Multilevel Analyses of the U235 Fission and Capture Cross Sections

The neutron capture and fission cross sections of $^{235}\mathrm{U}$ were analyzed up to 60 eV with the multilevel formalism of Reich and Moore. The statistical distribution of the $R$-matrix parameters obtained in this analysis has been investigated in detail. After corrections for the "missed levels," the observed statistical distributions of the parameters and level spacings agree well with the expected Porter-Thomas distributions and Wigner law, respectively. The average values of the resonance parameters do not agree for the same cross sections with the values obtained by other authors on the basis of the single-level formalism. The $R$-matrix parameters obtained in this analysis have been transformed into equivalent Kapur-Peierls parameters and compared with a set of Kapur-Peierls parameters obtained directly, from the same data, in a previous analysis. The comparison of the two sets of Kapur-Peierls parameters illustrates the nonuniqueness of the least-squares fit analysis of the same data with the Kapur-Peierls formalism. The set of resonance parameters obtained in this work has also been used to compute the fission cross section at liquid nitrogen temperature, for comparison with existing measurements, and to "mock up" the cross sections in the unresolved resonance region near 1 keV, where $S$-wave processes still dominate.