Single-photon two-electron rearrangement transitions

The observation and identification of $K$ x rays resulting from one-photon two-electron rearrangement are made for Mg, Al, and Si following heavy-ion bombardment. Two types of rearrangement processes, which lead to $K$ x rays below the energy of the characteristic $K\alpha$ x ray, are delineated: the radiative Auger effect (RAE) and radiative electron rearrangement (RER). The RAE process previously described by Åberg and Utriainen competes with the characteristic $K\alpha$ x ray. The observed energies and relative intensities $\frac{\mathrm{RAE}}{K\alpha }$ from heavy-ion bombardment agree with those from electron and photon excitation. The RER process which we have recently proposed is the emission of a photon from the ${\mathrm{}\left(1s\right)\mathrm{}}^{-1\mathrm{}}{\mathrm{}\left(2p\right)\mathrm{}}^{-n}$ to ${\mathrm{}\left(2s\right)\mathrm{}}^{-2\mathrm{}}{\mathrm{}\left(2p\right)\mathrm{}}^{-n+1\mathrm{}}$ electron rearrangement for $n=1-6\mathrm{}$. This model gives good agreement between measured and Hartree-Fock calculated RER energies. $K{L}^n$ RER and $K\alpha L^n$ satellites are competing decay branches of the ${\mathrm{}\left(1s\right)\mathrm{}}^{-1\mathrm{}}{\mathrm{}\left(2p\right)\mathrm{}}^{-n}$ initial configuration. The $\frac{\left(K{L}^n\mathrm{RER}\right)}{K\alpha L^n}$ branching ratios are measured. The RER transitions are shown to be allowed by configuration mixing of final states with the same spin and parity. The branching ratio is a product of the mixing coefficient and a ratio of fluorescence yields. The theoretical branching ratios $\frac{\left(K{L}^1\mathrm{RER}\right)}{K\alpha L^1}$ and $\frac{\left(K{L}^2\mathrm{RER}\right)}{K\alpha L^2}$ are calculated and compared to experiment.