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 $2s_{1/2}\to 1s_{1/2}+2\gamma$ 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.

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Cited by in corpus (3)

• Investigation of two-photon 2s -> 1s decay in one-electron and one-muon ions
• Comparison of two different integration methods for the (1+1)-Dimensional Schrödinger-Poisson Equation
• Finite-nuclear-size effect for hydrogenlike ions under high external pressure