In the electron-energy-loss or x-ray-absorption spectra of the 3d transition metals the onset of the $L_2$,3 edge (2p excitation) is marked by two sharp peaks often called white lines. The peaks are attributed to the excitation of the 2$p_{3/2}$ and 2$p_{1/2}$ subshells to unoccupied d levels but the observed ratio of their areas is not the statistical 2:1 ratio expected from initial-state occupation. In this paper we report the results of multiconfiguration Dirac-Fock calculations of the transition rates which should include atomic many-electron effects. We compare our results with experimental energy-loss measurements from a number of sources. There is good agreement for the ratio of the two components although the detailed shape can show additional solid-state effects. In particular, the $L_3$-$L_2$ ratio is very sensitive to the charge state for elements in the middle of the period such as Mn and Cr. This effect can therefore be used to measure ionicity in energy-loss microanalysis in the electron microscope.

• Received 28 January 1986

DOI:https://doi.org/10.1103/PhysRevB.34.1467