Sensitivity Analysis of Nuclide Importance to One-Group Neutron Cross Sections

The importance of nuclides is useful when investigating nuclide characteristics in a given neutron spectrum. However, it is derived using one-group microscopic cross sections, which may contain large errors or uncertainties. The sensitivity coefficient shows the effect of these errors or uncertainties on the importance. The equations for calculating sensitivity coefficients of importance to one-group nuclear constants are derived using the perturbation method. Numerical values are also evaluated for some important cases for fast and thermal reactor systems. Many characteristics of the sensitivity coefficients are derived from the derived equations and numerical results. The matrix of sensitivity coefficients seems diagonally dominant. However, it is not always satisfied in a detailed structure. The detailed structure of the matrix and the characteristics of coefficients are given. By using the obtained sensitivity coefficients, some demonstration calculations have been performed. The effects of error and uncertainty of nuclear data and of the change of one-group cross-section input caused by fuel design changes through the neutron spectrum are investigated. These calculations show that the sensitivity coefficient is useful when evaluating error or uncertainty of nuclide importance caused by the cross-section data error or uncertainty and when checking effectiveness of fuel cell or core design change for improving neutron economy.