SU(3) partial dynamical symmetry and nuclear shapes
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part of Springer Nature, 2020 https://doi.org/10.1140/epjst/e2020-000204-8
THE EUROPEAN PHYSICAL JOURNAL SPECIAL TOPICS
Regular Article
SU(3) partial dynamical symmetry and nuclear shapes A. Leviatana Racah Institute of Physics, The Hebrew University, Jerusalem 91904, Israel Received 25 August 2020 / Accepted 2 September 2020 Published online 23 October 2020 Abstract. We consider several variants of SU(3) partial dynamical symmetry in relation to quadrupole shapes in nuclei. Explicit construction of Hamiltonians with such property is presented in the framework of the interacting boson model (IBM), including higher order terms, and in its proton–neutron extension (IBM-2). The cases considered include a single prolate-deformed shape with solvable ground and γ or β bands, coexisting prolate-oblate shapes with solvable ground bands, and aligned axially-deformed proton–neutron shapes with solvable symmetric ground and γ bands and mixed-symmetry scissors and γ bands.
1 Introduction Symmetries play a key role in nuclei by providing quantum numbers for the classification of states, determining spectral degeneracies and selection rules, and facilitating the calculation of matrix elements. Models based on spectrum generating algebras form a convenient framework to study their impact and have been used extensively in nuclear spectroscopy. Notable examples include Elliott’s SU(3) model [1,2], symplectic model [3], pseudo SU(3) model [4], monopole and quadrupole pairing models [5], interacting boson models for even-even nuclei [6] and boson-fermion models for oddmass nuclei [7]. In such models, the Hamiltonian is expanded in elements of a Lie algebra (Gdyn ), called the dynamical (spectrum generating) algebra, in terms of which any operator of a physical observable can be expressed. A dynamical symmetry (DS) occurs if the Hamiltonian can be written in terms of the Casimir operators of a chain of nested algebras [8], Gdyn ⊃ G1 ⊃ G2 ⊃ . . . ⊃ Gsym , terminating in the symmetry algebra Gsym . In such a case, the spectrum is completely solvable and the eigenstates, |λdyn , λ1 , λ2 , . . . , λsym i, are labeled by quantum numbers which are the labels of irreducible representations (irreps) of the algebras in the chain. A given Gdyn can encompass several DS chains, each providing characteristic analytic expressions for observables and definite selection rules for transition processes. An attractive feature of such models is that they are amenable to both quantum and classical treatments. The classical limit is obtained by introducing coherent (or intrinsic) states [9,10], which form a basis for studying the geometry of algebraic models and their relation to intuitive notions of shapes and excitation modes. a
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The European Physical Journal Special Topics
A comprehensive framework for exploring the interplay of shapes and symmetries in nuclei, is provided by the interacting boson model (IBM) [6]. The latter describes low-lying quadrupole collective states in nuclei in terms of N monopole (s) and q
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