Polarization dependence of resonant X-ray emission spectra in early transition metal compounds

We calculate the polarization dependent spectra of resonant X-ray emission in TiF₃, VF₃ and Cr₂O₃, which have one, two and three 3d electron(s) in the ground state, respectively. We study the detailed mechanism of the spectral structures, comparing with a previous result of TiO₂. Then we discuss systematically the difference of spectra with the change of the 3d electron number from group theoretical consideration.