Eu(cm
−1) Irel
422.9178 44 993.5 324 422.5234 45 015.5 142 421.9484 45 047.8 215
422.8407w 44 997.8 97 422.5135 45 016.1 864 421.9195w 45 049.4 322
422.7662 45 002.0 53 422.4464w 45 019.9 263 421.9038 45 050.3 102
422.7396 45 003.4 28 422.3694w 45 024.2 244 421.8789 45 051.7 53
422.7091 45 005.2 454 422.2592w 45 030.4 314 421.8370w 45 054.1 130
422.6934w 45 006.0 372 422.1570 45 036.1 98 421.7745w 45 057.6 191
422.6407w 45 009.0 522 422.0817 45 040.3 167 421.7142 45 061.0 742
422.5985 45 011.3 136 422.0537 45 041.9 72
422.5439w 45 014.4 151 421.9727 45 046.4 754
TABLE IV. Ionizing transitions obtained in the three-step excitation scheme B1. Upper energy levels have even parity and
possible total angular momenta of J = 3/2, ..., 11/2. The transition wavenumber uncertainty is 0.06 cm−1. Resonances with a
gaussian width of > 0.5 cm−1 are marked with w. Relative line intensities are given.
λ (nm) Eu(cm
−1) Irel λ (nm) Eu(cm
−1) Irel λ (nm) E
−1
u(cm ) Irel
819.0206 44 893.4 72 810.7189w 45 018.4 774 787.3963 45 383.8 57
817.9992 44 908.6 47 810.6722 45 019.1 519 787.2544 45 386.1 25
816.8487 44 925.9 31 810.0609 45 028.4 382 787.1913 45 387.1 218
816.3039 44 934.0 56 809.9504 45 030.1 396 787.1447 45 387.8 321
815.2687 44 949.6 56 809.7886 45 032.6 535 786.9946 45 390.3 16
814.5609 44 960.2 29 809.7315w 45 033.5 135 786.5994 45 396.6 55
814.5238 44 960.8 40 809.6608 45 034.5 249 786.5150w 45 398.0 13
813.9676 44 969.2 20 809.5841w 45 035.7 53 786.3612 45 400.5 46
813.8146 44 971.5 39 809.4568w 45 037.7 114 786.2654 45 402.0 23
813.4912 44 976.4 88 809.3407 45 039.4 148 785.9697 45 406.8 12
813.4302 44 977.3 30 809.0619w 45 043.7 513 785.8403 45 408.9 69
813.3676w 44 978.3 10 808.9287w 45 045.7 172 785.7813w 45 409.9 99
813.2538 44 980.0 111 808.8858w 45 046.4 159 785.6933 45 411.3 162
812.8847 44 985.6 50 808.6691 45 049.7 102 785.4083 45 415.9 144
812.8334 44 986.3 28 808.5382w 45 051.7 62 785.2617 45 418.3 70
812.7397w 44 987.8 59 808.4302w 45 053.3 97 785.1844 45 419.6 46
812.6135 44 989.7 40 808.1689w 45 057.3 276 785.0768 45 421.3 19
812.5482 44 990.7 11 807.8098 45 062.8 329 784.3010w 45 433.9 19
811.9349 45 000.0 58 787.7888 45 377.5 58 783.7188w 45 443.4 25
811.6228 45 004.7 210 787.7083 45 378.7 132 783.2479w 45 451.0 35
811.4806w 45 006.8 339 787.6982 45 378.9 71 782.7559w 45 459.1 80
811.3164 45 009.3 609 787.5557 45 381.2 114 782.4369w 45 464.3 33
810.7948w 45 017.3 196 787.5276 45 381.7 52 782.1880w 45 468.3 94
6
TABLE V. Ionizing transitions obtained in the three-step excitation scheme B2. Upper energy levels have even parity and
possible total angular momenta of J = 3/2, ..., 11/2. The transition wavenumber uncertainty is 0.06 cm−1. Resonances with a
gaussian width of > 0.5 cm−1 are marked with w. Relative line intensities are given.
λ (nm) Eu(cm
−1) Irel λ (nm) Eu(cm
−1) Irel λ (nm) E (cm
−1
u ) Irel
822.4679 44 883.3 72 815.9752 44 978.0 421 807.0533w 45 115.5 370
821.9221 44 891.3 173 815.6037 44 985.6 242 806.7470w 45 120.2 921
821.9136 44 891.5 291 814.9075w 44 996.1 86 806.5472 45 123.3 181
821.7348 44 894.1 196 814.6500 44 999.9 74 806.5184 45 123.7 144
821.3921 44 899.2 111 814.3345 45 004.7 1206 806.3652 45 126.1 488
821.2155 44 901.8 39 814.1922 45 006.8 333 806.2119 45 128.4 195
821.1784 44 902.3 104 814.1767w 45 007.1 218 805.8802 45 133.5 193
821.1707 44 902.5 105 814.0297 45 009.3 197 805.7290 45 135.8 830
821.0480 44 904.3 46 813.4216 45 018.5 153 805.7057w 45 136.2 277
820.7501 44 908.7 614 813.3781 45 019.1 805 804.6297w 45 152.8 200
820.7361 44 908.9 74 812.7615 45 028.5 846 804.3002 45 157.9 747
820.5869 44 911.1 251 812.6715 45 029.8 299 803.8078w 45 165.5 101
820.2094 44 916.7 1402 812.4990 45 032.4 163 803.7406 45 166.6 170
819.9344w 44 920.8 94 812.2912w 45 035.6 66 803.5020w 45 170.2 114
819.8858 44 921.5 293 812.1569 45 037.6 580 803.3928w 45 171.9 134
819.7749 44 923.2 127 812.0366 45 039.4 92 802.6290 45 183.8 82
819.7096 44 924.2 602 811.7521w 45 043.8 857 802.2769 45 189.2 36
819.6391 44 925.2 261 811.3681 45 049.6 95 802.1959 45 190.5 64
819.5963 44 925.9 1875 811.1357w 45 053.1 445 801.7143w 45 198.0 194
819.5077 44 927.2 486 810.4948 45 062.9 260 800.7735w 45 212.7 592
819.0454 44 934.1 141 809.2524 45 081.8 65 800.4824w 45 217.2 136
818.7411 44 938.6 40 809.2072 45 082.5 90 800.3686 45 219.0 248
817.8426 44 952.0 86 809.1607 45 083.2 204 800.1738 45 222.0 72
817.7225 44 953.8 134 808.6827w 45 090.5 63 800.1267 45 222.7 148
817.2788w 44 960.5 366 808.4868w 45 093.5 154 799.8503w 45 227.1 245
817.1536 44 962.3 88 808.3572w 45 095.5 332 799.6636 45 230.0 518
816.5408 44 971.5 220 807.3360w 45 111.1 580 799.6239 45 230.6 1117
816.2223 44 976.3 796 807.1967 45 113.3 519
7
TABLE VI. Ionizing transitions obtained in the three-step excitation scheme C1. Upper energy levels have even parity and
possible total angular momenta of J = 7/2, 9/2. The transition wavenumber uncertainty is 0.06 cm−1. Resonances with a
gaussian width of > 0.5 cm−1 are marked with w. Relative line intensities are given.
λ (nm) Eu(cm
−1) Irel λ (nm) E (cm
−1
u ) Irel λ (nm) Eu(cm
−1) Irel
889.0614 44 551.8 43 876.4427 44 713.7 43 867.2276 44 835.0 246
888.8840 44 554.0 25 876.1254 44 717.9 18 867.0568 44 837.2 141
888.8003 44 555.1 36 876.0725 44 718.5 66 866.9393 44 838.8 109
887.8069 44 567.7 20 875.7511 44 722.7 17 866.7106 44 841.8 53
887.6414 44 569.8 18 875.4612 44 726.5 86 866.6362 44 842.8 31
887.5464 44 571.0 18 875.4122 44 727.2 62 866.4588 44 845.2 206
886.6061 44 582.9 58 875.3753 44 727.6 54 866.3693 44 846.4 58
886.4557 44 584.8 16 874.9650 44 733.0 14 866.2562 44 847.9 73
886.2651 44 587.3 10 874.4142 44 740.2 20 866.2098 44 848.5 24
885.9486 44 591.3 15 873.5054 44 752.1 13 865.7387 44 854.8 58
885.7865 44 593.4 23 873.4162 44 753.3 103 865.6799 44 855.6 243
885.5437 44 596.5 43 872.7596 44 761.9 14 865.5950 44 856.7 44
885.4058 44 598.2 8 872.3611 44 767.1 79 865.5561 44 857.2 12
885.2142 44 600.7 64 872.2642 44 768.4 106 865.4970 44 858.0 92
884.3971 44 611.1 22 872.1402 44 770.0 86 865.4187 44 859.1 21
884.1963 44 613.7 27 871.9050 44 773.1 211 865.3507 44 860.0 52
883.9162 44 617.3 7 871.5944 44 777.2 140 864.9712 44 865.0 151
883.7663 44 619.2 31 871.4806 44 778.7 14 864.9283 44 865.6 173
883.1731 44 626.8 35 871.3134 44 780.9 127 864.7110 44 868.5 38
883.0409 44 628.5 53 870.7984 44 787.7 124 864.5320 44 870.9 493
882.9753 44 629.3 51 870.6353 44 789.8 50 864.4389 44 872.2 29
882.6307 44 633.7 34 870.5361 44 791.1 24 864.2247 44 875.0 241
882.5431 44 634.9 39 870.4903 44 791.7 50 863.6797w 44 882.3 59
882.4323 44 636.3 12 870.4558 44 792.2 85 863.0059 44 891.4 60
882.1649 44 639.7 46 870.1038 44 796.8 57 862.6270 44 896.5 276
881.2510 44 651.5 23 869.8353 44 800.4 19 862.5894 44 897.0 144
881.2075 44 652.0 15 869.6539 44 802.8 133 862.5353 44 897.7 174
881.0871 44 653.6 14 869.5512 44 804.2 226 862.2423 44 901.6 283
880.5088 44 661.0 65 869.3946 44 806.2 26 862.1958 44 902.3 432
879.9638 44 668.1 16 869.3207 44 807.2 53 862.1348 44 903.1 26
879.9064 44 668.8 74 869.1559 44 809.4 299 861.9918 44 905.0 121
879.2710 44 677.0 9 869.0529 44 810.7 60 861.8088 44 907.5 108
878.4523 44 687.6 27 869.0115 44 811.3 26 861.4830 44 911.9 49
878.2950 44 689.7 55 868.8640 44 813.2 33 861.1429 44 916.4 53
878.0095 44 693.4 34 868.7286 44 815.0 11 861.0998 44 917.0 76
877.6725 44 697.7 14 868.5676 44 817.2 33 860.6458 44 923.1 83
877.1437 44 704.6 10 868.3480 44 820.1 220 860.4508 44 925.8 95
877.0735 44 705.5 94 868.1403 44 822.8 36 860.3987 44 926.5 29
876.9313 44 707.4 34 868.0815 44 823.6 157 860.3544 44 927.1 97
876.6993 44 710.4 59 867.7877 44 827.5 14 860.1982 44 929.2 25
876.6713 44 710.7 60 867.6025 44 830.0 25 860.0046w 44 931.8 14
876.4732 44 713.3 22 867.3289 44 833.6 211 859.9031 44 933.2 71
(Continued on next page.)
