Statistical Behavior of Atomic Energy Levels: Agreement with Random-Matrix Theory

The statistical behavior of complex atomic spectra of neutral and ionized rare-earth atoms has been examined. The authors found eight sets of atomic spectra of sufficient quality and statistics to compare with the predictions of random-matrix theory. Good agreement between theory and experiment was found for the covariance of adjacent spacings, Cov (S₈, S₈+₁), and the ₃ statistic.