Core-hole spectator Auger decay

For an atomic state with two electrons missing from different core orbitals one may assume that the deeper hole decays first. However, it is quite probable that the double core-hole state will decay by emission of a slow Auger electron where the deeper core hole remains a spectator, especially if the outer core hole can be filled by Coster-Kronig transition, while the deeper cannot. We study here the competition of both Auger decay channels in a model system, the $1s2s2{p}^{6}(3s/3p)$ states of $\mathrm{N}{\mathrm{e}}^{+}$ ions. As the phenomenon can take place in any decay chain involving multiple core-excited states it can be critical to understand the ion yields, the electron and x-ray emission spectra, and the molecular fragmentation.