Resonant photoemission involving super-Coster-Kronig transitions

We extend to photoemission the formal theory of the interaction of many discrete states with many continua and present three model calculations which illustrate the significant aspects of resonant photoemission. The first two models treat $3p$ core level to $3d$ band absorption, followed by super-Coster-Kronig decay (${3p}^{5}{3d}^{n+1}\ensuremath{\rightarrow}{3p}^{6}{3d}^{n\ensuremath{-}1}\ensuremath{\epsilon}f$), which interferes with the direct excitation of the $3d$ valence band. The first calculation is for a simple band model which applies approximately to Cr. No $d\ensuremath{-}d$ interactions or atomic effects are included, yet interference characteristic of Fano resonances is clearly evident. Specifically, a strong dip in the valence-band photoemission occurs near threshold. The second model contains hole-hole interactions and exhibits a resonant two-bound-hole satellite in photoemission. The dependence of the photoemission intensity on photon energy shows a larger Fano $q$ parameter for the satellite than for absorption, in agreement with an experiment on Ni. Further, the satellite shows strong enhancement at resonance, whereas the main line (valence-band emission) shows primarily an interference dip, as observed. The third model is for metals with filled $3d$ bands, such as Cu, Zn,.... The absorption is from $3p$ to the $4s\ensuremath{-}4p$ band. The resulting super-Coster-Kronig decay of the $3p$ hole gives rise to the ${M}_{2,3}{M}_{4,5}{M}_{4,5}$ Auger peak (fixed kinetic energy) as well as a resonant satellite at fixed binding energy. The latter is due to a singularity [$N(hv,{E}^{B})\ensuremath{\sim}{({E}^{B}\ensuremath{-}{E}_{0}^{B})}^{\ensuremath{-}\ensuremath{\lambda}}$] in the photoemission intensity caused by the strong interaction of the $4s\ensuremath{-}4p$ conduction electrons and the ${3d}^{8}$ configuration in the final state.