Evaluation of the covariance matrix of neutronic cross sections with the Backward-Forward Monte Carlo method

Abstract
With the advent of modern nuclear reaction modeling codes, it has become possible to produce evaluated data from model calculations only. However, the process of estimating of the uncertainties associated with nuclear data evaluated by model calculations is not as well defined as the assessment of uncertainties resulting from an experimental-data-driven evaluation process. In this paper, we propose a method, based on the Monte Carlo sampling of the model parameter space, that allows for a quantitative estimation the covariance matrix of the model parameters, as well as that of the derived cross sections. Constrains from experimental data are included by building a probability density function of the model parameter space as a function of the generalized χ² that estimates the calculation-data mismatch. The uncertainties of the model parameters are then propagated to the derived cross sections, whose distribution is analyzed in terms of a covariance matrix. As an example, this method is applied to the models used in the nuclear reaction code TALYS and a full covariance matrix for the evaluated cross sections of the n+⁸⁹Y system is obtained.