Self-shielding and energy dependence of dilution cross-section in the resolved resonance region

In the calculation of flux weighted multigroup neutron cross-sections of a nuclide present in a homogeneous mixture of several nuclides, by the well known Bondarenko approach, the contributions from the other nuclides to the flux weighting function, are contained in a parameter called 'dilution'. Under the narrow resonance approximation and with assumed non-overlap of resonances, the energy fluctuations of the dilution are usually ignored within an energy group. The 'self-shielding factor' (SSF), which is the ratio of the group cross section for a given dilution to that at infinite dilution, is a smooth function of dilution. A conventional multigroup cross section set, apart from the infinite dilution cross-sections, gives SSF over a dilution grid, from which the effective SSF for any dilution could be obtained by interpolation. The effective SSF multiplied by the infinite dilution cross-section then gives the effective cross-section to be used in the neutronic analyis. Though this conventional procedure works well, the accuracy of this procedure depends on the interpolation scheme used and on the fineness of the dilution grid. The effect of fineness of the dilution grid and the effect of energy dependence of the dilution on the effective SSF are observed, for a specific case, and the results presented in this paper. The JENDL-2 basic nuclear data was used and the benchmark fast critical assembly ZPR-6-7 anlaysed for a temperature of 300K. The study was restricted to the resolved resonance regions of the nuclides involved. The results appear significant with respect to the target accuracies demanded for the SSF.