  We use computer simulation results for a dense Lennard-Jones fluid for a
range of temperatures to test the accuracy of various binary collision
approximations for the memory function for density fluctuations in liquids. The
approximations tested include the moderate density approximation of the
generalized Boltzmann-Enskog memory function (MGBE) of Mazenko and Yip, the
binary collision approximation (BCA) and the short time approximation (STA) of
Ranganathan and Andersen, and various other approximations derived by us using
diagrammatic methods. The tests are of twotypes. The first is a comparison of
the correlation functions predicted by each approximate memory function with
the simulation results, especially for the self longitudinal current
correlation function (SLCC). The second is a direct comparison of each
approximate memory function with a memory function numerically extracted from
the correlation function data. The MGBE memory function is accurate at short
times but decays to zero too slowly and gives a poor description of the
correlation function at intermediate times. The BCA is exact at zero time, but
it predicts a correlation function that diverges at long times. The STA gives a
reasonable description of the SLCC but does not predict the correct temperature
dependence of the negative dip in the function that is associated with caging
at low temperatures. None of the other binary collision approximations is a
systematic improvement upon the STA. The extracted memory functions have a
rapidly decaying short time part, much like the STA, and a much smaller, more
slowly decaying part of the type predicted by mode coupling theory. Theories
that use mode coupling commonly include a binary collision term in the memory
function but do not discuss in detail the nature of that term. ...

Statistical Mechanics