Radiative corrections to the electrong-factor in H-like ions

Abstract

In view of the current interest of QED in strong fields, a complete set of one-photon radiative corrections to the bound-electron $g$ factor is evaluated for several hydrogenlike ions. The calculations are performed to all orders in the nuclear potential and compared to earlier results, based on the $\left(Z\alpha \right)$ expansion, which includes the Schwinger and the Grotch terms. For low $Z$ our all-order result approaches the $\left(Z\alpha \right)$ expansion, but for high $Z$ there is a substantial deviation. Furthermore, for high $Z$ our calculations show that the uncertainty due to nuclear structure is small and thus strongly motivate the bound $g$-factor experiment in progress.