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Relativistic atomic structure calculations are carried out inalkaline-earth-metal ions using a semiempirical-core-potential approach. Thesystems are partitioned into frozen-core electrons and an active valenceelectron. The core orbitals are defined by a Dirac-Hartree-Fock calculationusing the grasp2k package. The valence electron is described by a Dirac-likeHamiltonian involving a core-polarization potential to simulate thecore-valence electron correlation. The associated equation is solved with theLagrange-mesh method, which is an approximate variational approach having theform of a mesh calculation because of the use of a Gauss quadrature tocalculate matrix elements. Properties involving the low-lying metastable$^2D_{3/2,5/2}$ states of Ca$^{+}$, Sr$^{+}$, and Ba$^{+}$ are studied, such aspolarizabilities, one- and two-photon decay rates, and lifetimes. Goodagreement is found with other theory and observation, which is promising forfurther applications in alkali-like systems.

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