Theory of two-electron rearrangementKx-ray transitions

A two-configuration interaction model is developed to account for the branching ratios of the KL2,3ⁿ radiative electron rearrangement (KLⁿ RER) x-ray transitions. The mixing between the quasidegenerate 2p^-m and 2s^-22p^-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^-n-1 mixing coefficient in the final 2s^-22p^-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 KLⁿ 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 is shown to have a negligible influence on the KLⁿ RER transitions. The large widths of the KLⁿ RER lines are attributed to the short lifetime of the 2s^-22p^-n+1 final states which decay by L₁²-L₁L2,3M Coster-Kronig transitions.