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 (El amplitudes) between the 14 lower states wi th J(pi)=4(-) and 21st to 100th even states with J=4 in the Ce atom (1 120 lines). We show that the distribution of the matrix elements is cl ose to Gaussian, although the width of the Gaussian distribution, i.e. , the root-mean-square matrix element, changes with the excitation ene rgy. The corresponding line strengths an distributed according to the Porter-Thomas law which describes statistics of transition strengths b etween chaotic states in compound nuclei. We also show how to use a st atistical theory to calculate mean-squared values of the matrix elemen ts or transition amplitudes between chaotic many-body states. We draw some support for our conclusions from the analysis of the 228 experime ntal line strengths in Ce [J. Opt. Sec. Am. 8, 1545 (1991)], although direct comparison with the calculations is impeded by incompleteness o f the experimental data. Nevertheless, the statistics observed give ev idence that highly excited many-electron states in atoms are indeed ch aotic.