Isotope shift for total electron binding energy of atoms

TL;DR

This paper calculates isotope shifts in total electron binding energies for atoms up to Z=120 using relativistic methods, providing data and interpolation formulas useful for superheavy elements and ions.

Contribution

It offers comprehensive isotope shift coefficients for a wide range of elements and ions, including a simple power law interpolation for practical estimates.

Findings

Power law $bZ^k$ accurately reproduces field shifts within 1%.

Effective exponent $k$ increases from 5 to 12 across Z=50 to 118.

Differences between neutral and singly charged ions are generally small.

Abstract

We compute the isotope shifts of the \emph{total} electron binding energy of neutral atoms and singly charged ions up to element $Z=120$, using relativistic Hartree-Fock method including the Breit interaction. Field shift coefficients are extracted by varying the nuclear charge radius; a small quadratic term is retained to cover large radius changes relevant to superheavy nuclei. We tabulate isotope shift coefficients for closed shell systems from Ne to Og and benchmark selected open shell cases, used to test the interpolation formula. A simple power law interpolation $bZ^k$ reproduces calculated field shifts to within about 1\% across the table, with the effective exponent $k$ growing from roughly 5 near $Z \sim 50$ to about 12 at $Z \sim 118$. Due to the domination of inner shells, differences between neutrals and singly charged ions does not exceed few percent, becoming noticeable mainly when an outer $s$ electron is removed. Therefore, these results may also be used for higher charge ions.