Nuclear-size correction to the one-loop self-energy in hydrogenlike ions

Abstract

The nuclear-size effect on both diagonal and off-diagonal one-loop self-energy matrix elements is considered for hydrogenlike ions with $Z=60$, $82$, $90$, and $92$. Specifically, the $1s$, $2s$, $3s$, $2p_{1/2}$, and $2p_{3/2}$ states, as well as the off-diagonal $1s-2s$, $1s-3s$, and $2s-3s$ matrix elements are considered. The calculations are performed within the rigorous quantum-electrodynamics framework, nonperturbatively in the nuclear-strength parameter $\alpha Z$. Excellent agreement is found with results reported in the literature. Simple and useful approximate formulas to treat the nuclear-size correction are obtained, which, in particular, can be used to study the self-energy contributions to the field-shift factors.