Theory of two-electron rearrangement K x-ray transitions

A two-configuration interaction model is developed to account for the branching ratios of the KL/sup n/2,3 radiative electron rearrangement (KL/sup n/ RER) x-ray transitions. The mixing between the quasidegenerate 2p/sup -m/ and 2s-22p/sup -m+2/ L-shell configurations is considered both for the initial (m = n) and final (m = n + 1) states. The branching ratio is shown to be proportional to the square of the 2p/sup -n-1/ mixing coefficient in the final 2s-12p/sup -n+1/ states for any number of initial 2p vacancies. In cases where both initial- and final-state mixing occurs, the corresponding amplitudes are shown to add destructively. Branching ratios are calculated in LS coupling for Z varying from 10 to 30 by using the multiconfiguration Hartree--Fock method. Calculated ratios are in close accord with available experimental data for Mg, Al, and Si. The validity of the two-configuration interaction model is examined, and it is found that the KL/sup n/ RER transitions are almost entirely due to the 2s--2p quasidegeneracy. The 2s → 1s shake down, which has recently been found to be important for two-electron, one-photon K2-L2 x-ray transitions, isshown to have a negligible influence on the KL/sup n/ RER transitions. The large widths of the KL/sup n/ RER lines are attributed to the short lifetime of the 2s-22p/sup -n+1/ final states which decay by L12-L1L2,3M Coster--Kronig transitions