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

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.

Extrapolated results for Z=0, 1, and 2 are updated