Selection rules in X-ray second order optical processes for rare earths

The difference in 4f photoemission (PES), 4f-3d X-ray emission (XES) and 4f inverse photoemission spectra (IPES) between the 3d core on- and off-resonances in rare earths are discussed systematically on the basis of an atomic model taking into account the full multiplet. For PES and XES, the resonant process passing through the higher-energy intermediate state of each of 3d(5/2) and 3d(3/2) absorption thresholds is shown to produce the spectral intensity corresponding to the higher-energy multiplets not accessible in the off-resonance. For IPES in rare earths with less-than-half filled 4f shells, on the other hand, the resonant process passing through the lower-energy intermediate state of each of 3d(5/2) and 3d(3/2) thresholds is shown to suppress the intensity corresponding to higher-energy multiplets seen in the off-resonance. For the higher-energy intermediate state, the IPES intensity corresponding to even higher-energy multiplets is shown to become stronger. A systematic interpretation of these selection rules in terms of the 3d-4f exchange interaction, the 3d core spin-orbit interaction and the distribution of 4f electrons in the initial state is attempted.