Monte Carlo evaluation of multiple scattering and resolution effects in double-differential neutron scattering cross-section measurements

A Monte Carlo computer code, MSC, has been developed which is of general usefulness in analyzing double-differential neutron scattering measurements. This code is equivalent to a three-dimensional solution of the neutron transport equation for finite geometries. It is available for two geometrical configurations (slab geometry and tubular geometry), and is readily adapted to other geometrical configurations. Resolution effects are calculated in detail by including full time dependence in the calculation and considering individually the various factors which contribute to the experimental resolution. MSC uses statistical weights as a means to improve the convergence of the Monte Carlo method by forcing scattering collisions; the statistical estimation technique used allows every collision to contribute to every scattered energy and angular bin. Options have been developed which treat rigorously the coherent and incoherent elastic scattering from polycrystals.Scattered energy and angle are sampled at each Monte Carlo collision by means of a new method which samples alpha and beta from the scattering law. This sampling technique is exact within the framework of numerical integration and interpolation. It permits full kernel calculations, yet requires the storage of only two-dimensional arrays.The use of this code led to changes in procedure in the double-differential neutron scattering cross-section experiments at Rensselaer. Because calculated experimental corrections are strongly model dependent, the data have not been corrected for resolution and multiple scattering effects. Instead, resolution-broadened multiple-scattered theory is compared with uncorrected data. This avoids the pitfall of data "corrections" which may, in fact, be strongly model dependent and bias the final results according to the model assumed for the calculation of the correction. This use of uncorrected data enhances the practical value of the measurements as a model testing device.Use of MSC has made it possible to obtain good scattering results with relatively thick samples for several materials, notably water, polyethylene, and uranium carbide. Some examples are given of the verification of the methods used. Experience gained by the use of MSC is summarized.