  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.
