J. C. Hasted, C. J. Fairhall, O. R. Smits, B. M. Roberts, and J. S. M. Ginges, arXiv:2409.17979

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 hydrogen-like ions, though for all other states account of many-body effects - in particular, the polarization of the core - is needed to obtain the correct sign and magnitude of the effect.