Coordinate-space approach to the bound-electron self-energy

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Abstract
The self-energy correction for an electron bound in an electrostatic potential is examined in coordinate space. The binding potential is assumed to be spherically symmetric and local but not necessarily Coulomb. Subtractions that remove infinite renormalization terms and lower-order terms are given as operators in coordinate space in order to facilitate the numerical evaluation of the level shift. This approach is expected to be applicable to calculations of finite-nuclear-size corrections and electron-screening corrections to the self-energy, and to calculations of higher-order quantum-electrodynamic corrections where the self-energy diagram is part of a more complex external-field Feynman diagram.