Resonant Raman scattering at the L thresholds with final $3s$ hole in ${3d}^{2+}$ systems. I. Configuration interaction with two $3p$ hole final states in different systems

The resonant Raman scattering (RRS) at the L edges with final $3s$ hole is investigated in transition-metal oxides and oxidelike systems. Both theoretical and experimental work is presented showing that a satisfactory description can be obtained only by including the final state configuration interaction (CI) between the configuration with a single $3s$ hole interacting with the $3d$ shell and the configuration with two $3p$ holes. The effect is very well seen with $L_2$ excitation and is reflected in a strong decrease of the separation within the doublet seen in RRS with respect to the case without CI. We present calculations including CI on cluster and on ion with crystal field and new measurements on NiO, CoO, and ${\mathrm{MnFe}}_2{\mathrm{O}}_4$ with $L_2$ excitation; we also compare calculations with RRS measurements on ${\mathrm{CaF}}_2$ taken from the literature. We discuss the dependence on the atomic number and on the relevant parameters, by introducing a rationale explaining the nature of the coupling and the different behavior with $n<\mathrm{}5\mathrm{}$ and $n>~5,$ being n the $3d$ occupation in the ground state. This assessment is of importance in future applications to detailed studies of strongly correlated systems.