Calculation of Azimuthally Dependent Thermal-Neutron Albedos for Slab by Method of Invariant Embedding

Abstract

The method of invariant embedding has been applied to the calculation of differential thermal-neutron albedos for a semi-infinite ordinary concrete slab. The calculations have been performed in both cases of isotropic and anisotropic scattering in the laboratory system.

The calculated albedo data are compared with those obtained by the experiments and the semi-empirical formula fitted the detailed data obtained by Monte Carlo method. The calculated results assuming isotropic scattering are in good overall agreement with the values obtained by Monte Carlo and S_N methods, but there are some errors for azimuthally anisotropic scattering when azimuthal angle becomes large.

In this method, much less computing times within given accuracy are required for azimuthally isotropic scattering, but it is pronounced that the necessary computing times are heavily dependent on N in DP _(N/2)-1 (ξ)T_N(μ) quadrature sets when the azimuthally anisotropic scattering is considered.

It is found that, except for large N for the case of azimuthally anisotropic scattering, the calculation of differential albedo data by using invariant embedding method is much faster than those by using the Monte Carlo and the discrete ordinates methods.

KEYWORDS:

• albedo
• thermal neutrons
• invariant embedding
• slabs
• concretes
• shielding materials
• isotropic scattering
• anisotropic scattering
• experimental data
• comparative evaluations