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 quantum chaotic system: the spectrum and the eigenstates of the rare-earth atom of Ce. Using the relativistic configuration-interaction method the 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 states at excitation energies above 1 eV becomes similar to that of the compound states in heavy nuclei. The wave functions of the excited states are chaotic superpositions of the simple basis states (with the number of ‘‘principal’’ components N∼100), built of the 4f, 6s, 5d, and 6p single-electron orbitals. The localization of the eigenstates on the energy scale is characterized by the spread width Γ∼ND, where D is the average level spacing (D∼0.03 eV). The emergence of chaos in the spectrum and the dependence of the N and Γ parameters on the excitation energy are studied. The shape of the localization is shown to be Lorenzian around the maximum (principal components), whereas outside this region the squared components display a faster decrease, in agreement with the perturbation theory treatment of the band random matrix (BRM) model. The structure of the real interaction matrix is compared with that assumed in the BRM models. A formula expressing the mean-squared values of matrix elements between the eigenstates in terms of their parameters and single-particle occupancies is derived, and its applicabilility is checked with the results of numerical calculations. The hypothesis of a Gaussian distribution of the eigenstates’ components and matrix elements between the eigenstates has been checked. The existence of the statistical (dynamical) enhancement of weak perturbations in systems with dense spectra is demonstrated.