Producing uncertainties and covariance matrix from intermediate data using a Monte-Carlo method

¹ Université de Strasbourg, CNRS, IPHC/DRS UMR 7178, 23 Rue du Loess, F-67037 Strasbourg, France
² CEA, DES, IRESNE, DER, SPRC, LEPh, F-13108 Saint-Paul-lez-Durance, France

^* e-mail: ghenning@iphc.cnrs.fr

Published online: 17 April 2024

Abstract

The necessary improvement of evaluated nuclear data for nuclear applications development is possible through new and high quality experimental measurements. In particular, improving (n, n’) cross section evaluations for fast neutrons is a goal of interest for new reactor fuel cycles, such as ²³²Th/²³³U or ²³⁸U/²³⁹Pu. Our group at CNRS-IPHC developed an experimental program to measure (n, n’γ) cross section using prompt γ-ray spectroscopy and neutron energy determination by time-of-flight with a focus on reaching the highest achievable level of accuracy. The collected partial cross sections can then be used to infer the total (n, n’) one and contribute to evaluation improvement. The extraction of the exclusive (n, n’γ) cross sections from the recorded data involves using many parameters and processing that may introduce uncertainties and correlations. In that case, the usual method for combining and computing uncertainties based on the perturbation theory can be long and complex. It also makes the calculation of covariance hard and the inclusion of some unusual forms of uncertainty even more difficult. To overcome this issue, we developed a process relying on random sampling methods that processes intermediate analysis data to compute cross sections, uncertainties and covariance. As a benchmark, we used this Monte Carlo method on ²³²Th, ²³³U and ²³⁸U data and reproduced the central values and uncertainties calculated using the analytical method, while also producing covariance matrices for (n, n’γ) cross sections. For particular cases, the random sampling method is able to produce uncertainties that better reflect the input data, compared to the analytical method.