Neutron width statistics in a realistic resonance-reaction model

TL;DR

This study shows that when the correct energy dependence of neutron widths is used, the distribution aligns with the Porter-Thomas distribution, but near-threshold states can cause deviations if an incorrect dependence is assumed.

Contribution

It introduces a realistic resonance-reaction model that accounts for energy dependence and near-threshold states, explaining deviations from the Porter-Thomas distribution observed in experiments.

Findings

Proper energy dependence yields PTD agreement

Near-threshold states can cause broadening of distributions

Incorrect assumptions about energy dependence lead to deviations

Abstract

A recent experiment on s-wave neutron scattering from $^{192,194,196}$Pt found that the reduced neutron width distributions deviate significantly from the expected Porter-Thomas distribution (PTD), and several explanations have been proposed within the statistical model of compound nucleus reactions. Here, we study the statistics of reduced neutron widths in the reaction $n+ ^{194}$Pt within a model that combines the standard statistical model with a realistic treatment of the neutron channel. We find that, if the correct secular energy dependence of the average neutron widths is used, then the reduced neutron width distribution is in excellent agreement with the PTD for a reasonable range of the neutron-nucleus coupling strength and depth of the neutron channel potential. Within our parameter range, there can be a near-threshold bound or virtual state of the neutron channel potential that modifies the energy dependence of the average width from the $\sqrt{E}$ dependence, commonly assumed in experimental analysis, in agreement with the proposal of 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. We identify a relatively narrow range of parameters where this effect is significant.