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.
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