Theoretical description of the white lines in 3d transition metals

The $3d \to 2{p_j}\;(j = 3/2,\;1/2)$emission lines in the 3d transition metals ${}^{21}Sc$ through ${}^{27}Ni$ have been studied using a theoretical model based on autoionization and characteristic decay events following electron impact ionization of a core electron in solids. The theory primarily hinges on the Bethe-Born formalism of inelastic scattering of electrons on atoms with the inclusion of correlation effects via many-body perturbation techniques. The $2{p^5}3{d^{\,n\, + 1}}$ intermediate resonant configuration is diagonalized to provide the multiplet splitting and their corresponding intensities. By analyzing the relative magnitudes of the electrostatic and magnetic interactions of the $2p$and $3d$electrons, it is found that $LK$ coupling is suitable for the systems Sc, Ti, and V, while $jK$ coupling is appropriate for Cr to Ni. Applying the dipole approximation to the Coulomb transition matrix elements, the calculated electron-energy-loss- spectra separate into two distinct manifolds that arise from the $2{p_{3/2}}$ and $2{p_{1/2}}$ levels, namely, the white lines, and the calculations compare very well with measurements for x-ray absorption spectra. Reference: K. Nuroh, Physical Review B 78, 245116 (2008).