Resonance Theory of Neutron Cross Sections of Fissionable Nuclei

The general Wigner-Eisenbud resonance theory is used to develop a method of analysis for the neutron cross sections of fissionable nuclei. The method is employed in giving a reasonable description of the low-energy cross sections in ${\mathrm{U}}^{235}$. The single-level fit for ${\mathrm{U}}^{235}$ is known to be unreasonable. Many-level expressions for the cross sections are derived—the only approximation to the general theory being the neglect of all but a small group of resonances. No explicit reference to fission channels is needed and the many-level expressions require few level parameters: the $E_{\lambda }$, ${\Gamma }_{\lambda n}$, ${\Gamma }_{\lambda \gamma }$, and ${\Gamma }_{\lambda f}$ of the single-level theory for each resonance and a few additional parameters pertinent to the interference between levels. The interference terms are described and shown to be important. Their average value yields information about the number of channels involved in fission. The shape and size of the ${\mathrm{U}}^{235}$ cross sections below 2 ev are fitted to within one or two percent using: (a) only one negative energy resonance of smaller size than in the single-level fit; (b) no additional levels to fit the shape other than the observed levels at positive energies; (c) three interference parameters whose size suggests that there are several fission channels in ${\mathrm{U}}^{235}$.