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

摘要

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 investigatedwithin a full relativistic framework and a second-order perturbation theory. Wefocus our analysis on how electron correlation, as well as the negative-energyspectrum can affect the forbidden $E1M1$ decay rate. For this purpose weinclude the electronic correlation by an effective potential and within anactive-electron model. Due to its experimental interest, evaluation of decayrates are performed for berylliumlike xenon and uranium. We find that thenegative-energy contribution can be neglected in the present decay rate. On theother hand, if contributions of electronic correlation are not carefully takeninto account, it may change the lifetime of the metastable state by 20\%. Byperforming a full-relativistic $jj$-coupling calculation, we founddiscrepancies for the decay rate of an order of 2 compared to non-relativistic$LS$-coupling calculations, for the selected heavy ions.