A Case Study with ${{}^{241}}Am(n, 2n)$ EXFOR data Using Weighted Least Square Method

This case study with ${{}^{241}}Am (n, 2n)$ examines the assumption of the Correlation Coefficient of 0.5 in the Web tool of constructing Covariance matrix of the IAEA-EXFOR web retrieval system. The ( $n, 2n$ ) cross section data of ${{}^{241}}Am$ are retrieved from the IAEA-EXFOR (International Atomic Energy Agency - Experimental Nuclear Reaction Data) database. Of all the available datasets, the experimental data of Sage et.al. gives the experimentally derived correlation coefficients. In this work, we therefore performed regression analysis on the entire data keeping the Sage's correlation data intact, and varying the correlation in all other experimenters' data where correlations are not specified. The Web tool for constructing covariance matrix from EXFOR uncertainties in the IAEA-EXFOR Web retrieval system assumes a correlation coefficient of 0.5 in the absence of experimental correlation coefficients. We examine the assumption by varying the correlation coefficient from uncorrelated to fully correlated. The weighted least square technique is used to estimate the regression parameters which takes into account the correlation between the data at various energies. The changes in the cross section data include the effect of correlations on the fitted cross section values. We agree with the prescription in the IAEA-EXFOR Web tool system that whenever the experimental correlations are not available, and information is lacking, a correlation coefficient of 0.5 may be assumed and used to calculate covariance matrix.