8
TABLE VI: (Continued.)
λ (nm) Eu(cm
−1) Irel λ (nm) Eu(cm
−1) Irel λ (nm) E (cm
−1
u ) Irel
859.8467 44 933.9 56 848.9594 45 083.1 448 839.0356 45 222.4 1459
859.6537w 44 936.6 14 848.7971w 45 085.3 1100 838.7191w 45 226.9 1012
858.8990 44 946.8 13 848.5859w 45 088.3 363 838.5380 45 229.5 901
858.6784 44 949.8 50 847.4400w 45 104.2 1822 838.3684w 45 231.9 498
858.5892 44 951.0 57 847.2255w 45 107.2 257 838.0849w 45 235.9 528
858.4668 44 952.6 365 847.1284w 45 108.6 1690 837.9972 45 237.2 890
858.3100w 44 954.8 52 846.7275w 45 114.1 1199 837.8715 45 239.0 1525
858.0745w 44 958.0 20 846.6365w 45 115.4 547 837.8214w 45 239.7 1374
857.7520 44 962.3 232 846.2712w 45 120.5 234 837.7163 45 241.2 1317
857.7004w 44 963.0 59 845.4882 45 131.5 53 837.6036 45 242.8 328
856.9210w 44 973.7 73 845.3353 45 133.6 162 837.5629 45 243.4 854
856.6102 44 977.9 458 845.1430w 45 136.3 536 837.4225 45 245.4 204
856.0995 44 984.9 476 844.9208 45 139.4 181 837.2035 45 248.5 512
855.8272 44 988.6 45 844.6538w 45 143.1 751 837.0550 45 250.6 649
855.6656w 44 990.8 93 844.1612w 45 150.0 98 836.9868w 45 251.6 2151
855.3240w 44 995.4 20 843.5784 45 158.2 270 836.8740w 45 253.2 1648
853.6503w 45 018.4 2041 843.4756 45 159.7 1091 836.5837 45 257.3 1612
853.0070w 45 027.2 227 843.3950w 45 160.8 160 836.4971w 45 258.6 1084
852.8354 45 029.6 215 843.0637w 45 165.5 285 836.2994 45 261.4 1594
852.5481w 45 033.5 344 842.9915 45 166.5 258 836.2309 45 262.4 3881
852.4778 45 034.5 362 842.6284w 45 171.6 141 835.9462w 45 266.5 1149
852.2309w 45 037.9 129 842.5934w 45 172.1 395 835.5868w 45 271.6 1418
852.1223 45 039.4 405 842.2045 45 177.6 1664 835.4529w 45 273.5 1049
851.7982w 45 043.8 389 841.7833 45 183.5 121 835.3047 45 275.6 851
851.6871w 45 045.4 215 841.3731 45 189.3 226 835.1602 45 277.7 2111
851.5150w 45 047.7 444 841.1478 45 192.5 102 835.0929w 45 278.7 2625
851.3746 45 049.7 915 840.9101w 45 195.8 121 835.0005w 45 280.0 741
851.1256w 45 053.1 906 839.7309w 45 212.5 286 834.8671w 45 281.9 731
850.8642w 45 056.7 1007 839.6713 45 213.4 762 834.5098w 45 287.0 201
849.5410w 45 075.0 436 839.5690 45 214.8 313 834.2975w 45 290.1 315
849.0814 45 081.4 828 839.4982 45 215.8 99 834.1156 45 292.7 940
849.0247 45 082.2 142 839.1205 45 221.2 358
9
TABLE VII. Ionizing transitions obtained in the three-step excitation scheme C2. Upper energy levels have even parity and
possible total angular momenta of J = 5/2, 7/2, 9/2. The transition wavenumber uncertainty is 0.06 cm−1. Resonances with a
gaussian width of > 0.5 cm−1 are marked with w. Relative line intensities are given.
λ (nm) E (cm−1u ) Irel λ (nm) Eu(cm
−1) Irel λ (nm) E (cm
−1
u ) Irel
908.4307 44 360.1 20 893.7441 44 541.0 21 882.4787 44 683.9 200
908.3437 44 361.2 38 893.4710 44 544.5 12 882.2898 44 686.3 31
908.1052 44 364.1 52 893.4004 44 545.3 89 882.1919 44 687.6 15
906.7472 44 380.6 23 893.0931 44 549.2 41 882.0245 44 689.7 379
906.2476 44 386.7 18 892.7131 44 554.0 22 881.9699 44 690.4 155
905.6792 44 393.6 20 892.2981 44 559.2 259 881.9374 44 690.8 140
905.2883 44 398.4 22 891.8086 44 565.3 130 881.8875 44 691.5 64
904.8632 44 403.5 60 891.6292 44 567.6 40 881.7666 44 693.0 58
904.3479 44 409.8 24 891.2803 44 572.0 32 881.7434 44 693.3 160
903.8462 44 416.0 15 890.9916 44 575.6 70 881.7235 44 693.6 196
903.2961 44 422.7 14 890.4141 44 582.9 52 881.7021 44 693.9 79
903.1850 44 424.1 93 890.3165 44 584.1 126 881.4423 44 697.2 91
902.9641 44 426.8 45 890.2627 44 584.8 14 881.4014 44 697.7 26
902.3636 44 434.2 30 890.1781 44 585.9 25 881.2664 44 699.5 143
902.2528 44 435.5 75 889.9630 44 588.6 49 880.8024 44 705.4 126
902.1248 44 437.1 20 889.8799 44 589.6 31 880.6932 44 706.8 141
901.6221 44 443.3 67 889.8066 44 590.6 64 880.6584 44 707.3 137
901.2265 44 448.1 65 889.5909 44 593.3 44 880.4239 44 710.3 238
900.8133 44 453.2 46 889.4645 44 594.9 80 880.4042 44 710.6 152
899.8408 44 465.2 150 888.9105 44 601.9 23 880.2403 44 712.7 13
899.2636 44 472.4 13 888.4093 44 608.2 37 880.1998 44 713.2 33
898.9682 44 476.0 38 888.2963 44 609.7 186 879.8470 44 717.8 356
898.7558 44 478.6 106 888.1863 44 611.1 124 879.7907 44 718.5 88
898.4926 44 481.9 77 887.9857 44 613.6 77 879.7030 44 719.6 367
898.3547 44 483.6 70 887.7029 44 617.2 190 879.4721 44 722.6 52
898.0485 44 487.4 53 886.9932 44 626.2 314 879.3358 44 724.4 180
897.9627 44 488.5 66 886.8211 44 628.4 208 879.1412 44 726.9 126
897.7772 44 490.8 43 886.4033 44 633.7 39 879.0935 44 727.5 110
897.4490 44 494.8 11 886.3543 44 634.3 145 878.8141 44 731.1 85
896.9372 44 501.2 95 886.0495 44 638.2 42 878.6848 44 732.8 92
896.4072 44 507.8 83 885.9035 44 640.1 172 878.1224 44 740.1 96
896.2298 44 510.0 49 885.0968 44 650.4 292 877.9766 44 742.0 297
895.8598 44 514.6 51 885.0147 44 651.4 23 877.9150 44 742.8 23
895.7932 44 515.4 68 884.6771 44 655.7 246 877.6299 44 746.5 104
895.5056 44 519.0 30 884.5169 44 657.8 60 877.5133 44 748.0 1259
895.3596 44 520.9 94 884.2680 44 660.9 370 877.4145w 44 749.3 22
895.1220 44 523.8 83 883.7809 44 667.2 253 877.2190 44 751.8 101
894.9999 44 525.3 16 883.6585 44 668.7 214 877.1988 44 752.1 149
894.7310 44 528.7 27 883.4237 44 671.8 218 877.1120 44 753.2 150
894.4545 44 532.2 228 883.0137 44 677.0 112 876.7926 44 757.4 295
893.9296 44 538.7 123 882.9819 44 677.4 71 876.5812 44 760.1 541
893.7733 44 540.7 158 882.9349 44 678.0 28 876.4492 44 761.8 116
(Continued on next page.)
10
TABLE VII: (Continued.)
