Correlation effects in small-angle neutron scattering from closely packed spheres

Computer simulations are used to investigate the effects of interparticle correlations on small-angle neutron scattering spectra of systems of closely packed solid spheres. By the use of computer-generated systems containing large numbers of different sized spheres, the SANS spectra are calculated by exact summation of the form factors. The accuracy of the calculation is limited only by the maximum size of the system that can reasonably be run on the computer. The results from these simulations are compared with theoretical predictions and a simple generalization of the formula for monodisperse systems is tested. It is shown that, for a wide range of particle size distributions, this simple formula is sufficient to describe correlation effects in polydisperse systems.