Validity of the Convolution Approximation for the Van HoveG(r,t)Function

The validity of the convolution approximation is examined by expanding the spatial Fourier transforms of both the true and the approximate Van Hove $G(\mathbf{r},t)$ function in powers of the density. Only the lowest order terms in the expansions are explicitly calculated. However, comparison of the latter indicates that, for intermediate values of k, terms which are retained in the approximation are of magnitude comparable to that of terms which are neglected. It is concluded, therefore, that the convolution approximation fails at low density for intermediate values of k.