Relativistic calculation of the two-photon decay rate of highly-excited ionic states

TL;DR

This paper presents a relativistic quantum electrodynamics approach to calculating two-photon decay rates in highly-excited ionic states, addressing resonance effects and providing detailed results for hydrogen and hydrogen-like ions.

Contribution

It introduces a relativistic method for calculating two-photon decay rates that accounts for resonance peaks and is applicable to various ionic states, improving upon previous non-relativistic models.

Findings

Calculated two-photon decay rates for hydrogen and ions.

Resolved decay rates into electric and magnetic multipole components.

Demonstrated the method's applicability to resonance cases.

Abstract

Based on quantum electrodynamics, we reexamine the two-photon decay of one-electron atoms. Special attention is paid to the calculation of the (two-photon) total decay rates which can be viewed as the imaginary part of the two-loop self-energy. We argue that our approach can easily be applied to the cases with a virtual state having an intermediate energy between the initial and the final state of the decay process leading, thus, to the resonance peaks in the two-photon energy distribution. In order to illustrate our approach, we obtain fully relativistic results, resolved into electric and magnetic multipole components, for the two-photon decay rates of the 3S_{1/2} -> 1S_{1/2} transition in neutral hydrogen as well as in various hydrogen-like ions.