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Physical Review C

Excited states of many-body systems in the fermion dynamical symmetry model with random interactions

G. J. Fu, Y. M. Zhao, J. L. Ping, A. Arima

Published Sep 23, 2013• 9 citations
Publisher

Abstract

In this Brief Report we investigate excited yrast states under random interactions in the framework of the fermion dynamical symmetry model, for the ensemble with spin-0 ground states. Interesting correlations are seen between ${R}_{6}$ and ${R}_{4}$ (where ${R}_{I}\ensuremath{\equiv}{E}_{{I}_{1}^{+}}/{E}_{{2}_{1}^{+}}$) by using the Mallmann plot, for cases with both SP(6) symmetry and SO(8) symmetry.

DOI
10.1103/physrevc.88.037302

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In this Brief Report we investigate excited yrast states under random interactions in the framework of the fermion dynamical symmetry model, for the ensemble with spin-0 ground states. Interesting correlations are seen between R6{R}_{6}R6​ and R4{R}_{4}R4​ (where RI\ensuremath≡EI1+/E21+{R}_{I}\ensuremath{\equiv}{E}_{{I}_{1}^{+}}/{E}_{{2}_{1}^{+}}RI​\ensuremath≡EI1+​​/E21+​​) by using the Mallmann plot, for cases with both SP(6) symmetry and SO(8) symmetry.
We continue a series of numerical experiments on many-body systems with random two-body interactions, by examining correlations in ratios in excitation energies of yrast J=0,2,4,6,8J=0,2,4,6,8J=0,2,4,6,8 states. Previous studies, limited only to J=0,2,4J=0,2,4J=0,2,4 states, had shown strong correlations in boson systems but not fermion systems. By including $J\ensuremath{\geqslant}6$ states and considering different scatter plots, strong correlations between ratios of yrast excitation energies appear in both boson and fermion systems. Such correlations agree with real nuclear data and include the well-known limits of seniority, vibrations, and rotations.
In this work we study the yrast states of sd\mathit{sd}sd-boson systems in the presence of random interactions. It is found that the yrast states with spin-zero ground states among the random ensemble exhibit strong correlations, characterized by anharmonic vibration, sss-boson or ddd-boson condensation, as well as vibrational and rotational motions. We study these correlations explicitly based on their wave functions and the features of two-body interactions in the random ensemble.
In this article we study the behavior of collectivity under random two-body interactions in the framework of the fermion dynamical symmetry model (FDSM). We found that a Hamiltonian with the SO(8) symmetry of the FDSM does not give vibrational and rotational modes under random interactions while a Hamiltonian with the SP(6) symmetry does. It is suggested that collective motions such as vibration and rotation are closely related not only to the quadruple-quadruple correlation in the Hamiltonian but also to the dynamical symmetries of the Hamiltonian.
In this paper we study low-lying states of sdsdsd bosons under random interactions. We find that the yrast states are highly correlated, regardless of whether the ground state spin is zero or not. Many of the random samplings in the random ensemble well overlap with predictions of the U(5) limit in the interacting boson model.
An ensemble with random n-body interactions is investigated in the presence of symmetries. A striking emergence of regularities in the spectra, ground state spins, and isospins is discovered. In even-particle systems the strong preponderance of spin zero ground states is observed with three, four, and higher-order random many-body interactions, and similar trends are discovered in systems that possess both rotational and isospin symmetry. Various types of correlations from pairing to spectral sequences and correlations across different masses are explored. A search for an interpretation is presented.
We apply a two-body random ensemble to a hypothetical system of spinless fermions occupying a one-dimensional rotationally invariant orbit in order to study the statistical tendencies of spins of ground states for a random two-body interaction. We also investigate the origin of the dominance of spin-zero ground states of a single-j shell in the nuclear shell model, which can be interpreted geometrically as a particular case of the simple hypothetical model we consider. Assuming a specific symmetry, or the doublet structure due to time-reversal symmetry, it is found that the ensemble has a preference for a ground state whose spin is zero. We demonstrate how the time-reversal symmetry and its doublet structure affect this ground state tendency.