Proxy-$SU(4)$ symmetry in A=60-90 region

Abstract

Applications of the proxy-$SU(3)$ model of Bonatsos and collaborators to nuclei in A=60-90 region introduces proxy-$SU(4)$ symmetry. Shell model spaces with single particle (sp) orbits ${}^1{p}_{3/2}$, ${}^1{p}_{1/2}$, ${}^0{f}_{5/2}$ and ${}^0{g}_{9/2}$ are essential for these nuclei and also protons and neutrons in this region occupy the same sp orbits. With this and applying the "proxy scheme", the ${}^0{g}_{9/2}$ changes to ${}^0{f}_{7/2}$ giving the SGA $U(40)\supset [U(10)\supset G\supset SO(3)]\otimes [SU(4)\supset S{U}_S(2)\otimes S{U}_T(2)]$. With $G=SU(3)$, we have the proxy-$SU(3)$ model. It is easy to see that proxy-$SU(3)$ symmetry implies goodness of the $SU(4)$ symmetry appearing above, i.e. proxy-$SU(4)$ symmetry. Shell model calculations pointing out the need for ${}^0{g}_{9/2}$ orbit, ground state masses, shape changes and shape co-existence in A=60-90 region and GT distributions clearly show the importance of proxy-$SU(4)$ in this mass region. Besides presenting this evidence, new proxy schemes with $G=SU(5)$, $SO(6)$ and $SO(10)$ that are generated by good proxy-$SU(4)$ symmetry are described in some detail. An important feature is that the four proxy symmetries $SU(3)$, $SO(6)$, $SU(5)$ and $SO(10)$ appear twice.

arXiv commentBased on the talk given by the first author (VKBK) in SDANCA-23 held in Sofia (Bulgaria) during September 21-23, 2023

References in corpus (23)

• Evidence for Triangular D_3h Symmetry in 12C
• Spherical Shell Model description of rotational motion
• Evidence for tetrahedral symmetry in 16O
• Collective Modes in Light Nuclei from First Principles
• Symmetry-guided large-scale shell-model theory
• Symmetry restoration in mean-field approaches
• Nilsson-SU3 selfconsistency in heavy N=Z nuclei
• Analytic predictions for nuclear shapes, the prolate dominance and the prolate-oblate shape transition in the proxy-SU(3) model
• Proxy-SU(3) symmetry in heavy deformed nuclei
• Nuclear Dynamics and Reactions in the Ab Initio Symmetry-Adapted Framework
• Stellar weak decay rates in neutron-deficient medium-mass nuclei
• The proxy-SU(3) symmetry in atomic nuclei
• Classification of States in O(8) Proton-Neutron Pairing Model
• Evidence for Triangular D'(3h) Symmetry in 13C
• Spectroscopic Criteria for Identification of Nuclear Tetrahedral and Octahedral Symmetries: Illustration on a Rare Earth Nucleus
• Odd tensor electric transitions in high-spin Sn-isomers and generalized seniority
• Overview of Seniority Isomers
• Shell model analysis of the $B(E2,2^{+}\to 0^{+})$'s in the A=70 T=1 triplet
• Triaxial nuclei and analytical solutions of the conformable fractional Bohr Hamiltonian with some exponential-type potentials
• Multiple $SU(3)$ algebras in interacting boson model and shell model: Results for $(\beta ,\gamma$) bands and scissors $1^{+}$ band
• Shell model results for $T=1$ and $T=0$ bands in ${}^{66}$As
• Coexisting partial dynamical symmetries and multiple shapes
• Two species $k$-body embedded Gaussian unitary ensembles: $q$-normal form of the eigenvalue density

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