Development of Angular Eigenvalue Method for Radiation Transport Problems in Slabs and Its Application to Penetration of Gamma Rays.

Abstract

The present article describes a development of a new semi-analytical method for radiation transport problems in slabs, called “angular eigenvalue method”, and its application to the penetration of gamma rays in slabs. According to the present method, an exact solution of energy and angular distribution of transmitted radiations in a slab can be obtained, based on the multi-group approximation for energy and the discrete ordinate approximation for angular variable. The present method has a feature that it can be applied to the deep penetration of radiations more easily than other dependable methods, since a solution is expressed analytically as a function of the slab thickness. The present method was applied to the penetration of gamma rays. Calculations were made on the buildup factors of concrete slabs for plane oblique sources, those of water and iron for plane isotropic sources in infinite medium and those of water, iron and lead for point isotropic sources in infinite medium up to the distance of 40 mean free paths. Those buildup factors were found in good agreement with other dependable data. It was concluded that the present method can provide solutions with an accuracy comparable with other dependable methods, such as the Monte Carlo method and the moments method.