Nonuniform neutron-rich matter present in both core-collapse supernovae and
neutron-star crusts is described in terms of a semiclassical model that
reproduces nuclear-matter properties and includes long-range Coulomb
interactions. The neutron-neutron correlation function and the corresponding
static structure factor are calculated from molecular dynamics simulations
involving 40,000 to 100,000 nucleons. The static structure factor describes
coherent neutrino scattering which is expected to dominate the neutrino
opacity. At low momentum transfers the static structure factor is found to be
small because of ion screening. In contrast, at intermediate momentum transfers
the static structure factor displays a large peak due to coherent scattering
from all the neutrons in a cluster. This peak moves to higher momentum
transfers and decreases in amplitude as the density increases. A large static
structure factor at zero momentum transfer, indicative of large density
fluctuations during a first-order phase transition, may increase the neutrino
opacity. However, no evidence of such an increase has been found. Therefore, it
is unlikely that the system undergoes a simple first-order phase transition. It
is found that corrections to the commonly used single heavy nucleus
approximation first appear at a density of the order of 1013 g/cm3 and
increase rapidly with increasing density. Thus, neutrino opacities are
overestimated in the single heavy nucleus approximation relative to the
complete molecular dynamics simulations.Comment: 17 pages, 23 included ps figure