Mathematical formulae for neutron self-shielding properties of media in an isotropic neutron field

Abstract

In the current study, an ab initio derivation of the neutron self-shielding factor to solve the complex neutron transport problem of the decrease of the neutron flux as it penetrates into a material placed in an isotropic neutron field having equal flux in all directions. The theory of steady-state neutron transport was employed, starting from Stuart’s formula, to derive simple analytical formulae based on the integral cross-section parameters. The formulae could be adopted by the user according to various variables, such as the neutron flux distribution and geometry of the simulation at hand. The concluded formulae of the self-shielding factors comprise an inverted sigmoid function normalized with a weight representing the ratio between the macroscopic total and scattering cross-sections of the medium. The general convex volume geometries are reduced to a set of chord lengths, while the neutron interaction probabilities within the volume are parameterized to the epithermal and thermal neutron energies. The arguments of the inverted-sigmoid function were derived from a simplified version of neutron transport formulation. The derived analytic formulae agreed greatly with the experimental observations for different elements and geometries.