Numerical methods for calculation of low-energy neutron scattering cross sections

Various numerical methods are presented for calculating neutron scattering cross sections, both differential and total, in a macro-isotropic system for which a scattering law depends only on the magnitude of momentum transfer. First, a method for the finite Fourier transform of an intermediate scattering function is described so as to yield a differential cross section with a reasonable degree of accuracy over a wide range of incident neutron energies, i.e. from ultracold (similar to 0.1 mu eV) to epithermal (similar to 10 eV). Then, the method is applied to the calculation of a total scattering cross section for all incident energies mentioned above. Finally practical methods for generating cross section libraries such as a scattering-law map and a set of multigroup constants (energy-averaged cross sections) are described. Every method is illustrated with physical models for free gas, simple diffusion and molecular liquid. Relevant processing conditions are all specified, since they will be useful for further cross section calculation.