Nuclear magnetic shielding constants of Dirac one-electron atoms in some low-lying discrete energy eigenstates

TL;DR

This paper provides comprehensive tabulated data for the nuclear magnetic shielding constants of Dirac one-electron atoms across various low-lying energy states, covering a wide range of nuclear charges, using an exact analytical formula.

Contribution

The authors derive and utilize an exact analytical formula for nuclear magnetic shielding constants applicable to any discrete energy eigenstate of Dirac one-electron atoms, providing extensive numerical data.

Findings

Computed shielding constants for Z=1 to 137.

Compared results with previous studies for validation.

Provided data for multiple excited states.

Abstract

We present tabulated data for the nuclear magnetic shielding constants ($\sigma$) of the Dirac one-electron atoms with a pointlike, motionless and spinless nucleus of charge $Ze$. Utilizing the exact general analytical formula for $\sigma$ derived by us \mbox{[P. Stefa{\'n}ska, Phys. Rev. A. 94 (2016) 012508/1-15],} valid for an arbitrary discrete energy eigenstate, we have computed the numerical values of the magnetic shielding factors 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 relativistic hydrogenic ions with the nuclear charge numbers from the range $1 \leqslant Z \leqslant 137$. The comparisons of our results with the numerical values reported by other authors for some atomic states are also presented.