The radiative self-energy correction to the bound-electron $g$ factor of $2P_{1/2}$ and $2P_{3/2}$ states in one-electron ions is evaluated to order $\alpha (Z\alpha ){}^2$. The contribution of high-energy virtual photons is treated by means of an effective Dirac equation, and the result is verified by an approach based on long-wavelength quantum electrodynamics. The contribution of low-energy virtual photons is calculated both in the velocity and in the length gauge, and gauge invariance is verified explicitly. The results compare favorably to recently available numerical data for hydrogenlike systems with low nuclear charge numbers.

• Received 19 November 2009

DOI:https://doi.org/10.1103/PhysRevA.81.012512