This paper examines a new probabilistic formulation and development of a model for the investigation of three-dimensional gamma-ray transport problems. This model assumes that gamma-ray motion may be sampled at predetermined points. A medium is considered to be filled with a cubic lattice whose unit distance between lattice points may be some fraction of the mean-free-path. The random walk of gamma rays from one point to another is constructed using the lattice framework as reference points. Using this model, a new type of stochastic gamma-ray transport code, PUGT I (Purdue University Gamma Ray Transport I), has been developed based on direct simulation of physical transport process. In another version of the code (PUGT II), capture of gamma rays is taken into account analytically by associating a weight factor to the gamma rays. The codes are used to calculate the transmission and reflection characteristics of gamma rays for different thicknesses of slabs of aluminum and iron. The contribution of annihilation radiation to reflection and transmission is investigated. The results of our calculations are in good agreement with other similar calculations and with experimental results. Gamma-ray streaming through two-legged rectangular concrete ducts was investigated. Results of these studies are in very good agreement with experimental results and demonstrate the ability of the codes and the power of the lattice model to calculate quickly and efficiently the transmission of gamma rays in three-dimensional complex shielding geometries. The method is several times faster than ordinary Monte Carlo.
