Vacuum polarization corrections to hyperfine structure in many-electron atoms

We perform a theoretical study of vacuum polarization corrections to the hyperfine structure in many-electron atoms. Calculations are performed for systems of interest for precision atomic tests of fundamental physics belonging to the alkali-metal atoms and singly ionized alkaline earths. The vacuum polarization is considered in the Uehling approximation, and we study the many-body effects core relaxation, core polarization, and valence-core correlations in the relativistic framework. We find that for $s$ states, the relative vacuum polarization correction may be well approximated by that for hydrogenlike ions, though for all other states an account of the many-body effects, in particular, the polarization of the core, is needed to obtain the correct sign and magnitude of the correction.