Nuclear size corrections to the energy levels of single-electron atoms

TL;DR

This paper investigates how the finite size of the nucleus affects the energy levels of single-electron atoms, comparing perturbative and exact relativistic calculations to understand discrepancies.

Contribution

It provides a detailed comparison of nuclear size corrections using perturbation theory against exact relativistic results for hydrogen-like atoms.

Findings

Small discrepancies found between perturbative and exact relativistic results.

Finite nuclear size causes measurable shifts in atomic energy levels.

Relativistic effects are significant for high nuclear charge numbers.

Abstract

A study is made of nuclear size corrections to the energy levels of single-electron atoms for the ground state of hydrogen like atoms. We consider Fermi charge distribution to the nucleus and calculate atomic energy level shift due to the finite size of the nucleus in the perturbation theory context. The exact relativistic correction based upon the available analytical calculations is compared to the result of first-order relativistic perturbation theory and the non-relativistic approximation. We find small discrepancies between our perturbative results and those obtained from exact relativistic calculation even for large nuclear charge number .