Excited core-level dependence of entanglement between a photoelectron and an emitted X-ray photon in X-ray inner-shell excitation

We theoretically investigated how the quantum entanglement between the spin of the photoelectron and the polarization of the emitted X-ray photon depends on the excited core-level, using the 3d→\2p and 3d→\3p SPR-XEPECS (spin- and polarization-resolved XEPECS) processes for rm Ti₂O₃-type system, and the 4f→\4d SPR-XEPECS process for rm CeF₃-type system. In the calculation for rm Ti₂O₃-type system, we used rm TiO₆ cluster model with the full-multiplet structure of the Ti ion and the charge-transfer effect between Ti 3d and ligand O 2p orbitals. For rm CeF₃-type system, we used ionic model with the full-multiplet structure of the Ce ion. We found two distinct mechanisms for entanglement generation in the 3d→\2p and 4f→\4d cases. The first is generated by the spin-orbit interaction of the 2p core electron, whereas the second is generated by the spin-orbit interaction of the 4f valence electron and strong exchange interaction between the 4f and 4d electrons. However, in the 3d→\3p case with the strong 3d-3p exchange interaction, we found that the entanglement is not generated due to the crystal field effect. These results reveal the existence of two distinct mechanisms for entanglement generation in X-ray inner-shell excitation processes.