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

摘要: High-resolution experiments have recently lead to a complete identification (energy, spin, and parity) of 151 nuclear levels up an excitation energy ${E}_{x}=6.20\text{ }\text{ }\mathrm{MeV}$ in $^{208}\mathrm{Pb}$ [Heusler et al., Phys. Rev. C 93, 054321 (2016)]. We present thorough study the fluctuation properties spectra unprecedented set bound states. In first approach, we group states with same spin parity into 14 subspectra, analyze standard statistical measures for short- long-range correlations, i.e., nearest-neighbor spacing distribution, number variance ${\mathrm{\ensuremath{\Sigma}}}^{2}$, Dyson-Mehta ${\mathrm{\ensuremath{\Delta}}}_{3}$ statistics, novel distribution ratios consecutive spacings adjacent each sequence, then compute their ensemble average. Their comparison random matrix which interpolates between Poisson statistics expected regular systems Gaussian orthogonal (GOE) predicted chaotic shows that data are well described by GOE. second following idea Rosenzweig Porter [Phys. 120, 1698 (1960)], consider spectrum composed independent subspectra. using method Bayesian inference involving quantitative measure, called chaoticity parameter $f$, also ($f=0$) GOE ($f=1$). It turns out be $f\ensuremath{\approx}0.9$. This is so far closest agreement observed nucleus. The analysis performed computed on basis shell model calculations different interactions (surface-delta interaction, Kuo-Brown, Michigan-three-Yukawa). While simple surface-delta interaction exhibits features typical many-body dynamics, other, more realistic yield parameters $f$ close experimental values.