Effects of correlations in uncertainties of total cross section and elastic angular distribution for a deep-penetration of 14-MeV neutrons in Cu

ABSTRACTUncertainty in neutron reaction rates after penetrating a thick copper benchmark assembly was estimated based on two different kinds of Total Monte Carlo methods under random sampling methodology. 500 random nuclear data files were generated for 63Cu by Bayesian Monte-Carlo method by perturbing underlying nuclear model parameters. In the first method, these files were used directly to generate processed libraries preserving all the correlations among different physical quantities. In the second method, the random files generated in the first method were used but the angular distributions of elastic scattering were kept fixed to those of the non-perturbed nominal one. It was found that the two methods gave the same neutron reaction rate after 608 mm penetration of a copper. However, the uncertainty of the first method was smaller than that of the second method. It shows that the correlation between angular distribution of elastic scattering at 0 degrees and total cross section, which stems from Wick’s inequality, affects uncertainty of the calculated neutron reaction rate. It could be concluded that the uncertainty obtained by using the covariance files given in the ENDF-6 format may not give correct results for the uncertainty of neutron penetration calculations.KEYWORDS: Uncertainty of nuclear datacovariancecross-sections14MeV neutron63Cutotal Monte Carlo methodcorrelation of different physical quantitiesfusion neutronicsDisclaimerAs a service to authors and researchers we are providing this version of an accepted manuscript (AM). Copyediting, typesetting, and review of the resulting proofs will be undertaken on this manuscript before final publication of the Version of Record (VoR). During production and pre-press, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal relate to these versions also. Competing interestsThe authors declare that they have no competing interests.Figure 1. Calculation scheme of cross section and associated covariance (T6, upper part), and the Total Monte Carlo (TMC) method (lower part). TANES and TAFIS in T6 were not used in the present work.Display full sizeFigure 2. 63Cu neutron total cross sections estimated by T6 system (gray lines) compared with ENDF/B-VIII.0 (red line) and experimental data and the errors [Citation15–20].Display full sizeFigure 3. 63Cu neutron elastic cross sections estimated by T6 system (gray lines) compared with ENDF/B-VIII.0 (red line) and experimental data [Citation21–24].Display full sizeFigure 4. Computational geometry model of FNS copper benchmark experiment.Display full sizeFigure 5. Comparison of 90Zr(n,2n)89Zr reaction rate distribution and the standard deviation between T6 and the result ignoring perturbation of angular distribution.Display full sizeFigure 6. Comparison of 59Co(n,α)56Mn reaction rate distribution and the standard deviation between T6 and the result ignoring perturbation of angular distribution.Display full sizeFigure 7. Comparison of 56Fe(n,p)56Mn reaction rate distribution and the standard deviation between T6 and the result ignoring perturbation of angular distribution.Display full sizeFigure 8. Comparison of 64Zn(n,p)64Cu reaction rate distribution and the standard deviation between T6 and the result ignoring perturbation of angular distribution.Display full sizeFigure 9. Comparison of 115In(n,n’)115mIn reaction rate distribution and the standard deviation between T6 and the result ignoring perturbation of angular distribution.Display full sizeFigure 10. Comparison of 55Mn(n,γ)56Mn reaction rate distribution and the standard deviation between T6 and the result ignoring perturbation of angular distribution.Display full sizeFigure 11. Comparison of 63Cu(n,γ)64Cu reaction rate distribution and the standard deviation between T6 and the result ignoring perturbation of angular distribution.Display full sizeFigure 12. Correlation between 63Cu total cross section and elastic scattering cross section at 0 degrees of 1,000 random files generated by T6. Incident neutron energy is 14 MeV.Display full sizeFigure 13. Correlation between 63Cu total cross section and elastic scattering cross section at 0 degrees of 1,000 random files generated by T6. Incident neutron energy is 2.2 MeV.Display full sizeFigure 14. Correlation between 63Cu total cross section and elastic scattering cross section at 0 degrees of 1,000 random files generated by T6. Incident neutron energy is 1.0 MeV.Display full sizeFigure 15. Correlation between 63Cu total cross section and elastic scattering cross section at 0 degrees of 1,000 random files generated by T6. Incident neutron energy is 0.2 MeV.Display full size