Neutron width statistics using a realistic description of the neutron channel

Abstract: A basic prediction of the statistical model of compound nucleus reactions is that the partial widths for decay into any open channel channel fluctuate according to the Porter-Thomas distribution (PTD). A recent experiment on $s$- and $p$-wave neutron scattering from platinum isotopes found that the experimental $s$-wave partial neutron width distributions deviated substantially from the PTD. Several explanations for this finding have been proposed within the statistical model, but none has resolved this issue. Here, we review the application of a realistic resonance-reaction model to $s$-wave neutron scattering from $^{194}$Pt. Our main conclusion is that the PTD provides an excellent description of the partial neutron width distribution, provided that the secular energy dependence of the average neutron width is correctly described. Within a realistic range of model parameters, there can be a near-threshold bound or virtual state of the neutron channel that changes this secular dependence from the usual $\sqrt{E}$ dependence, as proposed by Weidenm\"uller [1]. In this case, the use of the $\sqrt{E}$ dependence to analyze the data will lead to apparent deviations from the PTD. We discuss the limited parameter range where such a near threshold state can have a significant effect.