On the Theory of Space Dependent Neutron Spectra in Heterogeneous Reactors

An analytical method is developed for determining the energy dependent neutron flux in homogeneous and heterogeneous media. Using the heavy gas model scattering operator, neutron spectra in two-dimensional rod reactors of various types are calculated in the diffusion approximation. They show a strong spatial dependence even in the epithermal region, which fact is neglected in the numerical treatment of the problem by Honeck and Kaplan. It is just this epithermal part of the spectrum, which mainly influences the values of the thermal utilization and the η-factor. The value obtained for the latter quantity is too large if the correct neutron spectra in moderator and fuel are replaced by Maxwellian distributions at moderator-temperature or a suitably displaced temperature, for example.