Excitation energies, E1, M1, and E2 transition rates, and lifetimes in Ca⁺, Sr⁺, Cd⁺, Ba⁺, and Hg⁺

Excitation energies of ns_1/2, np_j, and nd_j states in Cd⁺ (n = 5), Hg⁺ (n = 5) and ns_1/2, np_j, and (n - 1)d_j states in Ca⁺ (n = 4), Sr⁺ (n = 5), and Ba⁺ (n = 6) are evaluated using the linearized coupled-cluster (all-order) method. Reduced matrix elements, oscillator strengths, and transition rates are determined for the ns-np_j-nd_j (or ns-np_j-(n - 1)d_j) possible electric dipole transitions in Ca⁺, Sr⁺, Ba⁺, Cd⁺, and Hg⁺. Electric quadrupole matrix elements are evaluated to obtain ns_1/2-(n - 1)d_j transition rates in Ca⁺ (n = 5), Sr⁺ (n = 5), and Ba⁺ (n = 6). The matrix elements are calculated using both relativistic many-body perturbation theory, complete through third order, and the relativistic all-order method restricted to single and double (SD) excitations. The SD lifetime results for the np and nd states in Ca⁺, Sr⁺, Ba⁺, Cd⁺, and Hg⁺, are compared with the latest available experimental measurements. The contribution of the magnetic dipole nd_3/2-nd_5/2 transition to the lifetimes of the lowest nd_5/2 level ln Ca⁺, Sr⁺, and Ba⁺ ions is discussed. These calculations provide a theoretical benchmark for comparison with experiment and theory as well as data needed for various applications. (author)