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

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 → 1s 1/2 + 2γ and 2p 1/2 → 1s 1/2 + 2γ 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 → 1s 1/2 + 2γ transition. In contrast, they are much more pronounced for the 2p 1/2 → 1s 1/2 + 2γ 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.