Vacuum polarization and finite nuclear size effects in the two-photon decay of hydrogen-like ions

TL;DR

This paper investigates how finite nuclear size and vacuum polarization corrections influence the two-photon decay rates of hydrogen-like ions using relativistic QED and a B-spline based computational approach.

Contribution

It introduces a high-precision B-spline method to calculate QED and nuclear size effects on two-photon decay rates across the entire isoelectronic sequence.

Findings

QED and nuclear size effects are weak for 2s to 1s decay.

Effects are more significant for 2p_{1/2} to 1s decay.

Decay rate of hydrogen-like Uranium is affected by about 0.5% due to these corrections.

Abstract

The total two-photon decay rate of hydrogen-like ions is studied using relativistic quantum electrodynamics. In particular, we analyse how finite nuclear size and QED vacuum polarization corrections affect the decay rate. To calculate these corrections, a finite basis set method based on $B$-splines is used for the generation of quasi-complete atomic spectra and, hence, of the relativistic Green's function. By making use of this $B$-spline approach, high precision calculations have been performed for the $2s_{1/2} \to 1s_{1/2} + 2\gamma$ and $2p_{1/2} \to 1s_{1/2} + 2\gamma$ decay of hydrogen-like ions along the entire isoelectronic sequence. The results of these calculations show that both, QED and finite nuclear size effects, are comparatively weak for the $2s_{1/2} \to 1s_{1/2} + 2\gamma$ transition. In contrast, they are much more pronounced for the $2p_{1/2}\to 1s_{1/2} + 2\gamma$ decay, where, for hydrogen-like Uranium, the decay rate is reduced by 0.484% due to the finite nuclear size and enhanced by 0.239% if the vacuum polarization is taken into account.