Collision Probabilities and Resonance Integrals for Lattices

A formula for the escape probabilities of neutrons from the fuel lumps to the moderator and vice versa in a lattice is derived and the validity of simple approximations discussed. These formulas are applied to solve the coupled integral equations for the collision densities in a lattice. First-order corrections to the resonance integral are obtained both for the Narrow Resonance and the Narrow Resonance Infinite Absorber approximations. Numerical results are given for water lattices containing hexagonal arrays of U²³⁸ rods, of 0.25 and 0.60 in. diameter, at different water-to-metal volume ratios.