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

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.