Finite-nuclear-size effect in hydrogen-like ions with relativistic nuclear structure

TL;DR

This paper systematically investigates the finite-nuclear-size effects on atomic energy levels and g factors in hydrogen-like ions up to atomic number 118, emphasizing the importance of detailed nuclear charge distributions obtained from relativistic nuclear models.

Contribution

It introduces a comprehensive analysis using relativistic continuum Hartree-Bogoliubov nuclear charge densities to evaluate FNS corrections, highlighting the impact of nuclear shape and size on atomic properties.

Findings

FNS corrections increase significantly with nuclear charge.

The shape of nuclear charge density influences FNS effects.

Good agreement with analytical models, with notable differences indicating microscopic nuclear structure effects.

Abstract

The finite-nuclear-size (FNS) effect has a large contribution to the atomic spectral properties especially for heavy nuclei. By adopting the microscopic nuclear charge density distributions obtained from the relativistic continuum Hartree-Bogoliubov (RCHB) theory, we systematically investigate the FNS corrections to atomic energy levels and bound-electron $g$ factors of hydrogen-like ions with nuclear charge up to $118$. The comparison of the present numerical calculations with the predictions from empirical nuclear charge models, the non-relativistic Skyrme-Hartree-Fock calculations, and the results based on experimental charge densities indicate that both the nuclear charge radius and the detailed shape of charge density distribution play important roles in determining the FNS corrections. The variation of FNS corrections to energy levels and $g$ factors with respect to the nuclear charge are investigated for the lowest several bound states of hydrogen-like ions. It is shown that they both increase by orders of magnitude with increasing the nuclear charge, while the ratio between them has a relatively weak dependence on the nuclear charge. The FNS corrections to the $s_{1/2}$ and $p_{1/2}$ bound state energies from the RCHB calculations are generally in good agreement with the analytical estimations by Shabaev [J. Phys. B, 26, 1103 (1993)] based on the homogeneously charged sphere nuclear model, with the discrepancy indicating the distinct contribution of microscopic nuclear structure to the FNS effects.