Extrapolation of the Zα-expansion and two-loop bound-state energy shifts

Quantum electrodynamic (QED) effects that shift the binding energies of hydrogenic energy levels have been expressed in terms of a semi-analytic expansion in powers of Zα and ln[(Zα)−2], where Z is the nuclear charge number and α is the fine-structure constant. For many QED effects, numerical data are available in the domain of high Z where the Zα expansion fails. In this Letter, we demonstrate that it is possible, within certain limits of accuracy, to extrapolate the Zα-expansion from the low-Z to the high-Z domain. We also review two-loop self-energy effects and provide an estimate for the problematic nonlogarithmic coefficient B60.