Detailed Calculations in Energy and Space of Effective Neutron Resonance Cross Sections

A method is developed for calculating effective neutron cross sections in the resolved resonance groups of homogeneous mixtures of cylindrical cells in regular reactor lattices. A rigorous treatment of the nucleonic and neutronic problems provides accurate numerical solutions with detailed dependence in energy and space for both Doppler-broadened cross sections and self-shielded neutron fluxes. The common simplifying approximations are not introduced, so that the method is used as a reference to analyze some of the detailed self-shielding effects that are commonly ignored or approximated in applications ranging from homogeneous mixtures of different resonant nuclides to cylindrical cells with nonuniform temperatures and concentrations within the fuel.