Velocity autocorrelation function of interacting Brownian particles

We study the velocity correlation function of a selected particle in a suspension of interacting Brownian particles. Experimentally, the velocity correlation function can be observed with diffusing wave spectroscopy. The function has also been determined in computer simulation. We assume a wide separation of time scales between momentum relaxation and diffusive motion. The correlation function is found from linear hydrodynamics by use of the fluctuation-dissipation theorem. We propose a simple approximation based on the single particle result that is valid for a dilute suspension. The approximation is fully determined by the short-time self-diffusion coefficient and the effective mass of the selected particle. We discuss the concept of scaling within the framework of the approximation. We find that the amplitude of the t^-3/2 long-time tail is independent of the concentration of the suspension.