Bound-state self-energy calculation using partial-wave renormalization

A rigorous method to calculate the first-order self-energy in a model potential is presented. An alternative straightforward way of renormalization is introduced to avoid the commonly used potential expansion implying a larger number of diagrams in higher-order QED effects. The divergent mass term is defined in coordinate space and decomposed into a sum over finite partial-wave (l) contributions. The unrenormalized bound self-energy is similarly decomposed into a partial-wave sum and the renormalization is performed for each partial wave. The renormalized sum converges fairly rapidly (the asymptotic behavior is l^-3). The method is applied to lithiumlike uranium, for which the electron self-energy in the potential of a point nucleus, as well as the effects of the finite nucleus and of the screening by the remaining electrons on the self-energy, are obtained with an accuracy better than 0.1 eV. The results are in very good agreement with experiment and with calculations recently performed using other techniques.