Relativistic evaluation of the two-photon decay of the metastable ${1s}^{2} 2s 2p~^3\mbox{P}_0$ state in berylliumlike ions with an active-electron model

TL;DR

This paper presents a relativistic theoretical analysis of the two-photon decay in berylliumlike ions, highlighting the importance of electron correlation effects and relativistic coupling schemes on decay rate predictions.

Contribution

It introduces a full relativistic framework with an active-electron model to evaluate decay rates, emphasizing the significance of electron correlation and relativistic effects for heavy ions.

Findings

Negative-energy contributions are negligible.

Electron correlation can alter the lifetime by 20%.

Relativistic $jj$-coupling differs from non-relativistic $LS$-coupling by a factor of 2.

Abstract

The two-photon ${1s}^{2} 2s 2p~^3\mbox{P}_0 \rightarrow {1s}^{2} {2s}^2$ $^1\mbox{S}_0$ transition in berylliumlike ions is theoretically investigated within a full relativistic framework and a second-order perturbation theory. We focus our analysis on how electron correlation, as well as the negative-energy spectrum can affect the forbidden $E1M1$ decay rate. For this purpose we include the electronic correlation by an effective potential and within an active-electron model. Due to its experimental interest, evaluation of decay rates are performed for berylliumlike xenon and uranium. We find that the negative-energy contribution can be neglected in the present decay rate. On the other hand, if contributions of electronic correlation are not carefully taken into account, it may change the lifetime of the metastable state by 20\%. By performing a full-relativistic $jj$-coupling calculation, we found discrepancies for the decay rate of an order of 2 compared to non-relativistic $LS$-coupling calculations, for the selected heavy ions.