Abstract
In the interpretation of the fine structure of the x-ray absorption spectrum in solids, the life time of the state of the electron ejected by a photon is considered. With the assumption that the inelastic cross section of collision between the electron and an atom has a magnitude of the order of one square Angstrom, Kronig’s method for molecules is applied to solids in order to obtain the variation of the transition probability. The wave function of the final state of the transition is obtained as the sum of the plane wave, whose amplitude decreases with increasing distance from the atom which ejected the electron, and the waves scattered by the neighboring atoms. The scattering amplitude is calculated numerically for the Hartree field of the atom. Calculations are applied to the K-absorption spectra of copper and titanium and to K-absorption spectra of titanium in the two modifications of titanium dioxides, rutile and anatase. The calculated results agree well with experiments in copper and titanium, and the agreements become worse in titanium dioxides.
