Nuclear-size correction to the Lamb shift of one-electron atoms

Abstract

The nuclear-size effect on the one-loop self-energy and vacuum polarization is evaluated for the $1s$, $2s$, $3s$, $2{p}_{1/2}$, and $2{p}_{3/2}$ states of hydrogen-like ions. The calculation is performed to all orders in the nuclear binding strength parameter $Z\ensuremath{\alpha}$. Detailed comparison is made with previous all-order calculations and calculations based on the expansion in the parameter $Z\ensuremath{\alpha}$. Extrapolation of the all-order numerical results obtained toward $Z=1$ provides results for the radiative nuclear-size effect on the hydrogen Lamb shift.