Models for the Motion of a Molecule in a Liquid and Their Application to Slow-Neutron Scattering

A kinetic model for the calculation of Van Hove's $G_s(\mathbf{r},t)$ in a fluid is presented in which molecules move by Langevin diffusion between random binary collisions. Thus, the effects on the diffusive motions of molecules of both strong and weak interactions are considered in a manner similar to that of Rice and Allnatt. An expression is given for $S_s(\mathbf{\kappa },\omega )$, the double Fourier transform of $G_s(\mathbf{r},t)$, which is the quantity of interest in the incoherent scattering of slow neutrons. It is found that the Gaussian approximation to $S_s(\mathbf{\kappa },\omega )$ is independent of the ratio of the binary collision rate to the Langevin friction coefficient, but that the non-Gaussian portion is very sensitive to this ratio. It is also shown that the Gaussian approximation to this model is equivalent to making the Fokker-Planck approximation to a Boltzmann-like collision integral in a certain kinetic equation. The limited data available show the model to be superior to either the hard collision or Langevin model alone, but the agreement is still not satisfactory. Further modifications that can improve agreement are suggested.