Spectral Fluctuations in A=32 Nuclei Using the Framework of the Nuclear Shell Model

Adel Khalaf Hamoudi

doi:10.11648/j.ajpa.20170503.11

Abstract

Chaotic properties of nuclear energy spectra in A=32 nuclei are investigated via the framework of the nuclear shell model. The energies (the main object of this investigation) are calculated through accomplishing shell model calculations employing the OXBASH computer code with the realistic effective interaction of W in the isospin formalism. The A=32 nuclei are supposed to have an inert 16O core with 16 nucleons move in the 1d5/2, 2s1/2 and 1d3/2 orbitals. For full hamiltonian calculations, the spectral fluctuations (i.e., the nearest neighbor level spacing distributions P(S) and the Δ3 statistics) are well characterized by the Gaussian orthogonal ensemble of random matrices. Besides, they show no dependency on the spin J and isospin T. For unperturbed hamiltonian calculations, we find a regular behavior for the distribution of P(S) and an intermediate behavior between the GOE and the Poisson limits for the Δ3 statistics.

Highlights

Chaos in quantum system was studied extremely throughout the last three decades [1]
It is typically known that quantum analogs of most classically chaotic systems demonstrate spectral fluctuations that agree with the random matrix theory (RMT) [4, 5] while quantum analogs of classically regular systems reveal spectral fluctuations that agree with a Poisson distribution
For calculations with the unperturbed hamiltonian, we find a regular behavior for the P(s) distribution and an intermediate behavior between the Gaussian orthogonal ensemble (GOE) and the Poisson limits for the ∆ statistics

Summary

Introduction

Chaos in quantum system was studied extremely throughout the last three decades [1]. Bohigas et al [2] proposed a relation between chaos in a classical system and the spectral fluctuations of the analogous quantum system, where an analytical proof of the Bohigas et al conjecture is found in [3]. The electromagnetic transition intensities in a nucleus are observables that are sensitive to the wave functions, and the study of their statistical distributions should complement [11, 12] the more common spectral analysis and serve as another signature of chaos in quantum systems. Hamoudi et al carried out [20] the fp-shell model calculations to study the statistical fluctuations of energy spectrum and electromagnetic transition intensities in A=60 nuclei using the F5P [21] interaction. Hamoudi et al carried out [23] full fp-shell model calculations to investigate the regular to chaos transition of the energy spectrum and electromagnetic transition intensities in 44V using the interaction of FPD6 as a realistic interaction in the isospin formalism. For calculations with the unperturbed hamiltonian, we find a regular behavior for the P(s) distribution and an intermediate behavior between the GOE and the Poisson limits for the ∆ statistics

Theory

Results and Discussion

Conclusions