λ (nm) Eu(cm
−1) I −1 −1rel λ (nm) Eu(cm ) Irel λ (nm) Eu(cm ) Irel
876.3138 44 763.6 90 871.2505 44 829.9 427 867.2969 44 882.2 78
876.2793 44 764.0 613 871.1810 44 830.8 777 867.2778 44 882.5 126
876.0490 44 767.0 50 871.1541 44 831.2 342 867.2402 44 883.0 53
875.9719 44 768.0 63 871.0609 44 832.4 70 867.1895 44 883.7 76
875.9557 44 768.3 140 870.9931 44 833.3 649 867.0621 44 885.4 819
875.9419 44 768.4 139 870.9741 44 833.6 171 866.8238 44 888.5 108
875.6609 44 772.1 938 870.8716 44 834.9 907 866.7776 44 889.1 201
875.5881 44 773.0 34 870.7937 44 835.9 73 866.6763 44 890.5 28
875.2784 44 777.1 397 870.3478 44 841.8 1851 866.6140 44 891.3 133
875.1640 44 778.6 539 870.2859 44 842.6 537 866.5620 44 892.0 35
875.0448 44 780.1 595 870.2652 44 842.9 588 866.4707 44 893.2 73
874.9944 44 780.8 929 870.1765 44 844.1 204 866.2325 44 896.4 3314
874.6627 44 785.1 540 870.1396 44 844.6 3741 866.2024 44 896.8 600
874.3114 44 789.7 534 870.1161 44 844.9 794 866.1528 44 897.5 2191
874.2480 44 790.6 609 870.0432 44 845.8 789 866.0391 44 899.0 2525
874.2091 44 791.1 126 870.0098 44 846.3 945 866.0116 44 899.3 1088
874.1670 44 791.6 143 869.9787 44 846.7 798 865.9925 44 899.6 1794
874.1293 44 792.1 718 869.9010 44 847.7 89 865.9012 44 900.8 4945
873.9802 44 794.1 879 869.7253 44 850.0 302 865.8397 44 901.6 1131
873.8733 44 795.5 94 869.6004 44 851.7 560 865.7969 44 902.2 1725
873.7799 44 796.7 1151 869.3720 44 854.7 2400 865.7343 44 903.0 141
873.6756 44 798.1 213 869.3124 44 855.5 1567 865.6428 44 904.3 182
873.5031 44 800.3 109 869.2787 44 855.9 920 865.6079 44 904.7 209
873.4552 44 800.9 194 869.2593 44 856.2 1325 865.5735w 44 905.2 403
873.3209 44 802.7 580 869.2340 44 856.5 803 865.4210 44 907.2 260
873.2176 44 804.1 209 869.1874 44 857.2 1663 865.0560w 44 912.1 967
873.1679 44 804.7 471 869.0738 44 858.7 3445 864.9523 44 913.5 5188
872.9857 44 807.1 120 869.0422 44 859.1 495 864.8595 44 914.7 1633
872.8202 44 809.3 249 868.9788 44 859.9 1138 864.7354 44 916.4 1674
872.7286 44 810.5 414 868.7460 44 863.0 572 864.7220 44 916.6 2214
872.5254 44 813.1 175 868.6018 44 864.9 1943 864.6936 44 916.9 4467
872.3705 44 815.2 45 868.5551 44 865.5 3189 864.6634 44 917.3 267
872.3219 44 815.8 552 868.5185 44 866.0 158 864.6108 44 918.1 1110
872.3029 44 816.1 569 868.3592 44 868.1 132 864.5976 44 918.2 1697
872.2243 44 817.1 104 868.3198w 44 868.6 70 864.5630 44 918.7 430
872.1655 44 817.9 150 868.1776 44 870.5 124 864.5327 44 919.1 767
872.0049 44 820.0 1306 868.1553 44 870.8 1468 864.4839 44 919.8 81
871.8537 44 822.0 293 868.0735 44 871.9 422 864.4199w 44 920.6 1166
871.7352 44 823.5 285 868.0550 44 872.2 495 864.3675 44 921.3 1018
871.7042 44 823.9 1006 867.8507 44 874.9 424 864.2378 44 923.0 5697
871.6081 44 825.2 378 867.7536 44 876.2 2178 864.2009 44 923.5 3782
871.5590 44 825.8 176 867.5357 44 879.1 330 864.1723 44 923.9 660
871.4681 44 827.0 435 867.3899 44 881.0 68 864.1253 44 924.6 3043
871.4201 44 827.7 43 867.3165 44 882.0 33 864.0707 44 925.3 1197
(Continued on next page.)
11
TABLE VII: (Continued.)
λ (nm) E (cm−1u ) I
−1
rel λ (nm) Eu(cm ) Irel λ (nm) Eu(cm
−1) Irel
864.0401 44 925.7 1729 860.4861 44 973.5 195 854.6439w 45 052.9 4609
864.0149 44 926.0 4159 860.2910 44 976.1 864 854.5395 45 054.4 595
863.9874 44 926.4 1055 860.1686 44 977.8 347 854.3786w 45 056.6 2839
863.9410 44 927.0 2905 860.0060 44 980.0 4640 853.9320 45 062.7 499
863.7354 44 929.8 341 859.7277 44 983.7 162 853.0394w 45 074.9 174
863.6477w 44 930.9 385 859.6515 44 984.8 283 852.9241 45 076.5 2842
863.5913 44 931.7 292 859.4535 44 987.5 1378 852.5821 45 081.2 1104
863.4364 44 933.8 8744 859.3781 44 988.5 1631 852.5519 45 081.6 1333
863.3654w 44 934.7 4743 859.3097 44 989.4 2251 852.5213 45 082.1 2281
863.3196 44 935.4 994 859.2219w 44 990.6 416 852.4745 45 082.7 747
863.2604w 44 936.1 903 858.8613w 44 995.5 267 851.9071w 45 090.5 3618
863.0481 44 939.0 955 858.7671w 44 996.8 128 851.6947w 45 093.5 2713
862.7394 44 943.1 506 858.5465 44 999.7 2128 851.6200 45 094.5 524
862.4749 44 946.7 836 858.1964 45 004.5 5737 851.5465w 45 095.5 3603
862.2731 44 949.4 3560 857.8533 45 009.2 381 850.9228w 45 104.1 1522
862.2503 44 949.7 1117 857.2765 45 017.0 6712 850.6113 45 108.4 1138
862.1641 44 950.9 157 857.1811w 45 018.3 7584 850.4314w 45 110.9 2047
862.0918 44 951.8 4365 856.5425w 45 027.0 606 850.2721 45 113.1 3358
862.0373 44 952.6 1378 856.3281 45 029.9 2993 850.2017w 45 114.1 2840
861.8853w 44 954.6 121 856.1590 45 032.2 1169 850.1147w 45 115.3 2203
861.4825 44 960.1 1809 856.0752w 45 033.4 2323 849.7752w 45 120.0 7561
861.4608w 44 960.3 2500 855.7362w 45 038.0 1058 849.3482w 45 125.9 6235
861.3194 44 962.2 2903 855.6347w 45 039.4 2016 848.8412 45 132.9 1767
861.2873w 44 962.7 809 855.3382 45 043.4 547 848.7998 45 133.5 2887
860.9722 44 966.9 144 855.1990w 45 045.3 603 848.6396 45 135.7 11882
860.6996 44 970.6 2564 855.1470w 45 046.1 1823 848.6010 45 136.3 1114
860.6044 44 971.9 183 854.9058w 45 049.4 1772 844.4525 45 194.1 1031
860.5446 44 972.7 140 854.7518w 45 051.5 1818 833.3896 45 351.3 106
12
II. EXCITED LEVELS IN PM I BY ENERGY
TABLE VIII. Odd parity energy levels in neutral Pm, derived from lines in the excitation schemes SESA, SESB and SESC
(see TABLE II - III). According to the selection rules for dipole transitions ∆J = 0,±1, possible values for the total angular
momentum J are given. Values of 3/2 and 9/2, which are marked with an asterisk are deemed more likely, as a transition could
not be observed starting from a state at 7/2 and 5/2, respectively. The value of J = 7/2 for the state at 33352.3 cm−1 was veried
by a measurement of the hyperne structure of the 22020.08 cm−1 → 33352.3 cm−1 transition.
