Multiple neutron scattering corrections. Some general equations to do fast evaluations

Abstract

An efficient Monte Carlo algorithm has been developed aimed at simulating neutron tracing in a liquid or amorphous sample, during a diffraction experiment. At odds with approximated analytical estimates, such a method allows to easily take into account some physical and geometrical features, which play an important role in determining the measured scattered neutron intensity. Some general laws giving the multiple scattering intensity, in terms of few adimensional parameters, are provided. In particular, it results that the most relevant quantity involved in the neutron transport is the mean free path (defined as the inverse of the attenuation factor), which can be helpfully assumed as natural length unit. This yields to some important consequences: for istance, in the case of absorbing or structured samples, the mean free path can strongly depend on the neutron energy and this should be considered in the choice of the experimental apparatus.