Self-Energy Correction to the Bound-ElectrongFactor in H-like Ions

Abstract

The one-loop self-energy correction to the $1s$-electron $g$ factor is evaluated to all orders in $Z\alpha$ with an accuracy essentially better than that of previous calculations of this correction. As a result, the uncertainty of the theoretical prediction for the bound-electron $g$ factor in H-like carbon is reduced by a factor of 3. This improves the total accuracy of the recent electron-mass determination [T. Beier et al., Phys. Rev. Lett. 88, 011603 (2002)]. The new value of the electron mass is found to be $m_e=0.0005485799093(3)\mathrm{u}$.