The application of space-dependent multigroup theory to the analysis of neutron slowing down time experiments I. Light and heavy water moderators

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Abstract
A detailed study is made of some recent measurements by Möller and Chen and Lidofsky of the most probable slowing down times of neutrons in light and heavy water. Using both an energy multigroup and a mixed-energy group-energy point technique, together with a moments-matching technique, the P1 and the diffusion approximations to the time-dependent Boltzmann equation are solved numerically. Good agreement is obtained with the spatially-dependent results at 146 eV obtained by Möller in light and heavy water. It is demonstrated that in order to reproduce the measurements of Chen and Lidofsky, made with a cadmium-shielded 1/v detector, it is necessary to allow for the energy dependence of the detector response. Generally, it is found that the P1 approximation reproduces these measurements better than the diffusion approximation.