Developing diagnostic tools for low-burnup reactor samples

We test common fluence diagnostics in the regime of very low burnup natural uranium reactor samples. The fluence diagnostics considered are the uranium isotopics ratios $^{235}$U/$^{238}$U and $^{236}$U/$^{235}$U, for which we find simple analytic formulas agree well with full reactor simulation predictions. Both ratios agree reasonably well with one another for fluences in the mid $10^{19}\,\mathrm{n/cm^2}$ range. However, below about $10^{19}\,\mathrm{n/cm^2}$ the concentrations of $^{236}$U are found to be sufficiently low that the measured $^{236}$U/$^{235}$U ratios become unreliable. We also derive and test diagnostics for determining sample cooling times in situations where very low burnup and very long cooling times render many standard diagnostics, such as the $^{241}$Am/$^{241}$Pu ratio, impractical. We find that using several fragment ratios are necessary to detect the presence of systematic errors, such as fractionation.