Time-Relaxed Probability Densities and Correlation Functions for Moderately Dense Fluids

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Abstract
Kinetic equations are obtained for the purpose of describing the temporal evolution of two-time (conditional) probability densities for locating subsets of particles moving within an equilibrium assembly. The reduction and solution of the equation for the single-particle density is investigated in considerable detail. Information concerning the short-time evolution of the probability densities is explicitly retained, in order that the applicability of the equations for studying the properties of relatively dense systems be preserved. The expressions for probability densities are used to study the properties of certain associated correlation functions. Expressions for the momentum autocorrelation function are derived. Similarly, certain features of the cross sections for the scattering of slow neutrons are investigated.