Exponents in the Theory of the X-Ray Threshold Anomaly of Simple Metals

Abstract

The exponents at the threshold of soft X-ray absorption and emission spectra of metals in the theory of Nozières and De Dominicis are calculated. Effects of the periodic potential on an electron in a conduction band are formulated to be given in an effective mass approximation and the structures of the inner-shell holes are included in the hole potentials. In the present formulation, the change of the electronic wave function in metals due to the hole potential is expressible in terms of the phase shift which is obtained in the first Born approximation. The exponents obtained in this way give a satisfactory agreement with the experiments on the absorption and emission spectra of Na, Mg and Al within the precision of analysis. In particular, for Li our result agrees roughly with the experimental one obtained by Baer et al. (Phys. Rev. Letters 37 (1976) 49) using X-ray photoemission.