Atomic properties of Cd-like and Sn-like ions for the development of frequency standards and search for the variation of the fine-structure constant

A high-precision relativistic calculation of Cd-like $\mathrm{Nd}{}^{12+},\mathrm{Sm}{}^{14+}$ and Sn-like $\mathrm{Pr}{}^{9+},\mathrm{Nd}{}^{10+}$ atomic properties is carried out using an approach that combines configuration interaction and a linearized coupled-cluster method. These ions have long-lived metastable states with transitions accessible by laser excitations, relatively simple electronic structure, high sensitivity to $\alpha$ variation, and stable isotopes. Breit and QED corrections were included into the calculations. Energies, transition wavelengths, electric- and magnetic-multipole reduced matrix elements, lifetimes, and sensitivity coefficients $q$ and $K$ to the variation of the fine-structure constant $\alpha$ were obtained. A detailed study of uncertainties was performed. Energies for similar Cd-like $\mathrm{Ba}{}^{8+},\mathrm{La}{}^{9+},\mathrm{Ce}{}^{10+},\mathrm{Pr}{}^{11+}$ and Sn-like $\mathrm{Ba}{}^{6+}$ ions were calculated and compared with experiment for further tests of the accuracy.