Exit-Channel Suppression in Statistical Reaction Theory

Statistical reaction theories such as the Hauser-Feshbach theory assume that branching ratios follow Bohr’s compound nucleus hypothesis by factorizing into independent probabilities for different channels. Corrections to the factorization hypothesis are known in both nuclear theory and quantum transport theory, particularly an enhanced memory of the entrance channel. We apply the Gaussian orthogonal ensemble to study a complementary suppression of exit channel branching ratios. The combined effect of the width fluctuation and the limitation on the transmission coefficient can provide a lower bound on the number of exit channels. The bound is demonstrated for the branching ratio in neutron-induced reactions on a ${}^{235}\mathrm{U}$ target.

Figure 1

Cross section ratio ${\alpha }^{-1}=⟨{\sigma }_F⟩/⟨{\sigma }_{\text{cap}}⟩$ as a function of average fission width ${\mathrm{\Gamma }}_F^K$ assuming a single fission channel. Solid line: Eqs. (1)–(3). Dotted line: Hauser-Feshbach approximation, i.e., ${\alpha }^{-1}={\mathrm{\Gamma }}_F^K/{\mathrm{\Gamma }}_{\text{cap}}^K$. Dashed line: Hauser-Feshbach including the WFC correction, Eq. (8). Blue band: experimental range, taking uncertainty from Table 1. Widths are the statistical errors associated with the 1-keV cross section averaging interval.