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.Comment: 16 pages, REVTEX, 4 PostScript figures (submitted to Phys Rev A
