Density response functions for molten salts

Abstract

A theory of the density response functions of molten salts is given. The results are obtained by an extension of a theory given by Hubbard and Beeby for a single component liquid. The theory is based on the physical idea that the high frequency motions of the particles are similar to the motions in a disordered solid. The technique used is to consider the linear response of the system to an external disturbance and approximate the exact equation of motion by factoring the higher‐order correlation functions which appear therein. The result of Hubbard and Beeby is rederived here by a method which is shorter than the original method, and it is also applied to a charged system rather than to a neutral system. Then this method is generalized to the two‐component case. The expressions for the density response functions for the individual species are obtained in a mean‐field form appropriately generalized to two components. The screened response functions are determined by the self‐motion functions for the two different species, and the polarization potentials are determined by the potential energy part of the fourth moments of the exact density response functions. The moment relations obeyed by the approximate results for the density response functions and the transformation to response functions for the total number or mass density and charge density are given. Finally, approximate dispersion relations for density fluctuations are obtained. These have a branch of ’’acoustical’’ character with frequency tending linearly to zero for long wavelengths, and a branch of ’’optical’’ character with a finite frequency in the long wavelength limit. The factors entering into the limiting optical mode frequency are analyzed, and their magnitudes are estimated.