Many-body effects in nonresonant and resonant $4p$ spectroscopy of Gd metal

We present experimental and theoretical results on $4p$ spectroscopy from Gd metal with the aim to clarify in detail the effects of the final state interaction between the $4p$ and $4d$ levels which is of paramount importance in $4p$ spectroscopy of rare earths and their nearby preceding elements in the Periodic Table. In the nonresonant mode the problem was studied with photoemission (XPS at $h\nu =1140\mathrm{}\mathrm{eV}),$ where XPS denotes x-ray photoemission. In the $M_{4,5}$ resonant mode the problem was addressed with x-ray scattering with inner shell excitation, leading to final state with a $4p$ hole [resonant Raman scattering (RRS)]. Nonresonant photoemission spectra are calculated using a full multiplet splitting approach including final state configuration interaction (CI) with the ${4d}^8{4f}^8$ configuration which is close in energy to the ${4p}^5{4f}^7$ configuration leading to a coherent superposition of the $4p$ hole with two $4d$ holes in the final state. The calculated photoemission spectra agree well with the experiment and are used as a guideline to discuss the RRS data. In both cases (XPS and RRS) we point out the characteristic signature of the interaction with the configuration containing two $4d$ holes. This leads to high energy excitations in the final state, typically 20 eV above the main lines, with a spectral distribution over an energy scale that cannot be explained by ordinary multiplet splitting. On the other hand, we demonstrate that multiplet splitting cannot be neglected with respect to the above mentioned CI. RRS shows clearly that the CI is stronger in the ${4p}_{1/2}$ than in the ${4p}_{3/2}$ case in agreement with calculated average energies. When the excitation energy increases above $M_5$ the Raman component becomes broader than with excitation at threshold. This is interpreted as evidence for the increasing importance of excitations with lower spin. Besides the dispersive (Raman) component the RRS spectra show a strong nondispersive peak at constant scattered-photon energy. This behavior is briefly discussed in connection with the dynamics of the excited state.