Eigenvalue sensitivity and uncertainty analysis based on classical perturbation theory

The uncertainty of nuclear data is being paid to more and more attention because it is one of the most important uncertainty sources in lattice calculation. The expressions of sensitivity and uncertainty of k_eff with respect to the cross sections were deduced based on the classical perturbation theory. A covariance library was made based on ENDF/B-VII.1, and the individual covariance matrices of cross section were combined according to the cross section model for lattice calculation in this work. A code COLEUS (calculation tool for evaluating uncertainty and sensitivity) was developed for the sensitivity and uncertainty analysis, and a traditional PWR fuel pin cell problem was calculated and analyzed. Numerical results indicate that k_eff of lattice calculation is the most sensitive to the perturbation of the average number of neutrons released per fission of ²³⁵U, while the capture cross section of ²³⁸U has the biggest contribution to the final uncertainty. The measuring accuracy of present nuclear data will bring an uncertainty about 0.4%-0.5% for k_eff.