Chaos and localization in the wave functions of complex atoms Nd I, Pm I, and Sm I

Wave functions of complex lanthanide atoms Nd I, Pm I, and Sm I, obtained via multiconfiguration Dirac-Fock method, are analyzed for density of states in terms of partial densities, strength functions [F_k(E)], number of principal components [ξ₂(E)], and occupancies (⟨n_α⟩^E) of single-particle orbits using embedded Gaussian orthogonal ensemble of one plus two-body random matrix ensembles [EGOE(1+2)]. It is seen that density of states are in general multi-modal, F_k(E)’s exhibit variations as function of the basis states energy and ξ₂(E)’s show structures arising from localized states. The sources of these departures from EGOE(1+2) are investigated by examining the partial densities, correlations between F_k(E), ξ₂(E), and ⟨n_α⟩^E and also by studying the structure of the Hamiltonian matrices. These studies point out the operation of EGOE(1+2) but at the same time suggest that weak admixing between well separated configurations should be incorporated into EGOE(1+2) for more quantitative description of chaos and localization in Nd I, Pm I, and Sm I.