One-loop binding corrections to the electron $g$ factor

TL;DR

This paper calculates a specific one-loop quantum correction to the bound electron's g factor, confirming previous numerical estimates and setting the stage for future two-loop calculations.

Contribution

It provides an analytical calculation of the one-loop self-energy correction of order α(Zα)^5 to the bound electron g factor, aligning with previous numerical extrapolations.

Findings

Agreement with extrapolated numerical value

Foundation for two-loop correction calculations

Enhanced understanding of quantum electrodynamics effects in bound electrons

Abstract

We calculate the one-loop electron self-energy correction of order $\alpha\,(Z\,\alpha)^5$ to the bound electron $g$ factor. Our result is in agreement with the extrapolated numerical value and paves the way for the calculation of the analogous, but as yet unknown two-loop correction.