Magnetic moment of a bound electron

TL;DR

This paper reviews theoretical predictions and calculations related to the magnetic moment of a bound electron, focusing on corrections to the g factor, Lamb shift, and hyperfine splitting, crucial for fundamental constant determinations.

Contribution

It provides a comprehensive review of the theoretical status and recent efforts to calculate higher-order corrections to the bound electron's magnetic properties.

Findings

Progress in calculating O(alpha (Z alpha)^5) corrections to the g factor

Advances in reevaluating Lamb shift corrections

Summary of efforts to determine higher-order hyperfine splitting corrections

Abstract

Theoretical predictions underlying determinations of the fine structure constant alpha and the electron-to-proton mass ratio m_e/m_p are reviewed, with the emphasis on the bound electron magnetic anomaly g-2. The theory of the interaction of hydrogen-like ions with a magnetic field is discussed. The status of efforts aimed at the determination of O(alpha (Z alpha)^5) and O(alpha^2 (Z alpha)^5) corrections to the g factor is presented. The reevaluation of analogous corrections to the Lamb shift and the hyperfine splitting is summarized.