# One-loop electron self-energy for the bound-electron $g$ factor

## TL;DR

This paper presents highly accurate calculations of the one-loop self-energy correction to the bound-electron $g$ factor for light hydrogen-like ions, improving precision significantly over previous results.

## Contribution

The authors perform all-order calculations of the self-energy correction for $1s$ and $2s$ states, achieving two orders of magnitude better accuracy than prior work.

## Key findings

- Good agreement with previous calculations.
- Enhanced accuracy by approximately two orders of magnitude.
- Applicable to light hydrogen-like ions with $Z \,\le\, 20$.

## Abstract

We report calculations of the one-loop self-energy correction to the bound-electron $g$ factor of the $1s$ and $2s$ states of light hydrogen-like ions with the nuclear charge number $Z \le 20$. The calculation is carried out to all orders in the binding nuclear strength. We find good agreement with previous calculations and improve their accuracy by about two orders of magnitude.