Relativistic corrections to the Zeeman splitting of hyperfine structure levels in two-fermion bound-state systems

TL;DR

This paper develops a relativistic quantum electrodynamics-based theory to calculate corrections to the Zeeman splitting of hyperfine levels in two-fermion systems, applicable across all quantum states and mass ratios.

Contribution

It introduces a variational approach from QED to compute relativistic corrections to the g-factor up to O(alpha^2) for hyperfine structures.

Findings

Relativistic corrections to the g-factor are derived up to O(alpha^2).

Calculations cover all quantum states and arbitrary fermionic mass ratios.

Results align with Dirac equation predictions in the one-body limit.

Abstract

A relativistic theory of the Zeeman splitting of hyperfine levels in two-fermion systems is presented. The approach is based on the variational equation for bound states derived from quantum electrodynamics [1]. Relativistic corrections to the g-factor are obtained up to O(alpha^2). Calculations are provided for all quantum states and for arbitrary fermionic mass ratio. In the one-body limit our calculations reproduce the formula for the g-factor (to O((Z*alpha)^2)) obtained from the Dirac equation. The results will be useful for comparison with high-precision measurements.