Electron self-energy for the K and L shells at low nuclear charge - art. no. 042512

A nonperturbative numerical evaluation of the one-photon electron self-ener gy for the K- and L-shell states of hydrogenlike ions with nuclear charge n umbers Z = 1 to 5 is described. Our calculation for the S-1(1/2) state has a numerical uncertainty of 0.8 Hz in atomic hydrogen, and for the L-shell s tates (2S(1/2), 2P(1/2), and 2P(3/2)) the numerical uncertainty is 1.0 Hz. The method of evaluation for the ground state and for the excited states is described in detail. The numerical results are compared to results based o n known terms in the expansion of the self-energy in powers of Z alpha.