Self-energy correction to the E1 transition amplitudes in hydrogen-like ions

TL;DR

This paper calculates the self-energy correction to E1 transition amplitudes in hydrogen-like ions, revealing the dominant role of the perturbed-orbital part and highlighting limitations of effective QED operators for certain transitions.

Contribution

It provides all-order calculations of self-energy corrections to E1 transitions in hydrogen-like ions, emphasizing the dominance of the perturbed-orbital component and its implications.

Findings

Perturbed-orbital part accounts for ~99% of the correction in hydrogen.

Dominance of the perturbed-orbital part varies among different transitions.

Self-energy corrections for some matrix elements cannot be accurately modeled by effective QED operators.

Abstract

We present calculations of the self-energy correction to the $E1$ transition amplitudes in hydrogen-like ions, performed to all orders in the nuclear binding strength parameter. Our results for the $1s$-$2p_{1/2}$ transition for the hydrogen isoelectronic sequence show that the perturbed-orbital part of the self-energy correction provides the dominant contribution, accounting for approximately 99\% of the total correction for this transition. Detailed calculations were performed for $ns$-$n'p$ and $np$-$n'd$ transitions in H-like caesium. We conclude that the perturbed-orbital part remains dominant also for other $ns$-$n'p$ transitions, whereas for the $np$-$n'd$ matrix elements this dominance no longer holds. Consequently, the self-energy corrections for the $np$-$n'd$ one-electron matrix elements cannot be well reproduced by means of effective QED operators constructed for energy levels.