Self-energy correction to the hyperfine splitting and the electron g factor in hydrogen-like ions

TL;DR

This paper presents a numerical method to accurately compute self-energy corrections to hyperfine splitting and the electron g factor in hydrogen-like ions, especially for low nuclear charge states, advancing precision in atomic physics calculations.

Contribution

It introduces a nonperturbative numerical approach for calculating self-energy corrections to hyperfine structure and g factor in hydrogen-like ions with low nuclear charge.

Findings

Numerical values for remainder functions in 2P and nS states (n=1,2,3) are provided.

The method improves accuracy for low-Z hydrogen-like systems.

Calculations are nonperturbative in the Coulomb field.

Abstract

The hyperfine structure (hfs) and the g factor of a bound electron are caused by external magnetic fields. For the hfs, the magnetic field is due to the nuclear spin. A uniform-in-space and constant-in-time magnetic field is used to probe the bound-electron g factor. The self-energy corrections to these effects are more difficult to evaluate than those to the Lamb shift. Here, we describe a numerical approach for both effects in the notoriously problematic regime of hydrogen-like bound systems with low nuclear charge numbers. The calculation is nonperturbative in the binding Coulomb field. Accurate numerical values for the remainder functions are provided for 2P states and for nS states with n=1,2,3.