Proxy-$SU(4)$ symmetry in A=60-90 region
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866913372424896512 |
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| author | Kota, V. K. B. Sahu, R. |
| author_facet | Kota, V. K. B. Sahu, R. |
| contents | 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 $^1p_{3/2}$, $^1p_{1/2}$, $^0f_{5/2}$ and $^0g_{9/2}$ 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 $^0g_{9/2}$ changes to $^0f_{7/2}$ giving the SGA $U(40) \supset [U(10) \supset G \supset SO(3)] \otimes [SU(4) \supset SU_S(2) \otimes SU_T(2)]$. 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 $^0g_{9/2}$ 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2311_10479 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Proxy-$SU(4)$ symmetry in A=60-90 region Kota, V. K. B. Sahu, R. Nuclear Theory 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 $^1p_{3/2}$, $^1p_{1/2}$, $^0f_{5/2}$ and $^0g_{9/2}$ 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 $^0g_{9/2}$ changes to $^0f_{7/2}$ giving the SGA $U(40) \supset [U(10) \supset G \supset SO(3)] \otimes [SU(4) \supset SU_S(2) \otimes SU_T(2)]$. 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 $^0g_{9/2}$ 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. |
| title | Proxy-$SU(4)$ symmetry in A=60-90 region |
| topic | Nuclear Theory |
| url | https://arxiv.org/abs/2311.10479 |