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We present results on the self-energy correction to the energy levels ofhydrogen and hydrogenlike ions. The self energy represents the largest QEDcorrection to the relativistic (Dirac-Coulomb) energy of a bound electron. Wefocus on the perturbation expansion of the self energy of non-S states, andprovide estimates of the so-called A60 perturbative coefficient, which can beconsidered as a relativistic Bethe logarithm. Precise values of A60 are givenfor many P, D, F and G states, while estimates are given for other electronicstates. These results can be used in high-precision spectroscopy experiments inhydrogen and hydrogenlike ions. They yield the best available estimate of theself-energy correction of many atomic states.Comment: 18 pages (in 2-column format), 21 figures. Version 2 (June 20, 2003)  includes minor modification

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