The proxy-SU(3) symmetry in atomic nuclei

Abstract

The microscopic origins and the up-to-now predictions of the proxy-SU(3) symmetry model of atomic nuclei are reviewed. Starting from the experimental evidence for the special role played by nucleon pairs with maximal spatial overlap, the proxy-SU(3) approximation scheme is introduced and its validity is demonstrated through Nilsson model calculations, as well as through its connection to the spherical shell model. The major role played by highest weight irreducible representations of SU(3) in shaping up the nuclear properties is pointed out, resulting in parameter-free predictions of the collective variables beta and gamma for even-even nuclei, in the explanation of the dominance of prolate over oblate shapes in the ground states of even-even nuclei, in the prediction of a shape/phase transition from prolate to oblate shapes below closed shells, as well as in the prediction of specific islands on the nuclear chart in which shape coexistence is confined. Further developments within the proxy-SU(3) scheme are outlined.

arXiv comment27 pages, 9 figures, 8 tables

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Cited by in corpus (10)

• Shape coexistence in even-even nuclei: A theoretical overview
• Signatures for shape coexistence and shape/phase transitions in even-even nuclei
• Prolate-oblate asymmetric shape phase transition in the interacting boson model with SU (3) higher-order interactions
• Proxy-$SU(4)$ symmetry in A=60-90 region
• Bohr-Mottelson Hamiltonian with octic potential applied to the ${}^{106-116}$Cd isotopes
• Quadrupole-Octupole Residual Interaction in the Proxy-$SU(3)$ Scheme
• Shell-model description of collective deformation variables $\beta$ and $\gamma$ in ${}^{164-188}$Hf nuclei
• Shape transitions and ground-state properties of tungsten isotopes in covariant density functional theory
• Inter-band B(E1) Strengths in Heavy Nuclei based on the Proxy-SU(3) Scheme
• Shell-model representations of the microscopic version of the Bohr-Mottelson collective model