Characterization of the Thermalness of a Fissile System with a Two-Group Diffusion Theory Parameter

In tabulating critical data, the hydrogen-to-fissile atom ratio (H/X) is commonly used to characterize the amount of moderation in a system. Though adequate in many cases, H/X does not account for the moderating contribution of other light nuclei contained in common uranium-moderator mixtures. This ratio also does not account for enrichment of the system, which affects the resonance absorption characteristics and, therefore, the moderating behavior of that system. To alleviate these problems, a two-energy-group diffusion theory analogy to the six-factor formula was applied to define a new parameter p/(η₂ · f₂), which describes the moderation characteristics or the “thermalness” of a fissioning system and includes the effects of enrichment and the presence of moderators other than hydrogen. From an analysis of several low-enriched uranium systems with different moderators, it was found that the values of p/(η₂·f₂) corresponding to minimum critical mass and volume tend to center in a narrower range than do the values of H/X for the same systems. Also, the thermalness parameter does not vary with the addition of a reflector and is applicable to systems with other than hydrogenous moderators. Based on these results, the thermalness parameter p/(η₂ · f₂) provides an effective means of characterizing moderated systems relative to optimum conditions.