Intermediate Neutron Resonance Absorption in Heterogeneous Systems

A two-term rational approximation is proposed for the calculation of the collision probabilities for regular arrays of cylindrical fuel rods and cluster-type fuel elements. Comparisons with exact and Monte Carlo calculations show that its accuracy is quite adequate for the analytical approach to calculating resonance absorption under the flat-flux approximation.

Using the two-term approximation, an analytical expression for calculating resonance integral is given for intermediate resonances. Specific examples are computed numerically for the 6.7-eV resonance of ²³⁸U for the square lattices of ²³⁸UO₂ and ²³⁸U-metal rods in water and carbon. The present results are found to be in good agreement with Monte Carlo calculations, but are slightly higher in value due to the flat-flux approximation. The Bell factor proposed by Leslie et al. also overestimates the resonance integral of the 6.7-eV resonance of ²³⁸U.