Wave propagation through an assembly of spheres: III. The density of states in a liquid

Abstract

The expression for the density of states in a system of non-overlapping potentials by Lloyd in 1966 is investigated by means of a diagrammatic technique for the case where the system under discussion is a liquid. The resulting equations express the ensemble-averaged density of states of such a system in terms of the scattering phase shifts and the probability correlation functions for the positions of the scatterers. The formulae are applied in detail to a simple example in which the size of the scattering centres is limited to zero and in which probability distributions are completely uniform. It is found that when the individual scatterers contain a deep energy level a band of eigenstates about this energy exists in the liquid. Some evidence is presented that these levels are highly localized.