Explicit functional approximations for the Z dependence of self-energy radiative corrections in hydrogen-like atoms

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Abstract
Explicit approximate expressions are developed that accurately represent the self-energy radiative corrections of an electron in a hydrogen-like atom as a function of effective nuclear charge Z. Known perturbation expansions valid for low Z are compared with existing numerical calculations for the 1s, 2s and 2p shifts, and the differences are parameterised to extend their validity to include the Z values of all stable elements. These expansions are applied to make extrapolative predictions for principal quantum numbers n<or=4. The results have applications in the semi-empirical study of Rydberg states in complex atoms.