Theory of the Radiative Auger Effect

The probability of simultaneous emission of an x-ray photon and an electron is considered. It is shown that this process can occur as a consequence of the change in the average potential acting on the electrons when the x-ray hole is moving from an inner to an outer shell (shake-off) and as a consequence of interaction between single- and double-hole configurations in the final state. Relative shake-off probabilities of $K\to L^2$, $K\to M^2$, and $L_{2,3}\to M_1{M}_{2,3}$ transitions are calculated for ${\mathrm{F}}^{-}$, Ne, ${\mathrm{Na}}^{+}$, ${\mathrm{Cl}}^{-}$, Ar, and ${\mathrm{K}}^{+}$ from Bagus's self-consistent-field wave functions of single-hole x-ray states. The relative probability of $K\to L^2$ and $K\to M^2$ transitions is estimated for the rest of the atoms in the range $9<~Z<~22$. The estimated $K\to L^2$ and $K\to M^2$ probabilities are of the same order of magnitude as the observed probabilities. However, for low $Z$, they overestimate the observed probabilities, which may be because the shake-off calculations do not account properly for the interaction between single- and double-hole configurations in the final state.