Partial dynamical symmetries and shape coexistence in nuclei

Abstract

We present a symmetry-based approach for shape coexistence in nuclei, founded on the concept of partial dynamical symmetry (PDS). The latter corresponds to a situation when only selected states (or bands of states) of the coexisting configurations preserve the symmetry while other states are mixed. We construct explicitly critical-point Hamiltonians with two or three PDSs of the type U(5), SU(3), $\overline{\mathrm{SU}(3)}$ and SO(6), appropriate to double or triple coexistence of spherical, prolate, oblate and $\gamma$-soft deformed shapes, respectively. In each case, we analyze the topology of the energy surface with multiple minima and corresponding normal modes. Characteristic features and symmetry attributes of the quantum spectra and wave functions are discussed. Analytic expressions for quadrupole moments and $E2$ rates involving the remaining solvable states are derived and isomeric states are identified by means of selection rules.

25 pages, 14 figures, accepted for publication as a Special Issue on "Shapes and Symmetries in Nuclei: From Experiment to Theory" in Physica Scripta

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• The pervasiveness of shape coexistence in nuclear pair condensates
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• Aspects of Shape Coexistence in the Geometric Collective Model of Nuclei
• Bohr-Mottelson Hamiltonian with octic potential applied to the ${}^{106-116}$Cd isotopes
• SU(3) partial dynamical symmetry and nuclear shapes
• Dynamical Symmetries and Beyond: Lessons and Advances