Screening of fuel elements at neutron absorption resonances in a close-packed lattice

Abstract

The degree of mutual screening by resonance absorbing slugs or layers of fuel is calculated for the case where the thickness of moderator between adjacent elements is comparable with or less than the neutron mean free path in the moderating material. It is assumed that the fuel elements are small and that the absorption cross-section follows the Breit-Wigner law. Computations are made for a system of parallel plates; they provide a check on the accuracy of Petrov's earlier formulae, and lead to an expression for the screening coefficient of a nearly homogeneous system. The normally justifiable approximation of replacing the true cell in a lattice of cylindrical elements by a supposedly equivalent cell of circular section is shown to introduce substantial errors in problems of this type. An explicit formula is derived for the resonance self-absorption in elements of annular cross-section.