The fully relativistic theory of the g factor of hydrogenlike ions with nonzero nuclear spin is considered. The hyperfine-interaction correction to the atomic g factor is calculated for both point and extended chargedistribution models for nuclei. Both the magnetic dipole and the electric quadrupole interactions are taken into account. This correction is combined with corrections resulting from QED, nuclear recoil, and nuclear size, to obtain theoretical high-precision values for the g factor of hydrogenlike ions with nonzero nuclear spin. The results can be used for a precise determination of nuclear magnetic moments from g factor experiments.

The fully relativistic theory of the g factor of Li-like ions with nonzero nuclear spin is considered for the (1s) 2 2s state. The magnetic-dipole hyperfine-interaction correction to the atomic g factor is calculated including the one-electron contributions as well as the interelectronic-interaction effects of order 1/Z. This correction is combined with the interelectronic-interaction, QED, nuclear recoil, and nuclear size corrections to obtain highprecision theoretical values for the g factor of Li-like ions with nonzero nuclear spin. The results can be used for a precise determination of nuclear magnetic moments from g factor experiments.PACS number(s): 31.30.Jv, 31.30.Gs, 32.60.+i, 12.20.Ds combined with the other corrections to get accurate theoretical predictions for the g factor of lithiumlike ions with nonzero nuclear spin.Experimental investigations in this direction are anticipated in the near future at University of Mainz and GSI [39].Relativistic units ( = c = 1) and the Heaviside charge unit (α = e 2 /4π, e < 0) are used in the paper. In some important cases, the final formulas contain and c explicitly to be applicable for arbitrary system of units.2 The g factor in the lowest-order one-electron approximationWe consider a lithiumlike ion placed in a weak homogeneous magnetic field B directed along the z axis. Assuming that the energy level shift (splitting) due to interaction of the valent 2s electron with B is much smaller than the hyperfine-structure splitting, ∆E mag ≪ ∆E HFS , we can express the linear-dependent part of this shift in terms of the g factor,

The fully relativistic theory of the Zeeman splitting of the 1s hyperfine-structure levels in hydrogenlike ions 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. The results can be used for a precise determination of nuclear magnetic moments from g-factor experiments.

The fully relativistic theory of the Zeeman splitting of the ͑1s͒ 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 secondorder 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.