Radiative corrections to the electron<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>g</mml:mi></mml:math>-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 $(Z\ensuremath{\alpha})$ expansion, which includes the Schwinger and the Grotch terms. For low $Z$ our all-order result approaches the $(Z\ensuremath{\alpha})$ 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.