E (cm−1) J E (cm−1) J E (cm−1) J E (cm−1) J
∗ ∗
32 363.2 5 , 7 , 9 33 137.0 5 , 7 , 9 33 685.8 3 , 5 , 7 44 567.0 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2 2 2
32 366.0 5
∗
, 7 , 9 33 137.7 7 , 9 33 691.6 5 , 7 , 9 44 579.6 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2 2
32 390.1 5 , 7 , 9 33 142.3 7 , 9 33 703.0 3∗, 5 , 7 44 587.3 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2 2
32 449.0 5 7 9
∗ ∗
, , 33 168.2 3 , 5 , 7 33 710.7 3 , 5 , 7 44 600.5 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2 2 2
5 ∗32 474.9 , 7 , 9 33 190.8 3 , 5 , 7 33 711.7 7 , 9 44 602.0 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2 2
∗
32 489.5 5 , 7 , 9 33 209.9 3 , 5 , 7 33 720.9 5 , 7 , 9
∗
44 604.4 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2 2 2
∗
32 493.9 5 , 7 , 9 33 226.1 3 , 5 , 7 33 728.1 7 , 9 44 606.6 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2 2
∗ ∗
32 510.6 5 , 7 , 9 33 227.8 3 , 5 , 7 33 736.3 3 , 5 , 7 44 608.9 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2 2 2
∗
32 520.0 5 , 7 , 9 33 267.4 5 , 7 , 9 33 757.8 7 , 9 44 611.4 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2 2
5 7 9 7 9 ∗32 546.7 , , 33 304.0 , 33 760.3 3 , 5 , 7 44 612.1 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2 2
32 559.7 5 , 7 , 9 33 319.1 7 , 9 33 773.7 7 , 9 44 615.3 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2
32 578.4 5 , 7 , 9 33 338.1 7 , 9 33 782.3 7 , 9 44 618.0 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2
∗
32 587.5 5 , 7 , 9 33 352.3 7 33 793.2 5 , 7 , 9 44 629.1 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2
∗
32 604.7 5 , 7 , 9 33 359.7 5 , 7 , 9 33 831.6 7 , 9 44 630.2 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2 2
∗
32 616.6 5 , 7 , 9 33 361.9 7 , 9 33 832.8 5 , 7 , 9 44 635.5 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2 2
∗
32 624.5 5 , 7 , 9 33 374.7 7 , 9 33 841.2 5 , 7 , 9 44 654.5 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2 2
32 653.7 5 , 7 , 9 33 386.9 5
∗
, 7 , 9 33 860.9 7 , 9 44 658.8 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2 2
32 668.1 5 , 7 , 9 33 409.1 7 , 9 33 862.2 3 , 5 , 7 44 672.8 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2 2
32 683.7 5 , 7 , 9
∗
33 438.4 5 , 7 , 9 33 899.2 3 , 5 , 7 44 680.8 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2 2 2
32 686.1 5 , 7 , 9 33 452.8 7 , 9 33 920.5 3 , 5 , 7 44 682.2 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2 2
32 724.7 5 , 7 , 9 33 461.9 3
∗
, 5 , 7 33 922.1 3 , 5 , 7 44 685.6 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2 2 2
∗
32 730.9 5 , 7 , 9 33 463.1 5 , 7 , 9 33 929.2 3 , 5 , 7 44 699.8 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2 2 2
∗
32 740.4 5 , 7 , 9 33 479.4 3 , 5 , 7 33 943.6 3 , 5 , 7 44 703.6 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2 2 2
32 742.1 5 , 7 , 9 33 482.1 7 , 9 33 960.7 3 , 5 , 7 44 705.7 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2 2
∗
32 763.1 5 , 7 , 9 33 497.3 3 , 5 , 7 33 977.8 3 , 5 , 7 44 708.6 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2 2 2
32 767.1 5 , 7 , 9 33 510.6 7 , 9 33 991.0 3 , 5 , 7 44 720.9 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2 2
32 817.9 5 , 7 , 9 33 520.3 7 , 9 34 001.3 3 , 5 , 7 44 739.4 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2 2
32 860.4 5 , 7 , 9 33 531.4 7 , 9 34 014.1 3 , 5 , 7 44 743.7 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2 2
32 866.8 5 , 7 , 9 33 534.5 5 , 7 , 9
∗
34 021.6 3 , 5 , 7 44 748.6 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2 2 2
32 882.7 5 , 7 , 9 33 562.2 7 , 9 34 051.1 3 , 5 , 7 44 752.8 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2 2
32 905.4 5 , 7 , 9 33 566.7 7 , 9 34 057.2 3 , 5 , 7 44 758.0 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2 2
∗
32 943.4 5 , 7 , 9 33 610.9 3 , 5 , 7 44 472.0 5 , 7 , 9 44 762.1 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2 2 2
32 952.1 5 , 7 , 9 33 632.2 7 , 9 44 510.9 5 , 7 , 9 44 762.6 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2 2
32 973.1 5 , 7 , 9 3
∗
33 642.6 , 5 , 7 44 526.3 5 , 7 , 9 44 763.6 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2 2 2
32 980.8 5 , 7 , 9 33 647.7 7 , 9 44 527.0 5 , 7 , 9 44 780.9 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2 2
33 022.3 5 , 7 , 9 33 653.2 7 , 9 44 536.6 5 , 7 , 9 44 783.9 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2 2
3 ∗ 5 7 ∗33 079.8 , , 33 670.8 5 , 7 , 9 44 555.5 5 , 7 , 9 44 787.0 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2 2 2
33 102.9 7 , 9 33 685.3 7 , 9 44 565.6 5 , 7 , 9 44 787.6 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2
(Continued on next page.)
13
TABLE VIII: (Continued.)
E (cm−1) J E (cm−1) J E (cm−1) J E (cm−1) J
44 788.9 5 , 7 , 9 44 889.7 5 , 7 , 9 44 952.1 5 , 7 , 9 44 993.5 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2 2 2
44 791.9 5 , 7 , 9 44 892.9 5 , 7 , 9 44 953.8 5 , 7 , 9 44 997.8 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2 2 2
44 793.1 5 , 7 , 9 44 893.6 5 , 7 , 9 44 954.6 5 , 7 , 9 45 002.0 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2 2 2
44 808.3 5 , 7 , 9 44 897.3 5 , 7 , 9 44 956.5 5 , 7 , 9 45 003.4 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2 2 2
44 810.9 5 , 7 , 9 44 901.7 5 , 7 , 9 44 957.3 5 , 7 , 9 45 005.2 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2 2 2
44 814.7 5 , 7 , 9 44 908.2 5 , 7 , 9 44 958.2 5 , 7 , 9 45 006.0 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2 2 2
44 821.4 5 , 7 , 9 44 916.1 5 , 7 , 9 44 960.1 5 , 7 , 9 45 009.0 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2 2 2
44 823.4 5 , 7 , 9 44 920.5 5 , 7 , 9 44 962.7 5 , 7 , 9 45 011.3 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2 2 2
44 831.4 5 , 7 , 9 44 921.5 5 , 7 , 9 44 963.3 5 , 7 , 9 45 014.4 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2 2 2
44 835.5 5 , 7 , 9 44 923.4 5 , 7 , 9 44 963.9 5 , 7 , 9 45 015.5 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2 2 2
44 838.6 5 , 7 , 9 44 923.8 5 , 7 , 9 44 966.2 5 , 7 , 9 45 016.1 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2 2 2
44 841.1 5 , 7 , 9 44 924.4 5 , 7 , 9 44 967.8 5 , 7 , 9 45 019.9 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2 2 2
44 842.7 5 , 7 , 9 44 926.4 5 , 7 , 9 44 969.1 5 , 7 , 9 45 024.2 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2 2 2
44 846.8 5 , 7 , 9 44 927.9 5 , 7 , 9 44 971.1 5 , 7 , 9 45 030.4 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2 2 2
44 847.7 5 , 7 , 9 44 928.5 5 , 7 , 9 44 976.6 5 , 7 , 9 45 036.1 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2 2 2
44 849.7 5 , 7 , 9 44 929.1 5 , 7 , 9 44 978.3 5 , 7 , 9 45 040.3 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2 2 2
44 850.7 5 , 7 , 9 44 930.8 5 , 7 , 9 44 979.7 5 , 7 , 9 45 041.9 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2 2 2
44 857.5 5 , 7 , 9 44 931.9 5 , 7 , 9 44 980.4 5 , 7 , 9 45 046.4 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2 2 2
44 858.5 5 , 7 , 9 44 932.4 5 , 7 , 9 44 981.6 5 , 7 , 9 45 047.8 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2 2 2
44 860.7 5 , 7 , 9 44 934.0 5 , 7 , 9 44 982.9 5 , 7 , 9 45 049.4 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2 2 2
44 867.9 5 , 7 , 9 44 935.7 5 , 7 , 9 44 983.5 5 , 7 , 9 45 050.3 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2 2 2
44 871.1 5 , 7 , 9 44 939.2 5 , 7 , 9 44 984.1 5 , 7 , 9 45 051.7 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2 2 2
44 875.6 5 , 7 , 9 44 940.9 5 , 7 , 9 44 984.9 5 , 7 , 9 45 054.1 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2 2 2
44 878.6 5 , 7 , 9 44 942.4 5 , 7 , 9 44 986.7 5 , 7 , 9 45 057.6 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2 2 2
44 880.5 5 , 7 , 9 44 943.3 5 , 7 , 9 44 987.9 5 , 7 , 9 45 061.0 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2 2 2
44 883.0 5 , 7 , 9 44 945.5 5 , 7 , 9 44 991.2 5 , 7 , 9
2 2 2 2 2 2 2 2 2
44 887.4 5 , 7 , 9 44 948.9 5 , 7 , 9 44 992.6 5 , 7 , 9
2 2 2 2 2 2 2 2 2
14
TABLE IX. Even parity energy levels in neutral Pm, derived from lines in the excitation schemes B1, B2, C1 and C2 (see
TABLE IV - VII). According to the selection rules for dipole transitions ∆J = 0,±1, possible values for the total angular
momentum J are given.
