Self-energy screening effects in the $g$ factor of Li-like ions

TL;DR

This paper calculates and compares advanced quantum electrodynamics (QED) corrections to the $g$ factor of Li-like ions, improving the understanding of self-energy screening effects across different approaches.

Contribution

It provides all-order calculations of the leading screening contribution and extends the $Z ext{alpha}$ expansion with new logarithmic and higher-order terms.

Findings

Consistent results between all-order and $Z ext{alpha}$ expansion methods.

Improved estimates for higher-order screening effects.

Enhanced precision in theoretical predictions of the $g$ factor.

Abstract

We report an investigation of the self-energy screening effects for the $g$ factor of the ground state of Li-like ions. The leading screening contribution of the relative order $1/Z$ is calculated to all orders in the binding nuclear strength parameter $Z\alpha$ (where $Z$ is the nuclear charge number and $\alpha$ is the fine-structure constant). We also extend the known results for the $Z\alpha$ expansion of the QED screening correction by deriving the leading logarithmic contribution of order $\alpha^5\ln\alpha$ and obtaining approximate results for the $\alpha^5$ and $\alpha^6$ contributions. The comparison of the two approaches yields a stringent check of consistency of the two calculations and allows us to obtain improved estimations of the higher-order screening effects.