V. R. Manfredi

Quantum chaos in A = 46–50 atomic nuclei

Abstract 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.

Statistical theory versus shell model in a large pf configuration space

Spectral distribution method and exact shell-model predictions for the strength sums of different transition operators are compared in detail for the J=0, T−Tz=0 states of 46V and 50Sc using the full pf shell. Good agreement of both models is observed in the high level density region of the energy spectrum, where chaotic motion is dominant, and larger discrepancies are observed in the ground state region, where nuclear motion is more regular. The agreement in the chaotic region becomes especially good in the 5986 dimensional space of 50Sc, illustrating the quality of the statistical theory in large configuration spaces.

From regular to chaotic states in atomic nuclei

An interesting aspect of nuclear dynamics is the co--existence, in atomic nuclei, of regular and chaotic states. In the first part of the present work, we review the state of the art of nuclear dynamics and use a schematic shell model to show how a very simple and schematic nucleon--nucleon interaction can produce an order

Short orbit distribution in the semiclassical limit of the SU(3) nuclear model

to

Spectral distribution studies with a modified Kuo-Brown interaction in the upper half of thefpshell

chaos transition. The second part is devoted to a discussion of the wave function behaviour and decay of chaotic states using some simple models (to be published in Rivista Nuovo Cimento).

QUANTAL OVERLAPPING RESONANCE CRITERION: THE PULLEN–EDMONDS MODEL

Three different families of short periodic orbits in the semiclassical SU(3) nuclear model were studied and their stability calculated. Then, knowing the shortest periodTmin of the closed trajectories, the long-range behaviour of theΔ3 statistic was determined.

ORDER AND CHAOS IN ROTO-VIBRATIONAL STATES OF ATOMIC NUCLEI

The spectral distribution method with modified Kuo-Brown interaction is extended to the study of the upper half as well as to odd-A nuclei, of the fp shell. The calculations show similar success to that obtained for the lower half.

A Note on the Toda Criterion for Interacting Dipole–Quadrupole Vibrations

In order to highlight the onset of chaos in the Pullen–Edmonds model a quantal analog of the resonance overlap criterion has been examined. A quite good agreement between analytical and numerical results is obtained.

ANOMALOUS SPECTRAL STATISTICS OF THE ASYMMETRIC ROTOR MODEL

Using a classical analytical criterion (that of curvature) and numerical results (Poincare sections and spectral statistics), a transition order-chaos-order in the roto-vibrational model of atomic nuclei has been shown. Numerical calculations were performed for some deformed nuclei.

Wave function behaviours of the three-level Lipkin, Meshkov, Glick model

The Toda criterion of the Gaussian curvature is applied to calculate analytically the transition energy from regular to chaotic motion in a schematic model describing the interaction between collective dipole and quadrupole modes in atomic nuclei.