Understanding the L2,3 x-ray absorption spectra of early 3d transition elements

In this work we calculate the x-ray absorption spectra at the L-2,L-3 edges of the early 3d elements by solving the Bethe-Salpeter equation. We focus our discussion on the origin of the observed deviation of the branching ratio between L-2 and L-3 edges from its statistical value. Using the absorption edge of Ca in CaF2 we show that the deviation is related to the mixing between the excitations from 2p(1/2) and 2p(3/2) core levels. Furthermore we find that the mixing is triggered by the exchange term of the electron-hole Hamiltonian. This term does not depend on the dielectric function, therefore such coupling is also present in metals explaining the high values of the branching ratios observed in the metals Ca and Ti. The calculated Ti L-2,L-3 spectra of SrTiO3 and the anatase and rutile phases of TiO2 reproduce even all fine details of the experimental spectra.