Coordinate-space approach to the bound-electron self-energy: Coulomb field calculation

A formulation for calculating the one-photon self-energy of an electron in an external field completely in coordinate space, described in an earlier paper, is applied to the calculation of the self-energy of an electron in a Coulomb field by two different numerical methods. In one numerical approach, a high-order asymptotic expansion of the Coulomb Green function is employed to accelerate the convergence of the summation over angular momentum. In the other, a term-by-term subtraction of the divergent terms in the summation over angular momentum is employed. The latter method is found to be preferable from the point of view of both simplicity and precision. Numerical results are compared to the results of previous calculations.