Neutron Scattering by Liquid Neon

Abstract

A theory for neutron scattering by a semiclassical system, which is appropriate for liquid neon, is described. The theory is based on a generalized mean-field approximation involving the polarization potential and the screened response function, similarly to what has been done previously for argon and helium. The screened response function is assumed to be a sum of Gaussian functions weighted by the momentum-distribution function. The polarization potential and the width of the Gaussians are determined by the zeroth and third moments of the scattering law. The momentum distribution has the Maxwell—Boltzmann form, but includes quantum corrections to order ${\hslash }^2$. The quantum-mechanical zero-point energy is found to increase the kinetic energy per particle to a value of about 30% greater than the classical equipartition value. Calculations have been done for wave-vector transfers in the range 0.75-5.5 times the wave vector at the principal maximum in the static-structure factor, and the theoretical line shapes have been folded with the resolution function for the experiments of Buyers et al. Comparison of the position of the maximum, full width at half-maximum, and line shapes with the experimental results gives good agreement.