Neutron Scattering from a Liquid on a Jump Diffusion Model

TLDR

In liquids, atoms undergo large discrete jumps with solid‑like oscillations, producing vibrationally dominated pair correlations that influence coherent scattering. The authors model the incoherent inelastic neutron scattering cross section by treating the liquid as possessing short‑range quasi‑crystalline order. The model yields a calculable cross section that is not dominated by diffusion, displays a characteristic angular variation testable experimentally, and accounts for key features of Brockhouse and Pope’s 1959 observations.

Abstract

The incoherent inelastic scattering cross section of slow neutrons from liquids is calculated using a simple model in which the liquid is assumed to have appreciable short range order in a quasi-crystalline form. Diffusive motion takes place in large discrete jumps, between which the atoms oscillate as in a solid. The model predicts a definite, easily calculable cross section which is not dominated by diffusion effects as when continuous diffusion is assumed, but shows a characteristic variation with angle which could be looked for experimentally. The related pair correlation functions are dominated at small r and t by vibrational effects. Although simple and extreme the model explains several aspects of the observations of Brockhouse and Pope in 1959 and others. A brief discussion of the coherent scattering cross sections for the model is given although explicit formulae are not obtained.