Theory of the 4d → 2p and 4f → 4d x-ray emission spectroscopies in rare-earth compounds

The 4d → 2p x-ray emission spectra (XES) of rare-earth compounds are calculated with an impurity Anderson model with the full multiplet couplings, following the formula of a coherent second order optical process. Recent experiments are well reproduced with this model by using a constant value for the 4d core hole lifetime damping Γ(4d) in light rare-earth compounds. On the other hand, in heavy rare-earth compounds it is necessary to take into account the term dependence of Γ(4d). The 4f → 4d XES of Dy₂O₃ is also investigated theoretically. The multiplet term dependence of the 4d core hole lifetime affects more drastically the spectral shape in the 4f → 4d XES than in the 4d → 2p XES. Some theoretical predictions are also given on the coincidence spectra between the 4d-XPS and 4f → 4d XES.