The neutron scattering function for hard spheres

Abstract

Density, longitudinal, and transverse-current correlation functions for hard spheres at various densities and wavelengths have been generated by computer simulation and compared with both the generalized Enskog kinetic theory and wavelength-dependent hydrodynamics. It is shown that even for dense gases the generalized Enskog kinetic theory is quantitatively accurate in describing the thermal fluctuations at finite wavelengths and frequencies, as is wavelength-dependent hydrodynamics, as long as the wavelength is greater than the mean free path. At liquid densities neither theory can account for the viscoelastic relaxation effects, directly observed in the transverse-current correlation function by shear-wave propagation, at a wavelength somewhat above the first diffraction maximum. However, wavelength-dependent hydrodynamics quantitatively describes the neutron scattering function at wavelengths from this point (above the first diffraction maximum) through the diffraction maximum (where the de Gennes narrowing occurs) to the mean-free-path limit. Furthermore, viscoelastic effects in the long-wavelength regime can be accounted for by introducing into hydrodynamics time-dependent transport coefficients. At still longer wavelengths, viscoelastic relaxation times become short compared with hydrodynamic relaxation times and ordinary hydrodynamics with constant transport coefficients describes the neutron scattering function.