E (cm−1) J E (cm−1) J E (cm−1) J E (cm−1) J
44 360.1 5 , 7 , 9 44 541.0 5 , 7 , 9 44 634.9 5 , ..., 11 44 713.7 5 , ..., 11
2 2 2 2 2 2 2 2 2 2
44 361.2 5 , 7 , 9 44 544.5 5 , 7 , 9 44 636.3 5 , ..., 11 44 717.8 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2 2
44 364.1 5 , 7 , 9 44 545.3 5 , 7 , 9 44 638.2 5 , 7 , 9 44 718.5 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2 2 2
44 380.6 5 , 7 , 9 44 549.2 5 , 7 , 9 44 639.7 5 , ..., 11 44 719.6 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2 2
44 386.7 5 , 7 , 9 44 551.8 5 , ..., 11 44 640.1 5 , 7 , 9 44 722.7 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2 2
44 393.6 5 , 7 , 9 44 554.0 5 , 7 , 9 44 650.4 5 , 7 , 9 44 724.4 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2 2 2
44 398.4 5 , 7 , 9 44 554.0 5 , ..., 11 44 651.4 5 , 7 , 9 44 726.5 5 , ..., 11
2 2 2 2 2 2 2 2 2 2
44 403.5 5 , 7 , 9 44 555.1 5 , ..., 11 44 652.0 5 , ..., 11 44 726.9 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2
44 409.8 5 , 7 , 9 44 559.2 5 , 7 , 9 44 653.6 5 , ..., 11 44 727.2 5 , ..., 11
2 2 2 2 2 2 2 2 2 2
44 416.0 5 , 7 , 9 44 565.3 5 , 7 , 9 44 655.7 5 , 7 , 9 44 727.6 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2 2 2
44 422.7 5 , 7 , 9 44 567.6 5 , 7 , 9 44 657.8 5 , 7 , 9 44 731.1 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2 2 2
44 424.1 5 , 7 , 9 44 569.8 5 , ..., 11 44 660.9 5 , 7 , 9 44 732.9 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2 2
44 426.8 5 , 7 , 9 44 571.0 5 , ..., 11 44 661.0 5 , ..., 11 44 740.1 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2
44 434.2 5 , 7 , 9 44 572.0 5 , 7 , 9 44 667.2 5 , 7 , 9 44 742.0 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2 2 2
44 435.5 5 , 7 , 9 44 575.6 5 , 7 , 9 44 668.1 5 , ..., 11 44 742.8 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2 2
44 437.1 5 , 7 , 9 44 582.9 5 , 7 , 9 44 668.8 5 , 7 , 9 44 746.5 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2 2 2
44 443.3 5 , 7 , 9 44 584.1 5 , 7 , 9 44 671.8 5 , 7 , 9 44 748.0 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2 2 2
44 448.1 5 , 7 , 9 44 584.8 5 , 7 , 9 44 677.0 5 , 7 , 9 44 749.3 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2 2 2
44 453.2 5 , 7 , 9 44 585.9 5 , 7 , 9 44 677.4 5 , 7 , 9 44 751.8 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2 2 2
44 465.2 5 , 7 , 9 44 587.3 5 , ..., 11 44 678.0 5 , 7 , 9 44 752.1 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2 2
44 472.4 5 , 7 , 9 44 588.6 5 , 7 , 9 44 683.9 5 , 7 , 9 44 753.2 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2 2 2
44 476.0 5 , 7 , 9 44 589.6 5 , 7 , 9 44 686.3 5 , 7 , 9 44 757.4 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2 2 2
44 478.6 5 , 7 , 9 44 590.6 5 , 7 , 9 44 687.6 5 , 7 , 9 44 760.1 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2 2 2
44 481.9 5 , 7 , 9 44 591.3 5 , ..., 11 44 689.7 5 , 7 , 9 44 761.8 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2 2
44 483.6 5 , 7 , 9 44 593.3 5 , 7 , 9 44 690.4 5 , 7 , 9 44 763.6 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2 2 2
44 487.4 5 , 7 , 9 44 594.9 5 , 7 , 9 44 690.8 5 , 7 , 9 44 764.0 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2 2 2
44 488.5 5 , 7 , 9 44 596.5 5 , ..., 11 44 691.5 5 , 7 , 9 44 767.0 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2 2
44 490.8 5 , 7 , 9 44 598.2 5 , ..., 11 44 693.0 5 , 7 , 9 44 768.0 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2 2
44 494.8 5 , 7 , 9 44 600.7 5 , ..., 11 44 693.3 5 , 7 , 9 44 768.3 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2 2
44 501.2 5 , 7 , 9 44 601.9 5 , 7 , 9 44 693.6 5 , 7 , 9 44 768.4 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2 2 2
44 507.8 5 , 7 , 9 44 608.2 5 , 7 , 9 44 693.9 5 , 7 , 9 44 770.0 5 , ..., 11
2 2 2 2 2 2 2 2 2 2 2
44 510.0 5 , 7 , 9 44 609.7 5 , 7 , 9 44 697.2 5 , 7 , 9 44 772.1 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2 2 2
44 514.6 5 , 7 , 9 44 611.1 5 , 7 , 9 44 697.7 5 , 7 , 9 44 773.1 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2 2 2
44 515.4 5 , 7 , 9 44 613.6 5 , 7 , 9 44 699.5 5 , 7 , 9 44 777.1 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2 2 2
44 519.0 5 , 7 , 9 44 617.2 5 , 7 , 9 44 704.6 5 , ..., 11 44 778.6 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2 2
44 520.9 5 , 7 , 9 44 619.2 5 , ..., 11 44 705.5 5 , 7 , 9 44 780.1 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2 2
44 523.8 5 , 7 , 9 44 626.2 5 , 7 , 9 44 706.8 5 , 7 , 9 44 780.8 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2 2 2
44 525.3 5 , 7 , 9 44 626.8 5 , ..., 11 44 707.3 5 , 7 , 9 44 785.1 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2 2
44 528.7 5 , 7 , 9 44 628.4 5 , 7 , 9 44 710.3 5 , 7 , 9 44 787.7 5 , ..., 11
2 2 2 2 2 2 2 2 2 2 2
44 532.2 5 , 7 , 9 44 629.3 5 , ..., 11 44 710.6 5 , 7 , 9 44 789.7 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2 2
44 538.7 5 , 7 , 9 44 633.7 5 , 7 , 9 44 712.7 5 , 7 , 9 44 790.6 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2 2 2
44 540.7 5 , 7 , 9 44 634.3 5 , 7 , 9 44 713.3 5 , 7 , 9 44 791.1 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2 2 2
(Continued on next page.)
15
TABLE IX: (Continued.)
E (cm−1) J E (cm−1) J E (cm−1) J E (cm−1) J
44 791.7 5 , 7 , 9 44 842.8 5 , 7 , 9 44 888.5 5 , 7 , 9 44 921.3 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2 2 2
44 792.1 5 , 7 , 9 44 844.1 5 , 7 , 9 44 889.1 5 , 7 , 9 44 921.5 3 , ..., 11
2 2 2 2 2 2 2 2 2 2 2
44 794.1 5 , 7 , 9 44 844.6 5 , 7 , 9 44 890.5 5 , 7 , 9 44 923.1 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2 2 2
44 795.5 5 , 7 , 9 44 844.9 5 , 7 , 9 44 891.4 5 , 7 , 9 44 923.2 3 , ..., 11
2 2 2 2 2 2 2 2 2 2 2
44 796.7 5 , 7 , 9 44 845.2 5 , ..., 11 44 892.0 5 , 7 , 9 44 923.5 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2 2
44 798.1 5 , 7 , 9 44 845.8 5 , 7 , 9 44 893.2 5 , 7 , 9 44 923.9 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2 2 2
44 800.3 5 , 7 , 9 44 846.3 5 , 7 , 9 44 894.1 3 , ..., 11 44 924.2 3 , ..., 11
2 2 2 2 2 2 2 2 2 2
44 800.9 5 , 7 , 9 44 846.7 5 , 7 , 9 44 896.4 5 , 7 , 9 44 924.6 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2 2 2
44 802.7 5 , 7 , 9 44 847.8 5 , 7 , 9 44 896.9 5 , 7 , 9 44 925.2 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2 2 2
44 804.1 5 , 7 , 9 44 848.5 5 , ..., 11 44 897.5 5 , 7 , 9 44 925.7 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2 2
44 804.7 5 , 7 , 9 44 850.0 5 , 7 , 9 44 897.7 5 , ..., 11 44 925.9 3 , ..., 11
2 2 2 2 2 2 2 2 2 2
44 806.2 5 , ..., 11 44 851.7 5 , 7 , 9 44 899.0 5 , 7 , 9 44 926.0 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2 2
44 807.1 5 , 7 , 9 44 854.7 5 , 7 , 9 44 899.2 3 , ..., 11 44 926.4 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2 2
44 809.3 5 , 7 , 9 44 855.5 5 , 7 , 9 44 899.3 5 , 7 , 9 44 927.0 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2 2 2
44 810.5 5 , 7 , 9 44 855.9 5 , 7 , 9 44 899.6 5 , 7 , 9 44 927.2 3 , ..., 11
2 2 2 2 2 2 2 2 2 2 2
44 810.7 5 , ..., 11 44 856.2 5 , 7 , 9 44 900.8 5 , 7 , 9 44 929.2 5 , ..., 11
2 2 2 2 2 2 2 2 2 2
44 811.3 5 , ..., 11 44 856.6 5 , 7 , 9 44 901.6 5 , 7 , 9 44 929.8 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2 2
44 813.2 5 , 7 , 9 44 857.2 5 , 7 , 9 44 901.8 3 , ..., 11 44 930.9 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2 2
44 815.1 5 , 7 , 9 44 858.0 5 , ..., 11 44 902.2 5 , 7 , 9 44 931.7 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2 2
44 815.8 5 , 7 , 9 44 858.7 5 , 7 , 9 44 902.3 3 , ..., 11 44 933.2 5 , ..., 11
2 2 2 2 2 2 2 2 2 2
44 816.1 5 , 7 , 9 44 859.1 5 , 7 , 9 44 902.5 3 , ..., 11 44 933.8 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2 2
44 817.1 5 , 7 , 9 44 859.9 5 , 7 , 9 44 903.0 5 , 7 , 9 44 934.0 5 , ..., 11
2 2 2 2 2 2 2 2 2 2 2
44 817.9 5 , 7 , 9 44 863.0 5 , 7 , 9 44 904.3 5 , 7 , 9 44 934.7 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2 2 2
44 820.0 5 , 7 , 9 44 864.9 5 , 7 , 9 44 904.7 5 , 7 , 9 44 935.4 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2 2 2
44 820.1 5 , ..., 11 44 865.0 5 , ..., 11 44 905.1 5 , 7 , 9 44 936.1 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2
44 822.0 5 , 7 , 9 44 865.5 5 , 7 , 9 44 907.2 5 , 7 , 9 44 936.6 5 , ..., 11
2 2 2 2 2 2 2 2 2 2 2
44 822.8 5 , ..., 11 44 866.0 5 , 7 , 9 44 907.5 5 , ..., 11 44 938.6 3 , ..., 11
2 2 2 2 2 2 2 2 2
44 823.6 5 , 7 , 9 44 868.1 5 , 7 , 9 44 908.7 3 , ..., 11 44 939.0 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2 2
44 823.9 5 , 7 , 9 44 868.6 5 , 7 , 9 44 908.9 3 , ..., 11 44 943.1 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2 2
44 825.2 5 , 7 , 9 44 870.5 5 , 7 , 9 44 911.1 3 , ..., 11 44 946.7 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2 2
44 825.8 5 , 7 , 9 44 870.9 5 , 7 , 9 44 911.9 5 , ..., 11 44 949.4 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2 2
44 827.0 5 , 7 , 9 44 871.9 5 , 7 , 9 44 912.1 5 , 7 , 9 44 949.6 3 , ..., 11
2 2 2 2 2 2 2 2 2 2 2
44 827.6 5 , 7 , 9 44 872.2 5 , 7 , 9 44 913.5 5 , 7 , 9 44 949.7 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2 2 2
44 829.9 5 , 7 , 9 44 874.9 5 , 7 , 9 44 914.7 5 , 7 , 9 44 949.8 5 , ..., 11
2 2 2 2 2 2 2 2 2 2 2
44 830.8 5 , 7 , 9 44 876.2 5 , 7 , 9 44 916.4 5 , 7 , 9 44 950.9 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2 2 2
44 831.2 5 , 7 , 9 44 879.1 5 , 7 , 9 44 916.6 5 , 7 , 9 44 951.8 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2 2 2
44 832.4 5 , 7 , 9 44 881.0 5 , 7 , 9 44 916.9 5 , 7 , 9 44 952.0 3 , ..., 11
2 2 2 2 2 2 2 2 2 2 2
44 833.3 5 , 7 , 9 44 882.0 5 , 7 , 9 44 917.3 5 , 7 , 9 44 952.6 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2 2 2
44 833.6 5 , 7 , 9 44 882.3 5 , 7 , 9 44 918.1 5 , 7 , 9 44 953.8 3 , ..., 11
2 2 2 2 2 2 2 2 2 2 2
44 834.9 5 , 7 , 9 44 882.5 5 , 7 , 9 44 918.2 5 , 7 , 9 44 954.7 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2 2 2
44 835.9 5 , 7 , 9 44 883.0 5 , 7 , 9 44 918.7 5 , 7 , 9 44 958.0 5 , ..., 11
2 2 2 2 2 2 2 2 2 2 2
44 837.2 5 , ..., 11 44 883.3 3 , ..., 11 44 919.1 5 , 7 , 9 44 960.1 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2
44 838.8 5 , ..., 11 44 883.7 5 , 7 , 9 44 919.8 5 , 7 , 9 44 960.3 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2 2
44 841.8 5 , 7 , 9 44 885.4 5 , 7 , 9 44 920.7 5 , 7 , 9 44 960.5 3 , ..., 11
2 2 2 2 2 2 2 2 2 2 2
(Continued on next page.)
