Finite Nuclear Size Effect to the Fine Structure of Heavy Muonic Atoms

The finite-nuclear size correction to the fine structure of muonic atoms are considered. The procedure for the analytical calculation of the energies and wave functions has been derived in a homogeneously charged sphere nuclear charge distribution approximation. The finite-nuclear size effect was calculated in a first few orders of the perturbation energy, with the accurate estimations of the convergence. Finally, we present energies of the low-lying electronic and muonic states with the finite-nuclear size correction, calculated analytically, for ${}_{75}^{185}\text{Re}$ ion.