作为多电子原子混沌特征的电磁跃迁统计
Statistics of electromagnetic transitions as a signature of chaos in many-electron atoms
摘要：
利用组态相互作用方法研究了Ce原子1120条谱线的偶极矩阵元（E1振幅）在J=4的14个低奇态和J=4的21 ~ 100个偶态之间的统计特性.我们表明，矩阵元的分布接近高斯分布，尽管高斯分布的宽度（即均方根矩阵元）随着激发能而变化。相应的谱线强度分布符合描述复合核混沌态之间跃迁强度统计的波特-托马斯定律。我们还展示了如何使用统计理论来计算矩阵元素的均方值或混沌多体状态之间的跃迁振幅。我们从Ce [J. Opt. Soc. Am. v.8，p.1545（1991）]，尽管与计算的直接比较由于实验数据的不完整性而受到阻碍。然而，统计学观察到的证据表明，原子中高度激发的多电子态确实是混沌的。
英文摘要：
Using a configuration interaction approach we study statistics of the dipole matrix elements (E1 amplitudes) between the 14 lower odd states with J=4 and 21st to 100th even states with J=4 in the Ce atom (1120 lines). We show that the distribution of the matrix elements is close to Gaussian, although the width of the Gaussian distribution, i.e. the root-mean-square matrix element, changes with the excitation energy. The corresponding line strengths are distributed according to the Porter-Thomas law which describes statistics of transition strengths between chaotic states in compound nuclei. We also show how to use a statistical theory to calculate mean squared values of the matrix elements or transition amplitudes between chaotic many-body states. We draw some support for our conclusions from the analysis of the 228 experimental line strengths in Ce [J. Opt. Soc. Am. v. 8, p. 1545 (1991)], although direct comparison with the calculations is impeded by incompleteness of the experimental data. Nevertheless, the statistics observed evidence that highly excited many-electron states in atoms are indeed chaotic.
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