Electronic States in Liquid Metals: A Generalization of the Coherent-Potential Approximation for a System with Short-Range Order

Abstract

The problem of finding the ensemble averaged Green's function $〈G〉$ which describes an electron moving in the potential field of $N$ stationary scatterers is formulated in terms of multiple scattering theory. The correlations between the positions of the scatterers are explicitly taken into account. By making use of the quasicrystalline approximation and a generalization of the coherent-potential prescription, a procedure for calculating $〈G〉$ is proposed. Because of the use of the quasicrystalline approximation, it involves only the radial distribution function of the scatterers in addition to the scatterer-electron interaction potential. It is shown that the procedure reduces to the coherent-potential approximation for randomly distributed scatterers, i.e., no short-range order, and to Korringa's band-structure calculation for an order lattice. It is pointed out that the method is applicable to the problem of electronic states in random alloys and that of vibrational spectra of imperfect crystals.