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

TL;DR

This paper analytically calculates the finite-nuclear size correction to the fine structure of heavy muonic atoms, providing precise energy estimations for low-lying states in Re-185 considering nuclear size effects.

Contribution

It introduces an analytical method for calculating finite-nuclear size corrections in muonic atoms using a homogeneously charged sphere model, including convergence estimates.

Findings

Finite-nuclear size correction significantly affects muonic atom energy levels.

Analytical formulas for energies of low-lying states are derived.

Results are applied to Re-185 ion, showing practical relevance.

Abstract

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 ${}^{185}_{75}\text{Re}$ ion.