Magnetizability of the relativistic hydrogenlike atom in an arbitrary discrete energy eigenstate: Application of the Sturmian expansion of the generalized Dirac-Coulomb Green function

TL;DR

This paper derives a closed-form expression for the magnetizability of relativistic hydrogenlike atoms in any discrete energy state using Sturmian expansion of the Dirac-Coulomb Green function, and provides numerical results for various ions.

Contribution

It introduces a novel closed-form formula for the magnetizability of relativistic hydrogenlike atoms in arbitrary states, expanding on previous analytical methods.

Findings

Derived a double finite sum formula involving hypergeometric functions

Confirmed the formula's consistency with previous special-case results

Provided numerical magnetizability values for ions with Z from 1 to 137

Abstract

The Sturmian expansion of the generalized Dirac--Coulomb Green function [R.\/~Szmytkowski, J.\ Phys.\ B \textbf{30}, 825 (1997); \textbf{30}, 2747(E) (1997)] is exploited to derive a closed-form expression for the magnetizability of the relativistic one-electron atom in an arbitrary discrete state, with a point-like, spinless and motionless nucleus of charge $Ze$. The result has the form of a double finite sum involving the generalized hypergeometric functions ${}_3F_2$ of the unit argument. Our general expression agrees with formulas obtained analytically earlier by other authors for some particular states of the atom. We present also numerical values of the magnetizability for some excited states of selected hydrogenlike ions with $1 \leqslant Z \leqslant 137$ and compare them with data available in the literature.