First clear evidence of quantum chaos in the bound states of an atomic nucleus

TL;DR

This study provides the first experimental evidence of quantum chaos in the bound states of an atomic nucleus, specifically in $^{208}$Pb, by analyzing spectral fluctuations and comparing them to Random Matrix Theory predictions.

Contribution

It presents the first clear experimental evidence of quantum chaos in nuclear bound states, using spectral analysis and RMT comparison for $^{208}$Pb.

Findings

Natural parity states closely follow RMT predictions with a Brody parameter of 0.85

Unnatural parity states deviate significantly from RMT behavior

Chaotic and regular states coexist within the same energy spectrum

Abstract

We study the spectral fluctuations of the $^{208}$Pb nucleus using the complete experimental spectrum of 151 states up to excitation energies of $6.20$ MeV recently identified at the Maier-Leibnitz-Laboratorium at Garching, Germany. For natural parity states the results are very close to the predictions of Random Matrix Theory (RMT) for the nearest-neighbor spacing distribution. A quantitative estimate of the agreement is given by the Brody parameter $\omega$, which takes the value $\omega=0$ for regular systems and $\omega \simeq 1$ for chaotic systems. We obtain $\omega=0.85 \pm 0.02$ which is, to our knowledge, the closest value to chaos ever observed in experimental bound states of nuclei. By contrast, the results for unnatural parity states are far from RMT behavior. We interpret these results as a consequence of the strength of the residual interaction in $^{208}$Pb, which, according to experimental data, is much stronger for natural than for unnatural parity states. In addition our results show that chaotic and non-chaotic nuclear states coexist in the same energy region of the spectrum.