16
TABLE IX: (Continued.)
E (cm−1) J E (cm−1) J E (cm−1) J E (cm−1) J
44 960.8 3 , ..., 11 45 029.9 5 , 7 , 9 45 107.2 5 , ..., 11 45 213.4 5 , ..., 11
2 2 2 2 2 2 2 2 2
44 962.3 5 , 7 , 9 45 030.1 3 , ..., 11 45 108.5 5 , 7 , 9 45 214.8 5 , ..., 11
2 2 2 2 2 2 2 2 2 2
44 962.7 5 , 7 , 9 45 032.2 5 , 7 , 9 45 110.9 5 , 7 , 9 45 215.8 5 , ..., 11
2 2 2 2 2 2 2 2 2 2 2
44 963.0 5 , ..., 11 45 032.5 3 , ..., 11 45 111.1 3 , ..., 11 45 217.2 3 , ..., 11
2 2 2 2 2 2 2 2
44 966.9 5 , 7 , 9 45 033.4 5 , 7 , 9 45 113.2 5 , 7 , 9 45 219.0 3 , ..., 11
2 2 2 2 2 2 2 2 2 2 2
44 969.2 3 , ..., 11 45 034.5 5 , ..., 11 45 114.1 5 , 7 , 9 45 221.2 5 , ..., 11
2 2 2 2 2 2 2 2 2
44 970.6 5 , 7 , 9 45 035.6 3 , ..., 11 45 115.3 5 , 7 , 9 45 222.0 3 , ..., 11
2 2 2 2 2 2 2 2 2 2
44 971.5 3 , ..., 11 45 037.6 3 , ..., 11 45 115.5 3 , ..., 11 45 222.4 5 , ..., 11
2 2 2 2 2 2 2 2
44 971.9 5 , 7 , 9 45 037.9 5 , 7 , 9 45 120.0 5 , 7 , 9 45 222.7 3 , ..., 11
2 2 2 2 2 2 2 2 2 2 2
44 972.7 5 , 7 , 9 45 039.4 5 , 7 , 9 45 120.2 3 , ..., 11 45 227.0 5 , ..., 11
2 2 2 2 2 2 2 2 2 2
44 973.5 5 , 7 , 9 45 043.4 5 , 7 , 9 45 120.5 5 , ..., 11 45 229.5 5 , ..., 11
2 2 2 2 2 2 2 2 2 2
44 976.3 3 , ..., 11 45 043.7 3 , ..., 11 45 123.3 3 , ..., 11 45 230.0 3 , ..., 11
2 2 2 2 2 2 2 2
44 977.3 3 , ..., 11 45 045.3 5 , 7 , 9 45 123.7 3 , ..., 11 45 230.6 3 , ..., 11
2 2 2 2 2 2 2 2 2
44 977.8 5 , 7 , 9 45 045.7 3 , ..., 11 45 125.9 5 , 7 , 9 45 231.9 5 , ..., 11
2 2 2 2 2 2 2 2 2 2
44 978.3 3 , ..., 11 45 046.1 5 , 7 , 9 45 126.1 3 , ..., 11 45 235.9 5 , ..., 11
2 2 2 2 2 2 2 2 2
44 980.0 3 , ..., 11 45 046.4 3 , ..., 11 45 128.4 3 , ..., 11 45 237.2 5 , ..., 11
2 2 2 2 2 2 2 2
44 983.7 5 , 7 , 9 45 047.7 5 , ..., 11 45 131.5 5 , ..., 11 45 239.0 5 , ..., 11
2 2 2 2 2 2 2 2 2
44 984.8 5 , 7 , 9 45 049.4 5 , 7 , 9 45 132.9 5 , 7 , 9 45 239.7 5 , ..., 11
2 2 2 2 2 2 2 2 2 2 2
44 985.6 3 , ..., 11 45 049.7 5 , ..., 11 45 133.5 5 , 7 , 9 45 241.2 5 , ..., 11
2 2 2 2 2 2 2 2 2
44 986.3 3 , ..., 11 45 051.5 5 , 7 , 9 45 135.8 5 , 7 , 9 45 242.8 5 , ..., 11
2 2 2 2 2 2 2 2 2 2
44 987.5 5 , 7 , 9 45 051.7 3 , ..., 11 45 136.3 5 , 7 , 9 45 243.4 5 , ..., 11
2 2 2 2 2 2 2 2 2 2
44 987.8 3 , ..., 11 45 053.0 5 , 7 , 9 45 139.4 5 , ..., 11 45 245.4 5 , ..., 11
2 2 2 2 2 2 2 2 2
44 988.5 5 , 7 , 9 45 053.1 3 , ..., 11 45 143.1 5 , ..., 11 45 248.5 5 , ..., 11
2 2 2 2 2 2 2 2 2
44 989.4 5 , 7 , 9 45 053.3 3 , ..., 11 45 150.0 5 , ..., 11 45 250.6 5 , ..., 11
2 2 2 2 2 2 2 2 2
44 989.7 3 , ..., 11 45 054.4 5 , 7 , 9 45 152.8 3 , ..., 11 45 251.6 5 , ..., 11
2 2 2 2 2 2 2 2 2
44 990.6 5 , 7 , 9 45 056.6 5 , 7 , 9 45 157.9 3 , ..., 11 45 253.2 5 , ..., 11
2 2 2 2 2 2 2 2 2 2
44 995.5 5 , 7 , 9 45 057.3 3 , ..., 11 45 158.2 5 , ..., 11 45 257.3 5 , ..., 11
2 2 2 2 2 2 2 2 2
44 996.1 3 , ..., 11 45 062.8 3 , ..., 11 45 159.7 5 , ..., 11 45 258.6 5 , ..., 11
2 2 2 2 2 2 2 2
44 996.8 5 , 7 , 9 45 075.0 5 , 7 , 9 45 160.8 5 , ..., 11 45 261.4 5 , ..., 11
2 2 2 2 2 2 2 2 2 2
44 999.7 5 , 7 , 9 45 076.5 5 , 7 , 9 45 165.5 5 , ..., 11 45 262.4 5 , ..., 11
2 2 2 2 2 2 2 2 2 2
44 999.9 3 , ..., 11 45 081.3 5 , 7 , 9 45 166.5 5 , ..., 11 45 266.5 5 , ..., 11
2 2 2 2 2 2 2 2 2
45 004.5 5 , 7 , 9 45 081.7 5 , 7 , 9 45 170.2 3 , ..., 11 45 271.6 5 , ..., 11
2 2 2 2 2 2 2 2 2 2
45 004.7 3 , ..., 11 45 082.1 5 , 7 , 9 45 171.6 5 , ..., 11 45 273.5 5 , ..., 11
2 2 2 2 2 2 2 2 2
45 006.8 3 , ..., 11 45 082.2 5 , ..., 11 45 172.0 5 , ..., 11 45 275.6 5 , ..., 11
2 2 2 2 2 2 2 2
45 007.1 3 , ..., 11 45 082.5 3 , ..., 11 45 177.6 5 , ..., 11 45 277.7 5 , ..., 11
2 2 2 2 2 2 2 2
45 009.2 5 , 7 , 9 45 082.7 5 , 7 , 9 45 183.5 5 , ..., 11 45 278.7 5 , ..., 11
2 2 2 2 2 2 2 2 2 2
45 009.3 3 , ..., 11 45 083.1 5 , ..., 11 45 183.8 3 , ..., 11 45 280.0 5 , ..., 11
2 2 2 2 2 2 2 2
45 017.0 5 , 7 , 9 45 085.3 5 , ..., 11 45 189.3 5 , ..., 11 45 281.9 5 , ..., 11
2 2 2 2 2 2 2 2 2
45 017.3 3 , ..., 11 45 088.3 5 , ..., 11 45 190.5 3 , ..., 11 45 287.0 5 , ..., 11
2 2 2 2 2 2 2 2
45 018.4 5 , 7 , 9 45 090.5 5 , 7 , 9 45 192.5 5 , ..., 11 45 290.1 5 , ..., 11
2 2 2 2 2 2 2 2 2 2
45 019.1 3 , ..., 11 45 093.5 5 , 7 , 9 45 194.1 5 , 7 , 9 45 292.7 5 , ..., 11
2 2 2 2 2 2 2 2 2 2
45 027.1 5 , 7 , 9 45 094.5 5 , 7 , 9 45 195.8 5 , ..., 11 45 351.3 5 , 7 , 9
2 2 2 2 2 2 2 2 2 2 2
45 028.4 3 , ..., 11 45 095.5 5 , 7 , 9 45 198.0 3 , ..., 11 45 377.5 3 , ..., 11
2 2 2 2 2 2 2 2 2
45 029.6 5 , ..., 11 45 104.2 5 , 7 , 9 45 212.6 5 , ..., 11 45 378.7 3 , ..., 11
2 2 2 2 2 2 2 2 2
(Continued on next page.)
