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