$L_3{M}_{23}{M}_{23}$ Auger energies of metallic Ni, Cu, and Zn: Influence of $3d$-$4s$ admixed screening on calculating relaxation energies

A theory has been developed for predicting Auger energies with the use of x-ray photoemission binding energies which is rigorous within the framework of the theory of extra-atomic relaxation developed by Shirley et al. Calculations are given for the $L_3{M}_{23}{M}_{23}$ Auger energies of metallic Ni, Cu, and Zn. We argue that the atomistic approach to calculating Auger energies should be valid for Ni as it is for nontransition metals. By including the effect of the second screening orbital on the Auger energy and by taking into account the change in initial-state electronic configuration between gas-phase Ni atoms and metallic Ni, agreement with experiment can be nearly as good as for the Cu and Zn cases. The results strongly suggest that the first screening orbital is $3d$-$4s$ admixed while the second screening orbital is almost $4s$-like.