Theoretical prediction of the fine and hyperfine structure of heavy muonic atoms

Abstract

Precision calculations of the fine and hyperfine structure of muonic atoms are performed in a relativistic approach and results for muonic $^{205}\mathrm{Bi}, ^{147}\mathrm{Sm}$, and $^{89}\mathrm{Zr}$ are presented. The hyperfine structure due to magnetic dipole and electric quadrupole splitting is calculated in first-order perturbation theory, using extended nuclear charge and current distributions. The leading correction from quantum electrodynamics, namely vacuum polarization in Uehling approximation, is included as a potential directly in the Dirac equation. Also, an effective screening potential due to the surrounding electrons is calculated, and the leading relativistic recoil correction is estimated.