Chaos and Regularity in the Doubly Magic Nucleus ^{208}Pb

Area of Science:

• Nuclear Physics
• Quantum Chaos
• Statistical Mechanics

Background:

• High-resolution experiments have identified 151 nuclear levels in lead-208 up to 6.20 MeV excitation energy.
• Understanding nuclear level fluctuations is crucial for characterizing nuclear dynamics.

Purpose of the Study:

• To thoroughly study the fluctuation properties of nuclear bound states in lead-208.
• To compare experimental data with theoretical models, specifically random matrix theory (RMT).

Main Methods:

• Analysis of nearest-neighbor spacing, number variance, Dyson-Mehta Δ3 statistics, and ratio of consecutive spacings.
• Application of Bayesian inference to determine the chaoticity parameter (f).
• Comparison with Gaussian orthogonal ensemble (GOE) and Poisson statistics.

Main Results:

• Experimental data for nuclear level spectra are well described by the GOE, indicating chaotic behavior.
• The chaoticity parameter (f) for the experimental data is approximately 0.9, the closest agreement with GOE for bound states.
• Shell model calculations with realistic interactions also yield chaoticity parameters close to the experimental value.

Conclusions:

• The nuclear bound states in lead-208 exhibit a high degree of chaos, closely approaching predictions of the Gaussian orthogonal ensemble.
• This study provides significant evidence for chaotic dynamics in the energy spectra of nuclei.
• Realistic nuclear interactions in shell model calculations reproduce the observed chaoticity.