Nuclear size effects on hydrogenic atom energies: a semi-analytic formulation

Abstract

The hydrogenic energy level shifts of a Dirac lepton due to the finite size of the nucleus are developed as a double power series in nuclear/atomic size ratio R and (squared) fine structure constant α2. The method relies on matching small and large radius solutions and is much simpler than the perturbation approach of Friar (1979 Ann. Phys. 122 151). Seven terms are obtained for nS1/2, six for nP1/2 and four for nP3/2. Analytic expressions are given for the standard uniform, Gaussian and exponential models; also numerical values for various toy proton models that approximate the proton electric form factor reasonably well.