Relativistic semiempirical-core-potential calculations ofSr+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 ${\mathrm{Sr}}^{+}$. The magic wavelengths at which the Stark shifts between different pairs of transitions are 0 are computed. Determination of the magic wavelengths for the $5s\to 4d_{\frac{3}{2}}$ and $5s\to 4d_{\frac{5}{2}}$ transitions near 417 nm (near the wavelength for the $5s\to 5p_j$ transitions) would allow determination of the oscillator strength ratio for the $5s\to 5p_{\frac{1}{2}}$ and $5s\to 5p_{\frac{3}{2}}$ transitions.