17
TABLE IX: (Continued.)
E (cm−1) J E (cm−1) J E (cm−1) J E (cm−1) J
45 378.9 3 , ..., 11 45 390.3 3 , ..., 11 45 409.9 3 , ..., 11 45 443.4 3 , ..., 11
2 2 2 2 2 2 2 2
45 381.2 3 , ..., 11 45 396.6 3 , ..., 11 45 411.3 3 , ..., 11 45 451.0 3 , ..., 11
2 2 2 2 2 2 2 2
45 381.7 3 , ..., 11 45 398.0 3 , ..., 11 45 415.9 3 , ..., 11 45 459.1 3 , ..., 11
2 2 2 2 2 2 2 2
45 383.8 3 , ..., 11 45 400.5 3 , ..., 11 45 418.3 3 , ..., 11 45 464.3 3 , ..., 11
2 2 2 2 2 2 2 2
45 386.1 3 , ..., 11 45 402.0 3 , ..., 11 45 419.6 3 , ..., 11 45 468.3 3 , ..., 11
2 2 2 2 2 2 2 2
45 387.1 3 , ..., 11 45 406.8 3 , ..., 11 45 421.3 3 , ..., 11
2 2 2 2 2 2
45 387.8 3 , ..., 11 45 408.9 3 , ..., 11 45 433.9 3 , ..., 11
2 2 2 2 2 2
18
TABLE X. List of values for the rst ionization potential (IP) and uncertainties (∆IP) up to proton number Z = 103. For
elements where no reference is given see [2] and references therein. In the case of Rn no uncertainty is given in the reference.
Z Symb. IP (eV) ∆IP (eV) Ref. Z Symb. IP (eV) ∆IP (eV) Ref.
1 H 13.59843449 8.0E-08 53 I 10.451260 2.5E-05
2 He 24.58738880 1.5E-07 54 Xe 12.1298436 1.5E-06
3 Li 5.39171495 4.0E-08 55 Cs 3.893905695 2.4E-08
4 Be 9.322699 7.0E-06 56 Ba 5.2116646 1.2E-06
5 B 8.298019 3.0E-06 57 La 5.5769 6.0E-04
6 C 11.2602880 1.1E-06 58 Ce 5.5386 4.0E-04
7 N 14.53413 4.0E-05 59 Pr 5.47018 3.7E-04 [3]
8 O 13.618055 7.0E-06 60 Nd 5.5250 6.0E-04
9 F 17.42282 5.0E-05 61 Pm 5.58188 3.7E-05 this work
10 Ne 21.564540 7.0E-06 62 Sm 5.64371 1.7E-04
11 Na 5.1390769 3.0E-07 63 Eu 5.670385 5.0E-06
12 Mg 7.646236 4.0E-06 64 Gd 6.14980 4.0E-05
13 Al 5.985769 3.0E-06 65 Tb 5.8638 6.0E-04
14 Si 8.15168 3.0E-05 66 Dy 5.939061 6.2E-06 [4]
15 P 10.486686 1.5E-05 67 Ho 6.0214048 3.7E-07 [5]
16 S 10.36001 1.2E-04 68 Er 6.1077 1.1E-05
17 Cl 12.967632 1.6E-05 69 Tm 6.18431 6.0E-05
18 Ar 15.7596117 5.0E-07 70 Yb 6.254160 1.2E-05
19 K 4.34066369 9.0E-08 71 Lu 5.425871 1.2E-05
20 Ca 6.1131554 3.0E-07 72 Hf 6.825070 1.2E-05
21 Sc 6.56149 6.0E-05 73 Ta 7.549571 2.5E-05
22 Ti 6.828120 1.2E-05 74 W 7.86403 1.0E-04
23 V 6.746187 2.1E-05 75 Re 7.83352 1.1E-04
24 Cr 6.76651 4.0E-05 76 Os 8.43823 2.0E-04
25 Mn 7.4340379 1.2E-06 77 Ir 8.96702 2.2E-04
26 Fe 7.9024681 1.2E-06 78 Pt 8.95883 1.0E-04
27 Co 7.88101 1.2E-04 79 Au 9.225554 4.0E-06
28 Ni 7.639878 1.7E-05 80 Hg 10.437504 6.0E-06
29 Cu 7.726380 4.0E-06 81 Tl 6.1082873 1.2E-06
30 Zn 9.394197 6.0E-06 82 Pb 7.4166799 6.0E-07
31 Ga 5.9993020 1.2E-06 83 Bi 7.285516 6.0E-06
32 Ge 7.899435 1.2E-05 84 Po 8.418069 5.1E-06 [6, 7]
33 As 9.78855 2.5E-04 85 At 9.31751 8.0E-05
34 Se 9.752392 1.5E-05 86 Rn 10.74850 *
35 Br 11.81381 6.0E-05 87 Fr 4.0727410 1.1E-06
36 Kr 13.9996053 2.0E-06 88 Ra 5.2784239 2.5E-06
37 Rb 4.1771280 1.2E-06 89 Ac 5.380226 2.4E-05
38 Sr 5.69486740 1.3E-07 90 Th 6.30670 2.5E-04
39 Y 6.21726 1.0E-04 91 Pa 6.08 1.4E-02 [3]
40 Zr 6.63412 6.0E-05 92 U 6.19405 6.0E-05
41 Nb 6.75885 4.0E-05 93 Np 6.26554 2.5E-04
42 Mo 7.09243 4.0E-05 94 Pu 6.02576 2.5E-04
43 Tc 7.11938 3.0E-05 95 Am 5.97381 2.5E-04
44 Ru 7.36050 5.0E-05 96 Cm 5.99141 2.5E-04
45 Rh 7.45890 5.0E-05 97 Bk 6.19785 2.5E-04
46 Pd 8.336839 1.0E-05 98 Cf 6.28166 2.5E-04
47 Ag 7.576234 2.5E-05 99 Es 6.36758 2.5E-04
48 Cd 8.993820 1.6E-05 100 Fm 6.52 1.3E-01 [8]
49 In 5.7863556 7.0E-07 101 Md 6.59 1.3E-01 [8]
50 Sn 7.343918 1.2E-05 102 No 6.62621 5.0E-05 [9]
51 Sb 8.608389 1.2E-05 103 Lr 4.96 8.0E-02
52 Te 9.009803 5.5E-06 [10]
19
[1] J. Reader and S. P. Davis, Journal of Research of the National Bureau of Standards - A. Physica and Chemistry 71A, 587
(1967).
[2] A. Kramida and Y. Ralchenko, NIST Atomic Spectra Database, NIST Standard Reference Database 78,.
[3] K. Wendt, T. Gottwald, C. Mattolat, and S. Raeder, Hyperne Interactions 227, 55 (2014).
[4] D. Studer, P. Dyrauf, P. Naubereit, R. Heinke, and K. Wendt, Hyperne Interactions 238, 02A916 (2017).
[5] J. Hostetter, J. D. Pritchard, J. E. Lawler, and M. Saman, Physical Review A 91, 71 (2015).
[6] S. Raeder, H. Heggen, A. Teigelhöfer, and J. Lassen, Spectrochimica Acta Part B: Atomic Spectroscopy 151, 65 (2019).
[7] D. A. Fink, K. Blaum, V. N. Fedosseev, B. A. Marsh, R. E. Rossel, and S. Rothe, Spectrochimica Acta Part B: Atomic
Spectroscopy 151, 72 (2019).
[8] T. K. Sato, M. Asai, A. Borschevsky, R. Beerwerth, Y. Kaneya, H. Makii, A. Mitsukai, Y. Nagame, A. Osa, A. Toyoshima,
K. Tsukada, M. Sakama, S. Takeda, K. Ooe, D. Sato, Y. Shigekawa, S.-I. Ichikawa, C. E. Düllmann, J. Grund, D. Renisch,
J. V. Kratz, M. Schädel, E. Eliav, U. Kaldor, S. Fritzsche, and T. Stora, Journal of the American chemical society 140,
14609 (2018).
[9] P. Chhetri, D. Ackermann, H. Backe, M. Block, B. Cheal, C. Droese, C. E. Düllmann, J. Even, R. Ferrer, F. Giacoppo,
S. Götz, F. P. Heÿberger, M. Huyse, O. Kaleja, J. Khuyagbaatar, P. Kunz, M. Laatiaoui, F. Lautenschläger, W. Lauth,
N. Lecesne, L. Lens, E. Minaya Ramirez, A. K. Mistry, S. Raeder, P. van Duppen, T. Walther, A. Yakushev, and Z. Zhang,
Physical Review Letters 120, 263003 (2018).
