Self-Energy of Electrons in Critical Fields

Abstract

The energy shift of $K$ electrons in heavy atoms due to the self-energy correction has been calculated. This process is treated to all orders in $Z\alpha$, where $Z$ denotes the nuclear charge. For the superheavy system $Z=170\mathrm{}$, where the $K$-shell binding energy reaches the pair-production threshold (${E_{1s}}^b\sim 2m{c}^2$), a shift of +11.0 keV is found. This shift is almost cancelled by the vacuum polarization, leaving a negligible effect for all quantum-electrodynamical corrections of order $\alpha$ but all orders of $Z\alpha$.