Relativistic calculations of quasi-one-electron atoms and ions using Laguerre and Slater spinors

TL;DR

This paper develops a relativistic method using S-spinors and L-spinors to accurately calculate properties of heavy alkali atoms and ions, including energies, decay rates, and polarizabilities, with applications to identifying magic wavelengths.

Contribution

It introduces a novel relativistic approach combining S-spinors and L-spinors for quasi-one-electron atoms, demonstrating numerical stability and applying it to polarizability and magic wavelength calculations.

Findings

Accurate energies and decay rates for low-lying hydrogen states.

Computed polarizabilities of a $Z=60$ hydrogenic ion.

Identified magic wavelengths for Sr$^+$ transitions.

Abstract

A relativistic description of the structure of heavy alkali atoms and alkali-like ions using S-spinors and L-spinors has been developed. The core wavefunction is defined by a Dirac-Fock calculation using an S-spinors basis. The S-spinor basis is then supplemented by a large set of L-spinors for the calculation of the valence wavefunction 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 zero are computed. Determination of the magic wavelengths for the $5s \to 4d_{\frac32}$ and $5s \to 4d_{\frac52}$ transitions near $417$~nm (near the wavelength for the $5s \to 5p_j$ transitions) would allow a determination of the oscillator strength ratio for the $5s \to 5p_{\frac12}$ and $5s \to 5p_{\frac32}$ transitions.