Neutron resonance data exclude random matrix theory

Abstract

Key words Porter-Thomas distribution, random matrix theory.Almost since the time it was formulated, the overwhelming consensus has been that random matrix theory (RMT) is in excellent agreement with neutron resonance data. However, over the past few years, we have obtained new neutron-width data at Oak Ridge and Los Alamos National Laboratories that are in stark disagreement with this theory. We also have reanalyzed neutron widths in the most famous data set, the nuclear data ensemble (NDE), and found that it is seriously flawed, and, when analyzed carefully, excludes RMT with high confidence. More recently, we carefully examined energy spacings for these same resonances in the NDE using the ∆3 statistic. We conclude that the data can be found to either confirm or refute the theory depending on which nuclides and whether known or suspected p-wave resonances are included in the analysis, in essence confirming results of our neutron-width analysis of the NDE. We also have examined radiation widths resulting from our Oak Ridge and Los Alamos measurements, and find that in some cases they do not agree with RMT. Although these disagreements presently are not understood, they could have broad impact on basic and applied nuclear physics, from nuclear astrophysics to nuclear criticality safety.

Open problems in applying random-matrix theory to nuclear reactions

“…[14] and Ref. [7] show full agreement with GOE predictions. The higher-order correlations tested in Refs.…”

“…Given these facts we are left with the disagreement with GOE predictions found in Ref. [7] for the ∆ 3 statistic and for sequence lengths L > 20. Here several questions come to mind.…”

“…[7] suggest rejection of the GOE hypothesis. In its entirety, however, work on the level-spacing distribution suggests a different conclusion.…”

“…[6] shows that the number of sequences with L > 20 decreases strongly with increasing L. Estimates of the statistical uncertainty of the ∆ 3 statistic in Ref. [7] do not seem to reflect that fact. (ii) It is known that with increasing distance from neutron threshold, an increasing number of narrow resonances is missed experimentally.…”

Power-law random banded matrices and ultrametric matrices: Eigenvector distribution in the intermediate regime

“…Recently it was argued [19] that in certain models there may exist within the delocalised phase a new non-ergodic phase characterised by non-trivial fractal dimensions. The interval (8) is the only place where such non-ergodic states are possible for PLBM and UMM.…”