Analysis of coupled neutron-gamma radiations by the multigroup Albedo method applied to multilayered slab shieldings

Full text: The principal nuclear design tools available to the shielding designer include diffusion approximation, transport theory, and Monte Carlo techniques. Full transport theory or Monte Carlo methods are routinely used for shielding analyses, where penetration investigations are more sensitive to directional aspects. However, the aim of this paper is to illustrate the coupled neutron-gamma Albedo method particularly as applied to problems of shielding analysis. The multigroup Albedo method is applied to coupled neutron-gamma radiations considering 'n' neutron energy groups and 'g' gamma energy groups to estimate the probabilities of transmission through, absorption in, and reflection from shieldings composed by multiple material layers, 'm' slabs, in which no fission occurs. In this study, these energy groups were selected in order to minimize upscattering effects of the radiation from lower energy groups to higher energy groups. However, neutrons of all energies are assumed to generate gammas of all energies. The reflection coefficient or Albedo is defined as the current of the reflected radiation divided by the incident radiation current. The absorption coefficient is defined as the rate at which radiation is lost by absorption per second divided by the amount of incident radiation per second. The transmission coefficient is defined as the current of the transmitted radiation divided by the incident radiation current. The interaction probabilities can be arranged in matrix form where the rows indicate the energy group of the incident radiation and the columns indicate the energy group of the radiation after interaction. Thus, each material has 3 sets of distinct matrices, for the interactions neutron-neutron (N-N), neutron-gamma (N-G) and gamma-gamma (G-G). Each set is composed by 3 matrices, giving a total of 9 matrices per material. The first matrix set is for scattering/downscattering of neutrons (N-N); the next set is for scattering/downscattering of gammas (G-G), and the last set is for the coupling interactions (N-G), i.e. interactions of incident neutrons of any energy group originating gammas of all energy groups. The methodology used to calculate these radiation fractions in a system composed by multiple layers is to disassemble the system in individual layers, and solve the problem starting from two layers and successively adding another layer to the previous system and solve again. Then repeat this procedure up to the last layer 'm' is reached. This procedure creates an interactive process that is very suitable to be solved by computational means. An algorithm was developed and it was translated to a code in FORTRAN language. One dimensional static coupled neutron-gamma analysis has been performed on this shielding problem with the computer code ANIsotropic SN transport code ANISN, and the results were used as a standard for comparison with the results obtained by the code developed by the authors with success. (author)