Level statistics of near-yrast states in rapidly rotating nuclei

Abstract

The nearest neighbour level spacing distribution and the Δ 3 statistic of level fluctuations associated with very high spin states ( I ≳ 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 ≳ 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.