Motivated by recent experimental advances, including the ongoing development of an optical atomic clock in singly ionized radium, we perform a detailed theoretical characterization of ${\mathrm{Ra}}^{+}$ and its lighter analog ${\mathrm{Ba}}^{+}$. Both ions are of interest for precision studies, including for atomic parity violation and searches for new physics beyond the standard model. Using the all-order correlation potential method, including Breit and radiative quantum electrodynamics corrections, we perform high-accuracy calculations of electric dipole ($E1$), electric quadrupole ($E2$), and magnetic dipole ($M1$) transition matrix elements between the low-lying $s, p$, and $d$ states of these ions, as well as the excited-state lifetimes, polarizabilities, magic wavelengths, and magnetic dipole hyperfine-structure constants $A$. By combining lifetime measurements with accurate theoretical ratios, we extract high-precision determinations of the $s\text{−}{d}_{1/2,3/2} E2$ matrix elements. By combining hyperfine measurements with atomic theory, we extract parameters of the nuclear magnetization distribution (the Bohr-Weisskopf effect) for ${}^{135,137}\mathrm{Ba}$ and ${}^{223,225}\mathrm{Ra}$. These results provide theoretical input for ongoing and future experimental programs in fundamental physics and precision metrology.

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• Atomic & molecular processes in external fields
• Atomic & molecular structure
• Atomic, optical & lattice clocks
• Electronic transitions
• Fine & hyperfine structure
• Nuclear shapes and moments