Perturbation approach to the self-energy of non-Shydrogenic states

We present results on the self-energy correction to the energy levels of hydrogen and hydrogenlike ions. The self-energy represents the largest QED correction to the relativistic (Dirac-Coulomb) energy of a bound electron. We focus on the perturbation expansion of the self-energy of non-S states, and provide estimates of the so-called $A_{60}$ perturbation coefficient, which can be viewed as a relativistic Bethe logarithm. Precise values of $A_{60}$ are given for many P, D, F, and G states, while estimates are given for other states. These results can be used in high-precision spectroscopy experiments in hydrogen and hydrogenlike ions. They yield the best available estimate of the self-energy correction of many atomic states.