Normalization of ToF (n,f) Measurements in Fissile Targets: Microscopic cross-section integrals

Abstract

Precise normalization of ToF yield measurements of neutron induced fission in fissile targets is challenging, but the appropriate normalization is also of critical importance for nuclear energy and criticality safety, among other applications. A typical normalization relies on the Thermal Neutron Constants (TNC) recommended at the thermal point (fission ${\sigma }_f^0$ and capture ${\sigma }_{\gamma }^0$ thermal cross sections) by the Neutron Standards. However, many ToF experiments do not collect data down to the thermal energy and use normalization cross-section integrals defined at different arbitrary energy intervals. Normalization fission cross-section integrals $I_3$ are recommended in between-valleys energy regions 8.1–14.7 eV, 7.8–11 eV, 9–20 eV, and 11.7–19.5 eV for fissile targets ²³³U, ²³⁵U, ²³⁹Pu, and ²⁴¹Pu with values equal to 689.0(10.8), 245.7(4.1), 1059(6), and 1378(33) $b\cdot eV$, respectively. The ₂₃₅U normalization integral $I_3$ derived in this work of 245.7(4.1) $b\cdot eV$ is in good agreement within quoted uncertainties with the Neutron Standards value of 247.5(3.0) $b\cdot eV$.

Additional cross-section integrals $I_1$ in the thermal region from 20–60 meV are derived to fix both the normalization and the slope of the fission cross section at the thermal point providing additional constraints for R-matrix evaluations of experimental fission yields. Ratios ${\sigma }_f^0/I_1$ and $I_3/I_1$ feature very low uncertainty due to the strong positive correlations between the numerator and the denominator and are comprehensively derived for the first time. Integral ratios $I_3/I_1$ of 39.31(54), 13.08(20), 41.65(22), and 40.46(85) are recommended as reference for fissile targets ²³³U, ²³⁵U, ²³⁹Pu, and ²⁴¹Pu, respectively. Similarly, ratios ${\sigma }_f^0/I_1$ of 30.40(18), 31.22(12), 29.58(7), and 29.95(35) are also recommended as reference for corresponding fissile targets. These recommended ratios can be used by experimentalists to normalize their measured thin-target fission yield data, but also by evaluators to constrain their R-matrix analysis that use multiple sets of measured data renormalized as recommended in this work.

An evaluation of thermal (n,f) cross sections ${\sigma }_f^0$ presented in this work for all fissile targets is in excellent agreement with the Thermal Neutron Constants defined in the Neutron Standards within one-sigma uncertainty. Such agreement guarantees the reliability of our new evaluation of reference integrals based on the whole database of consistent experimental TOF data.