A NEW APPROACH TO THE ELECTRON SELF-ENERGY CALCULATION

We present a new practical way to calculate the first order self energy in any model potential (local or non-local). The main idea is to introduce a new straightforward way of renormalization to avoid the usual potential expansion implying a large number of diagrams in higher order QED effects. The renormalization procedure is based on defining the divergent mass term in coordinate space and decomposing it into a divergent sum over finite partial wave contributions. The unrenormalized bound self energy is equally decomposed into a partial wave (l) sum. For each partial wave the difference is taken and the sum becomes convergent. The comparably rapid asymptotic behaviour of the method is l-3. The method is applied to lithium-like uranium, and the self energy in a Coulomb field, the finite nucleus effect and the screened self energy is calculated to an accuracy of at least one tenth of an eV.