Neutron Thermalization Calculations for a Heterogeneous Lattice Containing Uranium and Plutonium Fuel in Water

In a low-enrichment reactor at sufficiently high temperature that the Pu²³⁹ absorption cross section departs appreciably from 1/υ, plutonium build-up increases the sensitivity of the calculated thermal cross sections to the thermalization techniques used. Thermal neutron spectra are compared for two thermalization models in a heterogeneous lattice of a low-enrichment water-moderated reactor. Using blackness theory, equivalent homogeneous, monoenergetic cross sections for the lattice are computed at closely spaced energy intervals over the thermal energy range. The energy distribution of the thermal neutron flux is then obtained using both the Wigner-Wilkins and the Wilkins thermalization equations. Calculations are made with the fuel elements assumed to contain only U²³⁵ and U²³⁸ yielding almost pure 1/υ absorption, and also for the case of appreciable Pu²³⁹ present in addition to the uranium resulting in a significant departure from 1/υ absorption. Sensitivity of the calculated spectrum to the effective mass of the hydrogen is tested by allowing wide variations of the ξσ_s values for water at low energies in several applications of the Wilkins equation. Variations in the thermal neutron spectra, resulting from the choice of the thermalization equation (Wigner-Wilkins or Wilkins), from changing ξσ_s, or as a result of plutonium build-up, are evaluated in terms of isotopic cross sections averaged over the spectrum in each case.