Quadratic Zeeman effect in light boron-like ions

Abstract

The quadratic Zeeman effect is calculated for the ground $^2P_{1/2}$ state of light boron-like ions in the range of nuclear-charge numbers $Z = 10-24$. The calculations are performed in the Furry picture using three models for the zeroth-order approximation potential: pure nuclear Coulomb potential and two effective screening potentials $-$ core-Hartree and Kohn-Sham. First-order perturbation-theory contributions are considered: the one-photon-exchange correction and the radiative corrections associated with the self-energy and vacuum-polarization diagrams. The dominant contributions from the self-energy diagrams are calculated within a rigorous QED approach. The vacuum polarization corrections are obtained within the electric-loop approximation in the leading order, which is given by the Uehling potential. As a result, theoretical predictions for the contribution of the quadratic Zeeman effect to the binding energy of the valence electron in the $^2P_{1/2}$ state are obtained. The results can be used for the analysis of high-precision $g$-factor and fine-structure splitting measurements in boron-like highly charged ions.