Basis-set approach to calculating the radiative self-energy in highly ionized atoms

Abstract

We present a complete numerical implementation of an alternative approach for evaluating the electron radiative self-energy in high-Z hydrogenic ions. Using basis-set techniques, we demonstrate that the partial-wave expansion of the most numerically intensive term converges relatively rapidly as approximately 1/${\mathit{L}}^3$, making this an attractive calculational approach. Numerical results extrapolated to zero nuclear size are in agreement with Mohr [Ann. Phys. (N.Y.) 88, 26 (1974); 88, 52 (1974); Phys. Rev. Lett. 34, 1050 (1975); Phys. Rev. A 26, 2338 (1982)] for the K and L shells, and with the graphical results of Mohr and Kim (unpublished) for higher excited states. The algorithm is suitable for immediate generalization to non-Coulombic potentials.