The theory of the electronic structure of liquid metals

Abstract

The [Green function] method of Korringa and of Kohn and Rostoker is generalized to the case of a disordered assembly of atoms. If it can be assumed that the wave-function of an electron has a [wave-vector] k, then its energy can be calculated. The equations depend only on the radial distribution function of the atoms in the liquid and on their phase shifts for electron scattering. But the wave-vector k is not real, as for a Bloch function in a solid. It has an imaginary part, which corresponds to the scattering of the electron by the irregular atomic arrangement. It is shown that the assumption that k exists is equivalent to assuming that the liquid is microscopically homogeneous. The method can be generalized to take account of inhomogeneities; a [local] value of k can be calculated for each configuration of the atoms in a finite cluster immersed in the fluid. No actual numerical calculations are reported in this paper, but the procedure is evidently capable of giving practical results without undue labour.