Relativistic semiempirical-core-potential calculations in ${\mathrm{Ca}}^{+},{\mathrm{Sr}}^{+}$, and ${\mathrm{Ba}}^{+}$ ions on Lagrange meshes

Relativistic atomic structure calculations are carried out in alkaline-earth-metal ions using a semiempirical-core-potential approach. The systems are partitioned into frozen-core electrons and an active valence electron. The core orbitals are defined by a Dirac-Hartree-Fock calculation using the grasp2k package. The valence electron is described by a Dirac-like Hamiltonian involving a core-polarization potential to simulate the core-valence electron correlation. The associated equation is solved with the Lagrange-mesh method, which is an approximate variational approach having the form of a mesh calculation because of the use of a Gauss quadrature to calculate matrix elements. Properties involving the low-lying metastable ${}^{2}D_{3/2,5/2}$ states of ${\mathrm{Ca}}^{+}, {\mathrm{Sr}}^{+}$, and ${\mathrm{Ba}}^{+}$ are studied, such as polarizabilities, one- and two-photon decay rates, and lifetimes. Good agreement is found with other theory and observation, which is promising for further applications in alkalilike systems.