Theory of the 4d→2p X-Ray Emission Spectroscopy in Ce₂O₃, Pr₂O₃ and Dy₂O₃

The 4d→2p X-ray emission spectra (XES) of Ce₂O₃, Pr₂O₃ and Dy₂O₃ have been calculated with an impurity Anderson model with the full multiplet couplings, following the Kramers-Heisenberg formula in the second order optical process. Experimental results have been well reproduced with this model by using a constant value for the 4d core hole lifetime damping Γ (4d) in the case of Ce₂O₃ and Pr₂O₃, while in the case of Dy₂O₃ it is necessary to take into account the term dependence of Γ (4d), which is consistent with the previous theoretical analyses of 4d X-ray photoemission spectra. It was also shown that both the spin-orbit couplings of the 4d core level in the final state and the 4f level in the initial state are key factors to cause the branching ratio in the L_γ line larger than that in the L_β line. The phase matching of the wave functions between the intermediate and final states smears out the hybridization effect in the 4d→2p XES in Ce₂O₃ and Pr₂O₃.