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 calculations of Cd-like Nd$^{12+}$, Sm$^{14+}$ and Sn-like Pr$^{9+}$, 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 Ba$^{8+}$, La$^{9+}$, Ce$^{10+}$, Pr$^{11+}$ and Sn-like Ba$^{6+}$ ions were calculated and compared with experiment for further tests of the accuracy.