Hydrogen and hydrogen-like-ion bound states and hyperfine splittings: finite nuclear size effects}

TL;DR

This paper investigates finite nuclear size effects on energy levels and hyperfine splittings in hydrogen-like ions using the Dirac equation, considering various nuclear models and comparing corrections across different atomic numbers.

Contribution

It provides a detailed analysis of finite nuclear size corrections to energy and hyperfine splittings, including relativistic and recoil effects, across a range of light and heavy atoms.

Findings

FNS corrections are smaller than reduced mass corrections for light atoms.

FNS corrections are comparable to QED radiative corrections in light nuclei.

FNS corrections dominate over other effects in heavy nuclei.

Abstract

Using the Dirac equation, we study corrections to electron binding energies and hyperfine splittings of atomic hydrogen and hydrogen-like ions due to finite nuclear size (FNS) effects, relativistic QED radiative corrections and nuclear recoil corrections. Three models for the charge distribution and the magnetic moment distribution within the nucleus are considered. Calculations are carried for light atoms (H, He and K) and heavy atoms (Rb, Cs, Pb, Bi, U). The FNS corrections to the ground-state energy are shown to be smaller than the electron-nucleus reduced mass corrections, and comparable to the relativistic QED radiative corrections for the light nuclei, but much larger than both these corrections for heavy nuclei. Comparison is made with an experiment on the $1s$-$2s$ transition frequency for hydrogen. FNS corrections to the ground state hyperfine splitting are comparable in size to the relativistic QED radiative corrections for light nuclei, but are larger for heavy nuclei.