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.

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

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Cited by in corpus (1)

• Coupling and Recoupling Coefficients for Wigner's U(4) Supermultiplet Symmetry