g factor of Li-like ions with a nonzero nuclear spin

Abstract

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,

Lifetimes and g-factors of the HFS states in H-like and Li-like bismuth

“…in good agreement to the theoretical value determined from [25] g theo e ( 209 Bi 80+ ) = 1.934739 ± 0.000003 .…”

Diamagnetic correction to the9Be+ground-state hyperfine constant

“…For recent calculations of g J for Be + and other three-electron atoms, see Refs. [49][50][51][52]. For a recent calculation of the nuclear diamagnetic shielding of Be + , see Ref.…”

Zeeman effect of the hyperfine-structure levels in lithiumlike ions

“…The integral along the contour C int describes the interaction of the valent electron with the closed shell electrons. Formula (38) allows one to evaluate the interelectronic-interaction correction B µ (αZ) [35]. The results of this evaluation will be presented in the next section together with other related corrections to the Breit -Rabi formula.…”