Magnetizabilities of relativistic hydrogenlike atoms in some arbitrary discrete energy eigenstates

TL;DR

This paper provides numerical calculations of the magnetizability for various energy states of relativistic hydrogenlike atoms across atomic numbers 1 to 137, using an analytical formula and comparing results with different fine-structure constants.

Contribution

It introduces a comprehensive numerical analysis of magnetizability for multiple energy states of relativistic hydrogenlike atoms using a recently derived analytical formula.

Findings

Magnetizability values are tabulated for Z=1 to 137.

Comparison of results using two different fine-structure constants.

Data covers ground and excited states up to n=3.

Abstract

We present the results of numerical calculations of magnetizability ($\chi$) of the relativistic one-electron atoms with a pointlike, spinless and motionless nuclei of charge $Ze$. Exploiting the analytical formula for $\chi$ recently derived by us [P. Stefa{\'n}ska, 2015], valid for an arbitrary discrete energy eigenstate, we have found the values of the magnetizability for the ground state and for the first and the second set of excited states (i.e.: $2s_{1/2}$, $2p_{1/2}$, $2p_{3/2}$, $3s_{1/2}$, $3p_{1/2}$, $3p_{3/2}$, $3d_{3/2}$, and $3d_{5/2}$) of the Dirac one-electron atom. The results for ions with the atomic number $1 \leqslant Z \leqslant 137$ are given in 14 tables. The comparison of the numerical values of magnetizabilities for the ground state and for each states belonging to the first set of excited states of selected hydrogenlike ions, obtained with the use of two different values of the fine-structure constant, i.e.: $\alpha^{-1}=137.035 999 139$ (CODATA 2014) and $\alpha^{-1}=137.035 999 074$ (CODATA 2010), is also presented.