Level Statistics of Near-Yrast States in Rapidly Rotating Nuclei

Abstract

The nearest neighbour level spacing distribution and the ${\Delta }_3$ statistics of level fluctuations associated with very high spin states ($I \gesim 30$) in rare-earth deformed nuclei are analysed by means of a cranked shell model. The many particle-many hole configurations created in the rotating Nilsson potential are mixed by the surface-delta two-body residual interaction. The levels in the near-yrast region show a Poisson-like level spacing distribution. As the intrinsic excitation energy $U$ increases, the level statistics shows a gradual transition from order to chaos, reaching at $U \gesim 2$ MeV the Wigner distribution typical of the Gaussian orthogonal ensemble of random matrices. This transition is caused by the residual two-body interaction. On the other hand, the level spacings between the yrast and the first excited state show a peculiar behaviour, displaying a Wigner-like distribution instead of the Poisson-like distribution seen for the other near-yrast rotational states. The lowest spacings reflect the properties of the single-particle orbits in the mean-field, and are only weakly affected by the residual two-body interaction.

20 pages, LaTeX

References in corpus (1)

• Shell Model for Warm Rotating Nuclei

Cited by in corpus (7)

• Random Matrices and Chaos in Nuclear Physics
• Statistics of Hartree-Fock Levels in Small Disordered Systems
• Shell Effects on Rotational Damping in Superdeformed Nuclei
• Level density for deformations of the Gaussian orthogonal ensemble
• Violation and persistence of the K-quantum number in warm rotating nuclei
• Chaos and rotational damping in particle-rotor model
• Rotational damping in a multi-$j$ shell particles-rotor model