Nuclear structure corrections in muonic atoms

Abstract

Muonic hydrogen-like atoms, bound systems of a muon and an atomic nucleus, are excellent probes for nuclear physics, because the muon is much heavier than the electron and its wavefunction overlaps significantly more with the nuclear charge distribution. This increased sensitivity to nuclear physics allows for precise extractions of nuclear charge radii by measuring the Lamb-shift. The precision of this extraction is currently limited by the uncertainty of nuclear structure effects, which are not known as precisely as quantum electrodynamics effects, due to the non-perturbative nature of the strong force at the low-energy scale relevant to muonic atoms. This work addresses the calculation of the nuclear structure corrections to the Lamb-shift of muonic helium and lithium atoms. For muonic lithium, we calculate the nuclear structure corrections to the Lamb-shift using a simplified model of the nuclear force. This allows us to perform estimates, which are useful in view of the future planned experimental activities. For muonic helium, the novelty of this work comes from the use of nuclear interactions derived from the chiral effective field theory and of Bayesian inference for quantifying the uncertainties. This combination of techniques puts the problem of quantifying theoretical uncertainties in nuclear physics into a more solid statistical ground and defines a systematically improvable method for calculating observables. The main results of this work are new high-precision values for nuclear structure corrections in muonic atoms, which can be used to update the charge radii of 3 He and 4 He extracted from the recent muonic-atoms spectroscopy experiments in muonic helium. Due to partial cancellation of uncertainties, the squared difference in the nuclear charge radii, δr2 = rc2 (3 He) − rc2 (4 He) can be obtained with more precision than the nuclear charge radii itself. This quantity can also be precisely obtained from spectroscopy experiments in ordinary helium atoms, which allows to perform consistency checks between theory and experiments in electronic and muonic atoms. Two publications of δr2 , one using muonic atoms and the other using ordinary helium atoms, were recently published, which resulted in a disagreement at the level of 3.6σ. Our updated theory of the nuclear structure effects supports the previous value of δr2 coming from muonic atoms, and intensifies the current disagreement.