The Influence of Crystalline Binding on Resonant Absorption and Reaction Rates

At this time, experimental transmission data are analyzed with codes like REFIT or SAMMY, which use the free gas model to fit the form of the resonances. The use of the resonance parameters issued from such analysis for further reconstruction of the cross section with codes like NJOY can result in nonnegligible errors in the cross sections as well as in the reaction rates.

To analyze the bias introduced on resonance parameters by the use of the free gas model and its consequences on reaction rates, we set up a numerical experiment that closely follows the actual scheme of the nuclear data evaluation.

First, we use resonance parameters from the JEF2.2 nuclear library to calculate our reference cross section with Lamb's harmonic crystal model. This cross section is then used to simulate transmission coefficients, and a new set of resonance parameters is obtained using the code REFIT to fit the shape of the transmission with the help of the free gas model. These resonance parameters are used to estimate the errors in the reaction rates.

We conclude that the free gas model does not ensure reaction rate conservation. A comparison of the capture rates showed that the discrepancy between this model (with the bias on the resonance parameters described here) and the harmonic crystal model (with initial JEF2.2 parameters) is important for reactor physics. For the first resonance of ²³⁸U, which represents 30% of the total ²³⁸U absorption in a thermal nuclear reactor, the error in the capture reaction rates reaches 3% for the biased resonance parameters issued from UO₂ analysis, and up to 1% for the biased resonance parameters issued from metallic uranium analysis. Such a discrepancy could be corrected using a crystal model for the experimental data analysis.