Chaos and regularity in the doubly magic nucleus 208Pb

TL;DR

This study analyzes the spectral fluctuations of 208Pb nuclear states, finding that their energy levels exhibit chaotic behavior consistent with GOE statistics, especially when using realistic shell model interactions.

Contribution

It provides the first detailed statistical analysis of the complete set of bound states in 208Pb, demonstrating a high degree of chaos in nuclear spectra.

Findings

Spectral fluctuations match GOE predictions for chaotic systems.

Realistic shell model interactions produce spectra with chaoticity close to experimental data.

The chaoticity parameter f is approximately 0.9, indicating near-complete chaos.

Abstract

High resolution experiments have recently lead to a complete identification (energy, spin, and parity) of 151 nuclear levels up to an excitation Energy of Ex= 6.20 MeV in 208Pb. We present a thorough study of the fluctuation properties in the energy spectra of the unprecedented set of nuclear bound states. In a first approach we grouped states with the same spin and parity into 14 subspectra, analyzed standard statistical measures for short- and long-range correlations and then computed their ensemble average. Their comparison with a random matrix ensemble which interpolates between Poisson statistics expected for regular systems and the Gaussian Orthogonal Ensemble (GOE) predicted for chaotic systems shows that the data are well described by the GOE. In a second approach, following an idea of Rosenzweig and Porter we considered the complete spectrum composed of the independent subspectra. We analyzed their fluctuation properties using the method of Bayesian inference involving a quantitative measure, called the chaoticity parameter f, which also interpolates between Poisson (f=0) and GOE statistics (f=1). It turns out to be f~0.9. This is so far the closest agreement with GOE observed in spectra of bound states in a nucleus. The same analysis has also been performed with spectra computed on the basis of shell model calculations with different interactions (SDI, KB, M3Y). While the simple SDI exhibits features typical for nuclear many-body systems with regular dynamics, the other, more realistic interactions yield chaoticity parameters f close to the experimental values.