The Velocity Autocorrelation Function of a Dense Fluid

Boltzmann-Enskog approximation consists of recollision terms that describe correlated binary collisions. The effects of these processes on the behavior of time correlation functions have not yet been fully studied because the calculations involved are considerably more complicated. The problem where the effects of recollisions have been most extensively investigated is that of the velocity autocorrelation function, which is a simpler function than the dynamic structure factor. From this problem we can already see the kind of analysis involved in treating correlated collisions.  

We now consider the motions of an atom as it moves in a fluid environment. The memory function for this case can be written in a form like (105)  

Note that the o o factors in Go will just cancel those that are included in the definition of T. If we carry out an analysis very similar to that given in 

Putting these results together and Fourier transforming over all spatial indices, we obtain 

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