Zeeman effect of the hyperfine structure levels in lithiumlike ions

TL;DR

This paper presents a high-precision relativistic calculation of the Zeeman effect on hyperfine levels in lithiumlike ions, incorporating various corrections to aid in precise nuclear magnetic moment measurements.

Contribution

It introduces a comprehensive relativistic QED-based approach to calculate Zeeman splitting in lithiumlike ions, including second-order and interelectronic-interaction corrections.

Findings

Calculated Zeeman splitting for Z=6-32 ions in 1-10 T fields.

Provided high-precision theoretical values for hyperfine structure levels.

Enhanced methods for determining nuclear magnetic moments from g-factor experiments.

Abstract

The fully relativistic theory of the Zeeman splitting of the $(1s)^2 2s$ hyperfine-structure levels in lithiumlike ions with $Z=6 - 32$ is considered for the magnetic field magnitude in the range from 1 to 10 T. The second-order corrections to the Breit -- Rabi formula are calculated and discussed including the one-electron contributions as well as the interelectronic-interaction effects of order 1/Z. The 1/Z corrections are evaluated within a rigorous QED approach. These corrections are combined with other interelectronic-interaction, QED, nuclear recoil, and nuclear size corrections to obtain high-precision theoretical values for the Zeeman splitting in Li-like ions with nonzero nuclear spin. The results can be used for a precise determination of nuclear magnetic moments from $g$-factor experiments.