(Australian Atomic Energy Commission, 1959-03) Hines, KC

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For neutrons slowing down in an infinite homogeneous moderator consisting of a single element the energy dependent flux of neutrons satisfies a simple integral equation when he sources of fast fission neutrons are uniformly distributed in space. This equation is readily soluble for neutrons slowing down in hydrogen and in heavier moderators for the energy range αEo ≤ E ≤ Eo (where αEo is the lowest energy that a neutron of initial energy Eo can have after a single collision in the moderator). For E < αEo, however, an analytical solution of the integral equation is not possible for moderators heavier than hydrogen. In the present work it is shown how a solution for lower energies may be obtained using a step-by-step procedure based on the simple solution of the problem for energies close to the initial energy. The method lends itself to programming for a digital computer and, for graphite, numerical results have been obtained using the I.B.M 650 Data Processing Machine. The results presented here take no account of absorption in the graphite during slowing down or of inelastic scattering by nuclei of the moderator and it is assumed that, for all energies, scattering is spherically symmetric in the centre of mass systems.

The slowing down spectra of neutrons are obtained for heavy water, light water, and mixtures of heavy water and light water. It is assumed that fission neutrons are produced uniformly throughout an infinite moderator and the only process considered is elastic scattering, spherically symmetric in the centre of mass system. The (n, 2n) reaction with the deuterium nucleus and absorption are assumed negligible.
The average transfer cross section, fast diffusion coefficient, the slowing down area, and average velocity ratio are obtained for two—group calculations using the epi — thermal spectra.