Effective Thermal-Neutron Cross Sections for Materials with Grain Structure

A method is given for the calculation of effective neutron cross sections for materials with grain structure. The method is particularly suited for the calculation of effective cross sections at thermal energies where the ratio of scattering to total cross section for absorbers is small. The grain shielding factors have been calculated through the 1.056-eV resonance of ²⁴⁰Pu for the case of 200-µ-diam plutonium oxide grains, containing 17%²⁴⁰Pu, homogeneously dispersed in BeO. It is shown that provided the centers of the grains are not less than 800 µ apart the method given in this paper is applicable and gives excellent agreement with the results obtained from a P₁ , S₈ neutron transport theory calculation.