Negative continuum effects on the two-photon decay rates of hydrogen-like ions

TL;DR

This paper investigates the impact of negative-energy states on two-photon decay rates in hydrogen-like ions using relativistic quantum theory, highlighting the importance of including these states for accurate calculations across different atomic numbers.

Contribution

It provides a detailed analysis of negative-energy state effects on two-photon decay rates, emphasizing their significance in both high and low atomic number systems.

Findings

Negative-energy states significantly affect decay rate calculations.

Proper summation over negative-energy states is essential for accuracy.

Results apply to hydrogen, xenon, and uranium ions.

Abstract

Two--photon decay of hydrogen--like ions is studied within the framework of second--order perturbation theory, based on relativistic Dirac's equation. Special attention is paid to the effects arising from the summation over the negative--energy (intermediate virtual) states that occurs in such a framework. In order to investigate the role of these states, detailed calculations have been carried out for the $2s_{1/2} - 1s_{1/2}$ and $2p_{1/2} - 1s_{1/2}$ transitions in neutral hydrogen H as well as for hydrogen--like xenon Xe$^{53+}$ and uranium U$^{91+}$ ions. We found that for a correct evaluation of the total and energy--differential decay rates, summation over the negative--energy part of Dirac's spectrum should be properly taken into account both for high--$Z$ and low--$Z$ atomic systems.