the “Gaussian approximation”. This Gaussian approximation is not related to the Gaussian approximation for the particle displacements as discussed below.

The intermediate structure factor is in turn determined by the time-dependent positions of the scattering particles via $$g^{(1)}(q,t) = \left\langle \sum_{i=1}^{N} \sum_{j=1}^{N} \exp(\imath {\bf q} \cdot ({\bf r}_{i}(t+\tau) -  {\bf r}_{j}(\tau) )) \right\rangle
    \label{eq:g1qgeneral}$$ In this equation, sums on $i$ and $j$ proceed separately over all $N$ particles in the system, while ${\bf r}_{i}(t+\tau)$ and ${\bf r}_{j}(\tau)$ are the locations of scatterers $i$ and $j$ at times $t+\tau$ and $\tau$, respectively.

In applying eq \[eq:g1qgeneral\], two particularly interesting experimental circumstances are described as mutual diffusion measurements and as probe diffusion measurements. In a measurement on a binary solvent: scatterer system, the scattering particles may be concentrated or dilute. Quasielastic scattering on such a system measures the mutual diffusion coefficient, which describes the diffusion of the scatterers down a concentration gradient[@phillies1974a; @phillies1974b]. Tracer diffusion experiments examine ternary solvent: matrix : probe systems. In these systems the matrix component may be dilute or concentrated, is substantially responsible for the system’s rheological and other interesting properties, but is nearly optically inert. Conversely, the probe (tracer) component is dilute, has virtually no effect on 