Para- and diamagnetic contributions to magnetic shielding constants of relativistic hydrogenlike atoms in some low-lying discrete energy eigenstates

TL;DR

This paper provides detailed numerical data on para- and diamagnetic contributions to magnetic shielding constants in relativistic hydrogenlike atoms across various energy states and nuclear charges, using analytical formulas and comparing with existing results.

Contribution

The authors derived and tabulated numerical values for magnetic shielding contributions in relativistic hydrogenic atoms for multiple states and nuclear charges, including comparisons with previous studies.

Findings

Numerical values of $\sigma_{d}/\sigma$ and $\sigma_{p}/\sigma$ for various states and Z.

Total magnetic shielding constants for selected states and different fine-structure constants.

Comparison of results with previous literature for some atomic states.

Abstract

We present tabulated data for numerical calculations of relative para- and diamagentic contributions to the magnetic shielding constant ($\sigma$) of the Dirac one-electron atoms with a pointlike, spinless and motionless nuclei of charge $Ze$. Exploiting the analytical formulas for the diamagnetic ($\sigma_{d}$) and paramagnetic ($\sigma_{p}$) terms of $\sigma$, valid for an arbitrary discrete energy state, recently derived by us with the aid of the Gordon decomposition technique, we have found the numerical values of $\sigma_{d}/\sigma$ and $\sigma_{p}/\sigma$ for the ground state and for the first two sets 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 relativistic hydrogenic ions with the nuclear charge number from the range $1 \leqslant Z \leqslant 137$. The comparisons of our results with those reported by other authors for some atomic states are also presented. We also compile here the numerical values of the total magnetic shielding constants for the ground state $1s_{1/2}$ and for each state belonging to the first set of excited states of selected hydrogenlike ions, obtained with the use of three different values of the fine-structure constant, i.e.: $\alpha^{-1}=137.035 \: 999 \: 139$ (from CODATA 2014), $\alpha^{-1}=137.035 \: 999 \: 084$ (from CODATA 2018) and $\alpha^{-1}=137.035 \: 999 \: 177$ (from CODATA 2024).