Statistics of electromagnetic transitions as a signature of chaos in many-electron atoms

Using a configuration-interaction approach, we study statistics of the dipole matrix elements (E1 amplitudes between the 14 lower states with J^π=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. 8, 1545 (1991)], although direct comparison with the calculations is impeded by incompleteness of the experimental data. Nevertheless, the statistics observed give evidence that highly excited many-electron states in atoms are indeed chaotic.