[10] T. Kieck, Y. Liu, R. Li, J. Lassen, and K. D. A. Wendt, submitted to Phys. Rev. A (2019).

List of Figures
1.1 Section of the Nuclear Chart in the Pm region close to the valley of
β-stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.2 Schematic of the RIMS principle . . . . . . . . . . . . . . . . . . . . . 6
2.1 Layout of the different Mainz University Ti:sapphire laser types . . . 12
2.2 Principle of Lyot Filter and Fabry-Pérot-Etalon . . . . . . . . . . . . . 13
2.3 Operation principle of a reflective diffraction grating . . . . . . . . . 14
2.4 Photograph of the standard Ti:sapphire resonator with intra-cavity
SHG . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.5 Sketch of a Fizeau interferometer for use in a wavelength meter. . . . 19
2.6 Schematic view of the Rb saturated absorption spectroscopy setup . 21
2.7 87Rb saturated absorption spectrum . . . . . . . . . . . . . . . . . . . 22
2.8 Relative frequency measurement with an S-FPI . . . . . . . . . . . . . 23
2.9 Overview of the RISIKO setup . . . . . . . . . . . . . . . . . . . . . . 25
2.10 Hot-cavity ion source of the RISIKO mass separator . . . . . . . . . . 26
2.11 Schematic layout of the Laser Ion Source and Trap (PI-)LIST . . . . . 27
2.12 Sketch of the mass separation principle with a focusing dipole magnet 29
2.13 Layout of the ISOLDE target and ion source unit . . . . . . . . . . . . 32
2.14 Laser spectroscopy on radioactive isotopes - an overview . . . . . . . 33
3.1 Lifetime measurement of the excited state at 23 083.3 cm−1 in Cm I . 42
3.2 Mass and temperature dependence of spectral Doppler broadening . 44
3.3 Laser-atom interaction in crossed-beam geometry . . . . . . . . . . . 45
3.4 Schematic description of RIS ionization mechanisms . . . . . . . . . 48
3.5 Graphical representation of electric field ionization . . . . . . . . . . 51
4.1 Nuclear energy level diagram of the shell model . . . . . . . . . . . . 82
4.2 Nilsson diagram for 40 < Z < 82 . . . . . . . . . . . . . . . . . . . . . 85
4.3 Exemplary hyperfine level scheme for J = 1 and I = 3/2. . . . . . . 88
A.1 Photograph of the compact-footprint injection-seeded laser . . . . . . 126
A.2 Calculated beam waist for the compact-footprint injection-seeded laser127
A.3 Photograph of the unseeded bowtie-resonator laser . . . . . . . . . . 128
A.4 Calculated beam waist for the unseeded bowtie-resonator laser . . . 129
155
List of Figures
A.5 Spectrum of the 741 nm line in Dy using the unseeded bowtie-
resonator laser . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
A.6 Spectrum of the second excitation step in Dy, starting from the
13 495.96 cm−1 excited state . . . . . . . . . . . . . . . . . . . . . . . . 132
156
List of Tables
2.1 Specifications for the output of the different Ti:sapphire laser types. 16
3.1 Selection rules for electronic dipole transitions . . . . . . . . . . . . . 41
157

List of Abbreviations
AEC-LHEP Albert Einstein Center for Fundamental Physics - Laboratory for High
Energy Physics, Bern. 107
AIS Auto-ionizing state. 47, 48
ASE Air-spaced etalon. 127
BBO Beta barium borate. 17, 18
CEM Channel electron multiplier. 30, 31
CERN European Organization for Nuclear Research, Geneva; acronym from
french: Conseil européen pour la recherche nucléaire. 5, 10, 24, 31, 92, 107, 123,
181
CRIS Collinear Resonance Ionization Spectroscopy; experiment at ISOLDE. 32
cw Continuous wave. 9, 14–16, 50, 123, 127
DC Direct current; opposite: AC for alternating current. 2, 51
ECDL External cavity diode laser. 15, 16, 21–24, 123
ECHo Electron Capture in 163Ho. 5, 24, 59, 122
FC Faraday cup. 30
FI Fizeau interferometer. 19, 20
FPE Fabry-Pérot etalon. 11, 13, 127
FPI Fabry-Pérot inteferometer. 19, 20, 23
FS Fine structure. 36, 37, 87
FSR Free spectral range. 11, 13, 19, 20, 23, 126, 127
FWHM Full width at half maximum. 11, 41, 43, 44, 48
159
List of Abbreviations
GANDALPH Gothenburg Anion Detector for Affinity Measurements by Laser
Photodetachment. 31
GSI Helmholtzzentrum für Schwerionenforschung, Darmstadt; formerly:
Gesellschaft für Schwerionenforschung. v, 92
HFS Hyperfine structure. 87, 89, 90, 129
IGISOL Ion Guide Isotope Separation On-Line. 5, 32
ILL Institut Laue-Langevin, Grenoble. 71, 107
IP Ionization potential. v, 2, 4, 27, 36, 39, 48–52, 59, 71, 122
IS Isotope shift. 87, 90
ISAC Isotope separator and Accelerator, TRIUMF. 5, 10, 32
ISOL Isotope separation on-line. 31
ISOLDE Isotope Separation On-Line Device, CERN. 5, 9, 10, 16, 24, 31, 32, 123,
126
JYFL Jyväskylä accelerator laboratory. 5, 32
LARISSA Laser Resonance Ionization Spectroscopy for Selective Applications. 5,
19, 20, 22, 24, 31, 50, 53
LF Lyot-Filter. 11, 13, 15, 127
LIST Laser Ion Source and Trap. 27, 28, 32
MABU Mainz Atomic Beam Unit. 30, 31, 71
MCU Micro controller unit. 30
MOT Magneto-optical trap. 53, 121
Nd:YAG Neodymium-doped yttrium aluminium garnet. 10, 47
NIST U.S. National Institute of Standards and Technology. 38, 87
OES Odd-even staggering. 87
PBE Prism beam expander. 14
PI-LIST Perpendicularly Illuminated Laser Ion Source and Trap. 27, 28, 32, 43,
107, 121, 123
160
List of Abbreviations
PSB Proton synchrotron booster. 31
PSI Paul Scherrer Institut, Villigen. 71, 107, 181
QMF Quadrupole mass filter. 31
QUANTUM Quanten-, Atom- und Neutronenphysik (research group at Mainz
University). v, 181
RESIST Resonance Ionization Techniques for Separators. 6, 24, 123
RF Radio frequency. 27
RI Resonance ionization. 5–7, 14, 38, 46, 47
RIB Radioactive ion beam. 5, 24, 123
RILIS Resonance Ionization Laser Ion Source. 5, 10, 16, 24, 27, 28, 31, 32, 46, 122,
123, 126
RIMS Resonance ionization mass spectrometry. 5, 6, 24
RIS Resonance ionization spectroscopy. 2, 5–7, 10, 18, 19, 40, 42, 45, 46, 49, 50, 53,
71, 89, 121, 122
RISIKO Resonance Ionization Spectroscopy in Collinear geometry; from german:
Resonanzionisations-Spektroskopie in kollinearer Geometrie. 10, 24–26, 28–32, 43,
107
SAS Saturated absorption spectroscopy. 20, 22, 92
SATLAS Statistical Analysis Toolbox for Laser Spectroscopy; python package. 45,
89
SFPI Scanning Fabry-Pérot inteferometer. 22, 23, 92
SHG Second harmonic generation. 17, 18
SIRIUS Secondary Ionisation of Radioactive Isotopes for Ultra trace analysis. 5
TRIUMF TRI University Meson Facility, Vancouver. 5, 14, 32
UV Ultraviolet. 10, 16
YAG Yttrium aluminium garnet. 13
161

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Acknowledgements
People always say you will miss your final years in school when starting with a
regular job or studies at the university. While I agree with this, I must say it wasn’t
so bad. In fact, I very much enjoyed the many years of being a student at Mainz
University. Eventually ending up in the LARISSA group, I was surprised by the
great atmosphere and teamwork. Starting completely clueless about almost any
device you can possibly find in the lab was not so much of an issue, since I never
had the feeling of being lost or left alone with the many problems one is facing in
experimental physics. With this in mind I would like to thank my colleagues from
the first hour, Tobi, Fabian, Sven, Pascal, Tom, Michael, Reinhard, Katerina, Marcel
and Patrick, who gave me a warm welcome and great support during my work.
Since then the group has changed a bit, but fortunately not for the worse. In this
sense I thank Vadim, Nina, Felix, Vlad and Johannes as the newer members of the
LARISSA family. The four o’clock tea and countless rounds of after-lunch kicker,
when normal people have coffee, brighten up the daily routine (despite struggling
to stay above the ”Guest” player in my personal ranking). And of course, not
to forget about the many successful and not-so-successful Pub-Quiz evenings
featuring Larissa-(Z)User. We all miss you as our team captain, Reinhard.
A special thanks goes to my mentor Klaus. I really appreciated the encouragement
towards independent work, leaving room for initiative and creativity, while I
could always count on advice and interest in details. Moreover, the introduction
to the international RIMS community was strongly supported by Klaus. The
many exciting experiments at CERN, GANIL or LLNL, and participation in
international conferences and meetings have been of great value to me. Apart
from that, being the guy responsible for any spontaneously upcoming projects,
I enjoyed the collaboration within the QUANTUM group. Searching for the
mysterious dysprosium-1000 line with Lena and trapping beryllium ions with
Sebastian was something refreshingly different.
Since I will stay in Mainz for a bit longer, this is not a goodbye and I am looking
forward to continue research without a PhD thesis looming on the horizon.
In addition to my closer colleagues, I would like to thank Seppl for the
great support during almost any experiment and the target production team of
PSI, Jiri, Stephan, Rugard and Dorothea for supplying me with these valuable Pm
samples, rendering our measurements possible in the first place.
Another special thanks goes to Dr. James for proofreading.
Finally, I thank my family and Sarah. I would not have made it here with-
out you Ω.
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