A collision model for a dilute hard sphere gas mixture

A successive uncorrelated binary collision model for a dilute hard sphere gas is presented and used to calculate the single particle phase space density f(r, v, t/v0) and related quantities like the space time self correlation function Gsub(s) (r, T) in the classical approximation and to first order in h for the quantum mechanical case. It is shown that the phase space density satisfies the linearized Boltzmann equation and that within the Gaussian approximation to G2(r, t) the usual expression for free particle motion and the Langevin diffusion are obtained, where all parameters are given by the model. As an example the motion of a tagged particle in an arbitrary binary mixture is given and the velocity autocorrelation and the self diffusion coefficient are calculated explicitly. In addition, the method has been successfully used to calculate transport coefficients such as the mutual diffusion coefficient, the shear viscosity, the bulk viscosity and the heat conductivity for moderately dense gases. (orig.)