Atomic properties of Ca$^+$, Sr$^+$, Cd$^+$, Hg$^+$, and Ra$^+$

We conducted a systematic study of the transition properties of Ca$^+$, Sr$^+$, Cd$^+$, Hg$^+$, and Ra$^+$ ions using a relativistic all-order method. Reduced electric-dipole matrix elements and transition rates are determined for the $ns-np_j$ and $np_j-n^{\prime}d_{j}$ transitions, where $ns$ is a ground state. The electric-quadrupole matrix elements are evaluated for the $ns-(n-1)d_j$ transitions in Sr$^+$ and Ra$^+$. The theoretical lifetimes for the $np_j$ and $nd_j$ states are compared with latest available experimental measurements. The energy levels and hyperfine constants are also calculated and compared with experiment. This work is motivated by recent lifetime measurements in Ca$^+$, Sr$^+$, and Cd$^+$.