4. METHOD OF SOLUTION
The method, called "orders of reflection", involves the following steps: (1) The penetration of the radiation (neutrons or gamma rays) through single straight ducts of various dimensions is first calculated in a one-velocity treatment, assuming an albedo with an angular dependence given by Chandrasekhar's theory, and assuming isotropic scattering. This penetration probability is calculated for the case of 0, 1, 2, ...n reflections from walls; (2) An estimate of the energy and angular characteristics of the radiation transmitted after 0, 1, 2, ..., n
reflections is then made by using the results of a Monte Carlo calculation in which the energy and angular characteristics of the multiply-reflected radiation is computed in a space-independent treatment; (3) The results of calculations (1) and (2) are combined to obtain a transfer function which relates the intensities, direction, and energy characteristics of the radiations entering and leaving a single straight duct or duct segment.
Using the output of one such calculation as the input for the next, the transmissions of the radiation through a sequence of ducts can readily be calculated for any spatial configuration of successive duct legs. The approximations made in the orders-of- reflection method are particularly applicable to neutrons. However, the method, with some adaptation, has also been found to be applicable to gamma rays.
An extensive data base of neutron and gamma albedo data has been incorporated into the system which allows very rapid calculations of radiation penetration of complex duct configurations. Trial calculations have indicated very good agreement with published Monte Carlo calculations. The method may also be applied to shielding problems pertaining to medical radiation sources and accelerators, but the code has not been tested for these applications.