Corrections for multiple scattering in spherical and circular geometries

Abstract

In this paper a method is considered of introducing corrections for multiple scattering into the results of measurements of angular distributions of elastically scattered neutrons. It is assumed that the mean path of the neutron in the sample in which scattering takes place is comparable with the neutron free path.

In the first part, using direct calculation of the integrals, we find the probability for double scattering and estimate the probabilities for triple and higher-order scattering for a sphere and for a ring of circular and rectangular cross section in the case of isotropic neutron scattering. In the case of anisotropic neutron scattering, at neutron energies of the order of several million electron volts the cross section may be given as a sum π (σ) = π₁ (σ) + π₂ (σ), where π₁(σ) is the forward peak and π₂(σ) is more or less isotropic. Using this representation all elastic scattering events may be provisionally divided into two groups while all double scattering events can be divided into four groups. The probabilities of double scattering for all four are calculated on the basis of results obtained for isotropic scattering. Triple and higher-order scattering are evaluated in similar fashion.