Basis-dependent measures and analysis uncertainties in nuclear chaoticity

Abstract

Chaoticity in nuclei is usually measured by the information entropy through analyzing wave functions, or by spectral statistics with the spectral rigidity and the nearest neighbor level spacing (NNLS) distribution. We show that although information entropy (or localization length) is a basis-dependent quantity, it is helpful for understanding the complexity of wave functions, especially when the corresponding levels lie in a highly-excited, dense region. On the other hand, although nuclear levels used for spectral statistics are quantum-mechanically observable, one has to treat them through a model- (and parameter-) dependent unfolding procedure, which may introduce large uncertainties for drawing a conclusion. By applying the projected shell model, we address these problems with an ensemble of ∼ 20,000 Jπ=1/2+ levels calculated for the well-deformed, odd-mass nucleus 153Nd. Residual interactions that are responsible for nuclear chaoticity are discussed as well.

Keywords

• Quantum chaos
• Information entropy
• Spectral statistics
• Odd-mass nuclei
• Angular-momentum projection