Calculations of the ground-state hyperfine structure for Rb, Cs, Fr, Ba$^+$, and Ra$^+$

We have performed a comprehensive and high-accuracy study of the ground-state hyperfine structure for heavy alkali-metal atoms Rb, Cs, Fr and alkali-metal-like ions Ba$^+$ and Ra$^+$ of interest for atomic parity violation studies. We have rigorously evaluated the quantum electrodynamic radiative corrections at one-loop level and have carefully considered the effect due to the magnetization distribution of the nucleus. Many-body calculations in the all-orders correlation potential method were performed.