The Bohr-Weisskopf effect: from hydrogenlike-ion experiments to heavy-atom calculations of the hyperfine structure

In this paper we study the influence of electron screening on the Bohr-Weisskopf (BW) effect in many-electron atoms. The BW effect gives the finite-nucleus magnetization contribution to the hyperfine structure. Relativistic atomic many-body calculations are performed for s and p_1/2 states of several systems of interest for studies of atomic parity violation and time-reversal-violating electric dipole moments -- Rb, Cs, Fr, Ba+, Ra+, and Tl. For s states, electron screening effects are small, and the relative BW correction for hydrogenlike ions and neutral atoms is approximately the same. We relate the ground-state BW effect in H-like ions, which may be cleanly extracted from experiments, to the BW effect in s and p_1/2 states of neutral and near neutral atoms through an electronic screening factor. This allows the BW effect extracted from measurements with H-like ions to be used, with screening factors, in atomic calculations without recourse to modelled nuclear structure input. It opens the way for unprecedented accuracy in accounting for the BW effect in heavy atoms. The efficacy of this approach is demonstrated using available experimental data for H-like and neutral Tl-203 and Tl-205.