Unified Approximation for the Velocity Autocorrelation Function and the Structure Function of a Simple Liquid
A theory of one-particle and two-particle motions in monatomic classical liquids, which employs the two-particle position-dependent Green's function in a fundamental way is developed. An equation of motion for the autocorrelation function is derived by assuming that a Brownian particle diffuses in a mean-time-dependent field. The motion of the atoms which generate the time-dependent field is described by the Green's function. In addition, the Green's function is directly related to the Van Hove scattering function in a simple way. The velocity autocorrelation function and neutron scattering cross sections are computed for liquid argon by assuming a relaxation approximation for the two-particle Green's function. Comparisons are made with recent experimental results.