Computational investigation of static multipole polarizabilities and sum rules for ground-state hydrogen-like ions

TL;DR

This paper calculates high-precision static multipole polarizabilities for hydrogen-like ions using the Dirac equation and B-spline methods, providing analytic formulas and verifying sum rules for oscillator strengths.

Contribution

It introduces accurate calculations of multipole polarizabilities for hydrogen-like ions and derives compact analytic expressions as a function of nuclear charge Z.

Findings

Polarizabilities for $ ext{Z} extless 100$ with 10$^{-6}$ accuracy

Verification of oscillator strength sum rules for multipoles

Dispersion coefficients for H-H and H-He$^+$ interactions

Abstract

High precision multipole polarizabilities, $\alpha_{\ell}$ for $\ell \le 4$ of the $1s$ ground state of the hydrogen isoelectronic series are obtained from the Dirac equation using the B-spline method with Notre Dame boundary conditions. Compact analytic expressions for the polarizabilities as a function of $Z$ with a relative accuracy of 10$^{-6}$ up to $Z = 100$ are determined by fitting to the calculated polarizabilities. The oscillator strengths satisfy the sum rules $\sum_i f^{(\ell)}_{0i} = 0$ for all multipoles from $\ell = 1$ to $\ell = 4$. The dispersion coefficients for the long-range H-H and H-He$^+$ interactions are given.