Electron self-energy in the presence of magnetic field: hyperfine splitting and g factor

TL;DR

This paper presents high-precision numerical calculations of the self-energy correction to hyperfine splitting and the g factor in hydrogenlike ions, including nonperturbative effects, providing insights into bound-state QED and experimental comparisons.

Contribution

The study offers the first comprehensive nonperturbative calculation of self-energy corrections for hyperfine splitting and g factor in low-Z ions, surpassing previous perturbative approaches.

Findings

Nonperturbative remainder contributes -450 Hz to hyperfine intervals in ^3He^+

Results provide the most stringent test of perturbative vs. nonperturbative methods in bound-state QED

Calculated corrections are comparable to experimental uncertainties, validating theoretical models

Abstract

A high-precision numerical calculation is reported for the self-energy correction to the hyperfine splitting and to the bound-electron g factor in hydrogenlike ions with low nuclear charge numbers. The binding nuclear Coulomb field is treated to all orders, and the nonperturbative remainder beyond the known $Z\alpha$-expansion coefficients is determined. For the $^3{\rm He}^+$ ion, the nonperturbative remainder yields a contribution of -450 Hz to the normalized difference of the 1S and 2S hyperfine-structure intervals, to be compared with the experimental uncertainty of 71 Hz and with the theoretical error of 50 Hz due to other contributions. In the case of the g factor, the calculation provides the most stringent test of equivalence of the perturbative and nonperturbative approaches reported so far in the bound-state QED calculations.