gfactor of hydrogenlike ions with nonzero nuclear spin

Abstract

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.

QED calculation of the nuclear magnetic shielding for hydrogenlike ions

“…It can be concluded from Table III and Fig. 5 that the present theory permits determination of nuclear magnetic moments with fractional accuracy ranging from 10 −9 in the case of 17 O 7+ to 10 −5 for 209 Bi 82+ . For most hydrogen-like ions, the dominant source of error in the theoretical predictions is the Bohr-Weisskopf effect.…”

“…For the point nuclear model, the sum over the Dirac spectrum in the above expression can be evaluated analytically [22][23][24], see also more recent studies [17,25],…”

“…[17]. In the present work, we go beyond the relativistic description of the nuclear magnetic shielding and calculate the dominant corrections to it, namely, the self-energy, the vacuum-polarization, and the nuclear magnetization distribution corrections.…”

Complete two-loop correction to the bound-electrongfactor

“…The anomalous magnetic moment F 2 (0) in the modified Dirac-Coulomb Hamiltonian (10) leads to the following energy shift linear in the magnetic field (d = 3) (19) where A = ( B × r )/2, and we denote the one-loop components of the form factors by the corresponding superscript. The corresponding correction to the g factor is…”

Theory of Bound-Electron g Factor in Highly Charged Ions

“…(28) for H-and Li-like ions as well as the corresponding corrections to the Breit-Rabi formula, which describes the Zeeman effect on the hyperfine-structure levels, were derived in Refs. [63][64][65][66][67][68] . As was discussed in detail in…”