标题： 208Pb双幻核中的混沌与规律性 显示英文标题

标题： Chaos and regularity in the doubly magic nucleus 208Pb

摘要： 高分辨率实验最近已完全确定了铅-208中激发能\( E_x = 6.20 \)MeV以下的151个核能级（能量、自旋和宇称）。 我们对前所未有的核束缚态能谱中的涨落性质进行了详细研究。 首先，我们将具有相同自旋和宇称的状态分为14种子光谱，分析了短程和长程相关性的标准统计量，并计算了它们的总体平均值。 将其与一个随机矩阵系综进行比较，该系综在预期正则系统的泊松统计和混沌系统预测的高斯正交系综（GOE）之间插值，结果显示数据很好地符合GOE。 在第二种方法中，遵循Rosenzweig和Porter的想法，我们考虑了由独立子光谱组成的完整光谱。 我们使用贝叶斯推理方法分析了它们的涨落性质，这种方法涉及一个称为混沌参数\( f \)的定量度量，它也在泊松统计（\( f=0 \)）和GOE统计（\( f=1 \)）之间插值。 结果发现\( f\sim 0.9 \)。 这是迄今为止在原子核束缚态谱中观察到的与GOE最接近的一致性。 同样的分析也基于壳模型计算的不同相互作用（SDI、KB、M3Y）得到的谱上进行。 虽然简单的SDI表现出典型核多体系统规则动力学的特征，但其他更现实的相互作用产生的混沌参数\( f \)接近实验值。 显示英文摘要

摘要： 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.