Neutron width statistics in a realistic resonance-reaction model

Recent experiments on $s$-wave neutron scattering from $^{192,194,196}$Pt found that the reduced neutron width distributions deviated significantly from the expected Porter-Thomas distribution (PTD). Several explanations have been proposed for this PTD violation within the statistical model of compound nucleus reactions. Here, we study the statistics of the reduced neutron widths in the reaction $n+ ^{194}$Pt within a model that combines the standard statistical model of the compound nucleus with a realistic treatment of the neutron channel. We find that the reduced width distribution is well described by the PTD for a reasonable range of the neutron-nucleus coupling strength and depth of the neutron channel potential. We also find that the energy dependence of the average width in the presence of a near-threshold bound or virtual state of the neutron channel potential differs from the $\sqrt{E}$ dependence, commonly assumed in experimental analysis, and is in excellent agreement with the analytic form proposed by H. A. Weidenm\"uller [1]. In these cases, the reduced neutron width distributions extracted using the $\sqrt{E}$ dependence are significantly broader than the PTD.