Impact of the nuclear charge distribution on the g-factors and ground state energies of bound muons

TL;DR

This paper investigates how different nuclear charge distribution models affect the calculated g-factors and ground state energies of muonic atoms, emphasizing the need for precise nuclear models for accurate quantum electrodynamics predictions.

Contribution

It provides both approximate and exact solutions to the Dirac equation for various nuclear models, including deformation effects, and evaluates vacuum polarization corrections.

Findings

Results depend heavily on the nuclear model used.

Nuclear deformation significantly influences g-factors and energies.

Accurate nuclear models are essential for precise QED predictions.

Abstract

The finite nuclear size corrections to the ground state energies and g-factors in muonic atoms are investigated for several elements. Both approximative and exact solutions of the one-particle Dirac equation with both the homogeneous sphere nucleus model and the Fermi distribution nucleus model are presented, and the leading nuclear deformation effects on the g-factors and ground state energies are also evaluated. The electronic, muonic, and hadronic electric-loop vacuum polarization corrections are calculated for point-like, spherical, and Fermi nucleus models. The obtained results show a heavy dependence on the chosen nuclear model, and highlight the importance of constructing precise theoretical models for the nucleus for accurate QED predictions of the observables of muonic atoms.