Partial Dynamical Symmetry in the Symplectic Shell Model

Abstract

We present an example of a partial dynamical symmetry (PDS) in an interacting fermion system and demonstrate the close relationship of the associated Hamiltonians with a realistic quadrupole-quadrupole interaction, thus shedding new light on this important interaction. Specifically, in the framework of the symplectic shell model of nuclei, we prove the existence of a family of fermionic Hamiltonians with partial SU(3) symmetry. We outline the construction process for the PDS eigenstates with good symmetry and give analytic expressions for the energies of these states and E2 transition strengths between them. Characteristics of both pure and mixed-symmetry PDS eigenstates are discussed and the resulting spectra and transition strengths are compared to those of real nuclei. The PDS concept is shown to be relevant to the description of prolate, oblate, as well as triaxially deformed nuclei. Similarities and differences between the fermion case and the previously established partial SU(3) symmetry in the Interacting Boson Model are considered.

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References in corpus (4)

• Partial Dynamical SU(3) Symmetry and the Nature of the Lowest K=0 Collective Excitation in Deformed Nuclei
• Partial dynamical symmetry in a fermion system
• F-spin as a Partial Symmetry
• Partial Dynamical SU(3) Symmetry in Deformed Nuclei

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• Partial dynamical symmetries and shape coexistence in nuclei
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• Symplectic symmetry approach to clustering in atomic nuclei: The case of ${}^{24}$Mg
• Partial dynamical symmetries in quantum systems
• Simultaneous occurrence of distinct symmetries in nuclei