Neutron transport calculations involving a mixture of group and discrete-energy fluxes

In order to treat problems typically calling for fine detail in a resonance region covering only a small portion of the overall energy range, a mixed or hybrid treatment has been developed. It envisions one or more restricted energy intervals where the flux is calculated on a discrete energy grid, while elsewhere the spectrum is treated on a multigroup basis. The scattering matrix in the hybrid formulation requires the calculation of four types of transfer coefficients: group-to-group, group-to-point, point-to-point, and point-to-group. Correspondingly there are one-dimensional arrays of cross sections representing, e.g., the total cross section, which contain group-averaged cross section in the energy ranges described by groups, and point cross sections where there is a discrete energy description. These cross sections may be used as the input library to standard transport codes, such as ANISN, which will then compute group fluxes and discrete-energy fluxes in the appropriate regions. No changes need be made in these codes except for such auxiliary portions as involve an integration over energy, e.g., an overall-system checking routine. Preparation of the cross section quantities required in this mixed group-discrete energy scheme has been implemented in the framework of the MINX processing code, and associated handling programs. The processing code incorporates a program forcalculating the infinite-medium spectrum and the corresponding slowing-down rate in an infinite medium, thus providing a check to insure the cross sections conserve neutrons. Several illustrative problems have been run, for various combinations of groups and points, in iron and iron-water mixtures. Typical spectra are presented, showing the detail that can be calculated for the flux spectrum in the resolved resonance region for iron