Second-Order Electron Self-Energy in Hydrogenlike Ions

Abstract

A calculation of the loop after loop irreducible contribution of the second-order electron self-energy for hydrogenlike ions with nuclear charge numbers $3\ensuremath{\le}Z\ensuremath{\le}92$ is presented. The interaction with the nuclear Coulomb potential is treated nonperturbatively in the coupling constant $Z\ensuremath{\alpha}$. Our results are in strong disagreement with recent calculations of Mallampalli and Sapirstein for low- $Z$ values but are compatible with the two known terms of the analytical $Z\ensuremath{\alpha}$ expansion.