Relativistic semiempirical-core-potential calculations of Sr+ using Laguerre and Slater spinors

A relativistic description of the structure of heavy alkali-metal atoms and alkali-like ions using S-spinors and L-spinors is developed. The core wave function is defined by a Dirac-Fock calculation using an S-spinor basis. The S-spinor basis is then supplemented with a large set of L-spinors for calculation of the valence wave function in a frozen-core model. The numerical stability of the L-spinor approach is demonstrated by computing the energies and decay rates of several low-lying hydrogen eigenstates, along with the polarizabilities of a Z = 60 hydrogenic ion. The approach is then applied to calculate the dynamic polarizabilities of the 5s, 4d, and 5p states of Sr+. The magic wavelengths at which the Stark shifts between different pairs of transitions are 0 are computed. Determination of the magic wavelengths for the 5s -> 4d(3/2) and 5s -> 4d(5/2) transitions near 417 nm (near the wavelength for the 5s -> 5(pj) transitions) would allow determination of the oscillator strength ratio for the 5s -> 5p(1/2) and 5s -> 5(p3/2) transitions.