Correlations in Space and Time and Born Approximation Scattering in Systems of Interacting Particles

A natural time-dependent generalization is given for the well-known pair distribution function $g\left(\mathrm{r}\right)$ of systems of interacting particles. The pair distribution in space and time thus defined, denoted by $G(\mathrm{r}, t)$, gives rise to a very simple and entirely general expression for the angular and energy distribution of Born approximation scattering by the system. This expression is the natural extension of the familiar Zernike-Prins formula to scattering in which the energy transfers are not negligible compared to the energy of the scattered particle. It is therefore of particular interest for scattering of slow neutrons by general systems of interacting particles: $G$ is then the proper function in terms of which to analyze the scattering data.