Pathological Behavior in the Spectral Statistics of the Asymmetric Rotor Model

The aim of this work is to study the spectral statistics of the asymmetric rotor model (triaxial rigid rotator). The asymmetric top is classically integrable and, according to the Berry-Tabor theory, its spectral statistics should be Poissonian. Surprisingly, our numerical results show that the nearest neighbor spacing distribution $P(s)$ and the spectral rigidity $\Delta_3(L)$ do not follow Poisson statistics. In particular, $P(s)$ shows a sharp peak at $s=1$ while $\Delta_3(L)$ for small values of $L$ follows the Poissonian predictions and asymptotically it shows large fluctuations around its mean value. Finally, we analyze the information entropy, which shows a dissolution of quantum numbers by breaking the axial symmetry of the rigid rotator.Comment: 11 pages, 7 figures, to be published in Phys. Rev.

Quantum Chaos in A=46--50 Atomic Nuclei

The spectral statistics of low--lying states of several $fp$ shell nuclei are studied with realistic shell--model calculations. For Ca isotopes, we find significant deviations from the predictions of the random--matrix theory which suggest that some spherical nuclei are not as chaotic in nature as the conventional view assumes.Comment: 12 pages, LaTex, 2 figures available upon request, to be published in Physics Letters

ÉTATS A GRAND NOMBRE DE QUASI-PARTICULE DANS LES ISOTOPES PAIRS DE PLOMB

Une étude par distribution spectrale dans les sous-espaces définis par leur nombre de quasi-particules a été effectuée dans les isotopes pairs de plomb. La comparaison avec des résultats obtenus dans les isotopes d'étain montre que le recouvrement entre les différents sous-espaces est fortement lié à l'interaction résiduelle utilisée. En particulier des états à grand nombre de quasi-particules sont présents à basse énergie. Le problème des états spurieux inhérent à cette méthode, qui sont responsables d'une surestimation du couplage, est abordé et différentes corrections sont proposées aussi bien sur les dimensions, les centroïdes et les largeurs des sous-espaces.The even lead isotopes have been studied by means of a spectral distribution calculation in the sub-spaces defined by their number of quasi-particles. The comparison with results obtained in the tin isotopes shows that the overlap of the various sub-spaces is strongly dependant on the residual interaction used ; namely, states with a great number of quasi-particles do exist in the low energy part of the spectra. The problem of spurious states implied by this method, responsible for an over-estimation of the sub-space coupling, is treated and various corrections are proposed for the dimensions as well as for the centroids and widths of the sub-spaces