This paper considers the problem of accurately representing the temperature dependence of neutron cross-section data in neutron transport problems when there are many nuclides and when the temperature distributions vary significantly with both space and time. An approach involving interpolation between nuclear data libraries at various reference temperatures is investigated. Reference nuclear data libraries are obtained by Doppler broadening cross sections to the desired temperatures using the NJOY code system. Several interpolation schemes over various temperature intervals are studied. Interpolated values at intermediate temperatures are compared to NJOY Doppler-broadened results for the same temperature. Differences relative to the Doppler-broadened results are calculated in order to judge the suitability of the interpolation scheme and temperature interval. The total, elastic scattering, capture, and fission (if applicable) reactions for 238U, 235U, natural Zr, 16O, 10B, and 1H are considered in this study, over a temperature range of 294 to 811 K (~70 to ~1000°F). The nuclides and temperature range are selected to best represent typical light water reactor calculations.
This work covers only the free-atom cross section and does not explore the many nuances of temperature treatment of nuclear data in the thermal energy range for nuclides where molecular binding effects are significant, e.g., water, beryllium, and graphite. Additionally, dilute-average cross sections are used in the unresolved resonance range (URR) for this study. Temperature treatment of probabilistic methods used to construct cross sections in the URR are not considered for this work.
The study shows that cross sections can be interpolated within an accuracy of 0.1% over a temperature interval of 111 K (200°F) for 1H, 10B, and 16O. Smaller intervals are required for nuclides with more complex resonance behavior. Some values of the interpolated cross sections for natural Zr, 238U, and 235U remain greater than the target 0.1% relative difference even with a 28 K (50°F) interval, suggesting that a smaller interval is necessary for these nuclides.