STRUCTURE OF COMPOUND STATES IN THE CHAOTIC SPECTRUM OF THE CE ATOM -LOCALIZATION PROPERTIES, MATRIX-ELEMENTS, AND ENHANCEMENT OF WEAK PERTURBATIONS

The aim of the present paper is to analyze a realistic model of a quan tum chaotic system: the spectrum and the eigenstates of the rare-earth atom of Ce. Using the relativistic configuration-interaction method t he spectra and the wave functions of odd and even levels of Ce with J = 4 are calculated. It is shown that the structure of the excited stat es at excitation energies above 1 eV becomes similar to that of the co mpound states in heavy nuclei. The wave functions of the excited state s are chaotic superpositions of the simple basis states (with the numb er of ''principal'' components N approximately 100), built of the 4f, 6s, 5d, and 6p single-electron orbitals. The localization of the eigen states on the energy scale is characterized by the spread width GAMMA approximately ND, where D is the average level spacing (D approximatel y 0.03 eV). The emergence of chaos in the spectrum and the dependence of the N and GAMMA parameters on the excitation energy are studied. Th e shape of the localization is shown to be Lorenzian around the maximu m (principal components), whereas outside this region the squared comp onents display a faster decrease, in agreement with the perturbation t heory treatment of the band random matrix (BRM) model. The structure o f the real interaction matrix is compared with that assumed in the BRM models. A formula expressing the mean-squared values of matrix elemen ts between the eigenstates in terms of their parameters and single-par ticle occupancies is derived, and its applicability is checked with th e results of numerical calculations. The hypothesis of a Gaussian dist ribution of the eigenstates' components and matrix elements between th e eigenstates has been checked. The existence of the statistical (dyna mical) enhancement of weak perturbations in systems with dense spectra is demonstrated.