Collective Effects and the Hydrodynamic Approximation in Neutron Scattering from Fluids

Abstract

The scattering law is investigated for gases and liquids. It is shown that the convolution approximation ignores perturbations caused by the test particle for $t>\mathrm{}0\mathrm{}$. For a dilute gas, a normal-mode expansion of the Boltzmann equation is made to estimate the size of the "collective effects" contribution to the scattering law. It is found that for small energy and momentum transfers the "collective-effects" contribution dominates the solution. The hydrodynamic and convolution approximations are compared to experimental results for liquid sodium.