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

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

Covariance matrices for cross sections issued from optical model calculations

Our interest is particularly focused at the study of uncertainties propagation within nuclear models. In this paper, a comparison between the most convenient approaches for generating covariance matrices for evaluations based on nuclear modeling calculations is presented. The first method involves the conventional matrix error propagation approach based on sensitivity matrix calculation. In the second one, uncertainties associated to the model parameters are propagated with a Monte Carlo simulation. To perform a quantitative uncertainty analysis, probability distributions must be assigned to each of the varied parameters, Monte Carlo procedures are used to simulate alternative distributions of parameter values

Pseudo-measurement simulations and bootstrap for the experimental cross-section covariances estimation with quality quantification

The classical use of a generalized X2-distance to determine the evaluated cross section uncertainty requires the values of the experimental cross sections covariance matrix. The usual propagation error method to estimate the covariances is hardly usable and the lack of data prevents from using the direct empirical estimator. Thus we present an alternative which exploits a regression model of the experimental cross section to generate pseudo-measurements and thereby allows an estimation of experimental covariances. The problem of assessing the quality of the estimate still remains. In our approach, we propose to determine the estimation quality through the means of the bootstrap method. We show on numerical examples that the bootstrap allows to have an order of magnitude of the estimation quality through a matrix norm. All the results are illustrated with a toy model (where all quantities are known) and also with real cross-section data measurements

Kriging approach for the experimental cross-section covariances estimation

In the classical use of a generalized χ2 to determine the evaluated cross section uncertainty, we need the covariance matrix of the experimental cross sections. The usual propagation error method to estimate the covariances is hardly usable and the lack of data prevents from using the direct empirical estimator. We propose in this paper to apply the kriging method which allows to estimate the covariances via the distances between the points and with some assumptions on the covariance matrix structure. All the results are illustrated with the 2555Mn nucleus measurements

Coherent investigation of nuclear data at CEA DAM: Theoretical models, experiments and evaluated data

The domain of evaluated nuclear data involves at the same time, a close interaction between the field of nuclear applications and that of nuclear physics, and a close interaction between experiments and theory. The final product, the evaluated data file, synthesises vast amounts of information stemming from all of the above fields. In CEA DAM, all these aspects of nuclear data are investigated in a consistent way, making full use of experimental facilities and high-performance computing as well as numerous national and international collaborations, for the measurement, calculation, evaluation, and validation of nuclear data