Partial dynamical symmetry versus quasi dynamical symmetry examination within a quantum chaos analyses of spectral data for even\u2013even nuclei

A J Majarshin,S K Mousavi Mobarakeh,H Sabri,Feng Pan,Yan-An Luo

doi:10.1038/s41598-021-95847-1

A J Majarshin, S K Mousavi Mobarakeh + Show 3 more

Open Access

https://doi.org/10.1038/s41598-021-95847-1

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Abstract

Statistical analyses of the spectral distributions of rotational bands in 51 deformed prolate even–even nuclei in the 152 ≤ A ≤ 250 mass region R_{{4_{1}^{ + } /2_{1}^{ + } }} ge 3.00 are examined in terms of nearest neighbor spacing distributions. Specifically, the focus is on data for 0+, 2+, and 4+ energy levels of the ground, gamma, and beta bands. The chaotic behavior of the gamma band, especially the position of the 2_{gamma }^{ + } band-head compared to other levels and bands, is clear. The levels are analyzed within the framework of two models, namely, a SU(3)-partial dynamical symmetry Hamiltonian and a SU(3) two-coupled quasi-dynamical symmetry Hamiltonian, with results that are further analyzed using random matrix theory. The partial and quasi dynamics both yield outcomes that are in reasonable agreement with the known experimental results. However, due to the degeneracy of the beta and gamma bands within the simplest SU(3) picture, the theory cannot be used to describe the fluctuation properties of excited bands. By changing relative weights of the different terms in the partial and quasi dynamical Hamiltonians, results are obtained that show more GOE-like statistics in the partial dynamical formalism as the strength of the pairing term is increased. Also, in the quasi-dynamical symmetry limit, more correlations are found because of the stronger couplings.

Highlights

We studied the fluctuation properties of energy spectra, which yield via Eqs. (1, 3) for Partial dynamical symmetries (PDS) and quasi dynamical symmetry (QDS) formalisms
Similar to what we have done by PDS formalism, we focused on Eq (3) and determined different energy levels as the expectation value of Hamiltonian QDS formalism in different coupling conditions defined as the χ values
We have seen the spectral statistics of different levels of rotational bands in deformed prolate even–even nuclei of both PDS and QDS formalisms in the framework of Nearest Neighbor Spacing Distribution (NNSD) statistics of RMT

Summary

Introduction

In PDS formalism, by adding a term to Hamiltonian of SU(3) dynamical symmetry, the β–γ degeneracy is broken, and theoretical energy levels have good conformity with experimental levels. The breaking of K-symmetry in the considered nuclei are strong in the gamma band and it makes more regular of the levels of the beta band in comparison with other rotational bands.

Results

Conclusion