$M_{4,5}$ resonant Raman scattering with final $4p-4d$ holes in Te, La, and Gd: Trends of the many-body effects

We present experimental results on resonant Raman scattering in Te, La, and Gd with $M_5$ and $M_4$ excitation. The spectra show clearly the importance of the final-state interaction between the configuration having one $4p$ hole and that having two $4d$ holes. The weight of the spectral region at higher transferred energies is very much dependent on Z and it is higher at low Z. Moreover, the sensitivity to the change of the excitation energy is quite different in the three cases, while the energy extension of the spectra is not very different in the three cases (typically 50–55 eV with $M_5$ excitation). We show how these findings can be rationalized in a simple and expressive way by considering the interplay between all energy scales characteristic of the process. These are the multiplet splitting, the spin orbit, the strength of the configuration interaction, and the energy separation between the two configurations.