SELECTION-RULES IN X-RAY 2ND-ORDER OPTICAL PROCESSES FOR RARE-EARTHS

The difference in 4f photoemission (PES), 4f-3d X-ray emission (XES) a nd 4f inverse photoemission spectra (IPES) between the 3d core on- and off-resonances in rare earths are discussed systematically on the bas is of an atomic model taking into account the full multiplet. For PES and XES, the resonant process passing through the higher-energy interm ediate state of each of 3d(5/2) and 3d(3/2) absorption thresholds is s hown to produce the spectral intensity corresponding to the higher-ene rgy multiplets not accessible in the off-resonance. For IPES in rare e arths with less-than-half filled 4f shells, on the other hand, the res onant process passing through the lower-energy intermediate state of e ach of 3d(5/2) and 3d(3/2) thresholds is shown to suppress the intensi ty corresponding to higher-energy multiplets seen in the off-resonance . For the higher-energy intermediate state, the IPES intensity corresp onding 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 d istribution of 4f electrons in the initial state is attempted.