The NEACRP Criticality Working Group has examined the validity of computational methods used in the evaluation of the criticality safety for several different operations involving fissile material through various benchmark problems, and presented a preliminary report summarizing the results from various contributors
(1). A hypothetical criticality problem among a variety of benchmark problems proposed by the Working Group represents a system where pellets are surrounded by a fuel solution. A feature of the problem is that the same resonant nuclide exists in adjacent two materials. For methods using multigroup cross sections, this pellet/fuel-solution type system presents a difficulty for treating the resonance absorption in one material which is affected by the adjacent material. The Dancoff factor method is not considered to be valid for the pellet/fuel-solution type system, which evaluates the resonance absorption with the table-look-up method of self-shielding factor based on the narrow resonance approximation (NRA) using the background cross section of the resonant nuclide whose heterogeneity term is estimated by the Dancoff correction factor. Because this method estimates the heterogeneity term of the background cross section by regarding each material as an extreme ; "white" or "black". In the present study, we examine the validity of the Dancoff factor method and two other methods, Tone's method
(2) and the PEACO method
(3), for the pellet/fuel-solution type system. A practical method using multigroup cross section was proposed by Tone for a system where the same nuclide exists in different materials. In this method, the background cross section of the resonant nuclide in one material is evaluated by considering a contribution from each material via collision probabilities, that is to say, materials can be regarded as "gray" and the resonance absorption is evaluated by the table-look-up method based on NRA. Tone's method has been reported to give an accurate evaluation for the resonance absorption in the analysis of the critical experiment using fuel elements made of a combination of different kinds of plate-type fuels
(4). The PEACO method implemented in the SRAC code evaluates the resonance absorption by calculating the hyperfine group flux distribution with the collision probability method. The PEACO method has been demonstrated to show good agreement for a large number of benchmarks and reactor calculations
(5). The validity of these methods for the pellet/fuel-solution system is examined in comparison with a continuous energy Monte Carlo code VIM
(6) used as the reference calculation.
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