Reduced neutron widths in the nuclear data ensemble: Experiment and theory do not agree

Abstract

I have analyzed reduced neutron widths (${\ensuremath{\Gamma}}_{n}^{0}$) for the subset of 1245 resonances in the nuclear data ensemble (NDE) for which they have been reported. Random matrix theory (RMT) predicts for the Gaussian orthogonal ensemble that these widths should follow a ${\ensuremath{\chi}}^{2}$ distribution having one degree of freedom ($\ensuremath{\nu}=1$)---the Porter Thomas distribution (PTD). Careful analysis of the ${\ensuremath{\Gamma}}_{n}^{0}$ values in the NDE rejects the validity of the PTD with a statistical significance of at least 99.97% ($\ensuremath{\nu}=0.801\ifmmode\pm\else\textpm\fi{}0.052$). This striking disagreement with the RMT prediction is most likely due to the inclusion of significant $p$-wave contamination to the supposedly pure $s$-wave NDE. When an energy-dependent threshold is used to remove the $p$-wave contamination, the PTD is still rejected with a statistical significance of at least 98.17% ($\ensuremath{\nu}=1.217\ifmmode\pm\else\textpm\fi{}0.092$). Furthermore, examination of the primary references for the NDE reveals that many resonances in most of the individual data sets were selected using methods derived from RMT. Therefore, using the full NDE data set to test RMT predictions seems highly questionable. These results cast very serious doubt on claims that the NDE represents a striking confirmation of RMT.