Evaluation of multiple small-angle neutron scattering including magnetic interactions

Analytical formulae describing multiple small-angle neutron scattering in ferromagnetic materials are derived from transport equations. The derivation is based on Moliere's theory of multiple small-angle scattering assuming that the mean free path of the neutrons is large compared to the size of the scatterers. In addition to the formalism developed earlier for nuclear scattering, the new formulation takes into account the spin dependence of the scattering cross section and spin flips caused by subsequent scattering events. This leads to an anomalous distribution of scattering intensity and polarization, as demonstrated by examples of model calculations and Monte Carlo simulations. In particular, multiple scattering of polarized neutrons can lead to either smoothing or sharpening of the scattered beam anisotropy depending on the polarization of the primary beam and the nuclear and magnetic contrasts of the scatterers. The presented theory has been implemented in the data-fitting program SASProFit suitable for both the modelling of multiple scattering effects and the analysis of experimental data.