Auger transition rate for the noble-gas satellite spectra

Expressions are derived for double-vacancy Auger transition rates, specifically for the noble-gas Auger satellite spectra. It is found that in the most general case, when both initial and final states are in intermediate coupling, there can be interference between final-state terms. When the final state is not in intermediate coupling, the interference vanishes and the transition rate can be written as a linear combination of transition rates in $\mathrm{LS}$ coupling. Expressions are given for the $\mathrm{dp}\to s{p}^2$ and $\mathrm{dp}\to p^3$ Auger transition rates in $\mathrm{LS}$ coupling.