The Effect of Wide Scattering Resonances on Neutron Multigroup Cross Sections

The influence of wide scattering resonances on group-averaged uranium and plutonium resonance cross sections and on group elastic removal cross sections is examined; the consequences for a Bondarenko-type LMFBR multigroup cross-section scheme are discussed. An analytical expression is derived for a constant effective cross section which adequately accounts for the sodium resonance in the computation of group-averaged uranium and plutonium resonance cross sections. Analytical expressions are derived for the group elastic removal cross sections, also. These latter are superior to the Bondarenko prescriptions in that they account for the location of a scattering resonance within a group and thus account for both the relative probability that a neutron scattered in the resonance will be scattered out of the group and for the relative flux shape within the group. The composition dependence of these expressions is shown to be characterized by a single parameter. Numerical results are presented for compositions that are typical of proposed LMFBRs.