Irreducible representations of SU(3) for nucleons in a oscillator shell η with η≤ 8: Application to nuclei with proxy-SU(4) symmetry
Abstract
Applying some simple rules, established in group theory literature, generated are codes (easy to modify as required) for obtaining SU(3) irreducible representations (irreps) for a given number of nucleons in a given oscillator shell η with η≤ 8. In this approach, first the SU(3) irreps are obtained for spinless fermions in a given η shell. Using the codes developed, tables of SU(3) irreps are generated for identical nucleons (protons or neutrons) with a given total spin S. Similarly, the SU(3) irreps are generated for nucleons with a given spin-isospin SU(4) irrep. Some applications of these tables for η=4 shell for 52 ≤ Z,N ≤ 78 nuclei with proxy-SU(4) symmetry are presented. Also, the procedure used for the shell model SU(3) limits is easy to be extended for the SU(3) limit of various interacting boson models and some examples for these are also presented.
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BibTeX
@misc{kota2026irreducible,
title = {{Irreducible representations of $SU(3)$ for nucleons in a oscillator shell $η$ with $η\le 8$: Application to nuclei with proxy-$SU(4)$ symmetry}},
author = {V. K. B. Kota},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.39357},
eprint = {2610.39357},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.39357},
}
RIS
TY - UNPB
TI - Irreducible representations of SU(3) for nucleons in a oscillator shell η with η≤ 8: Application to nuclei with proxy-SU(4) symmetry
AU - V. K. B. Kota
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2610.39357
UR - https://arxiv.org/abs/2610.39357
AB - Applying some simple rules, established in group theory literature, generated are codes (easy to modify as required) for obtaining SU(3) irreducible representations (irreps) for a given number of nucleons in a given oscillator shell η with η≤ 8. In this approach, first the SU(3) irreps are obtained for spinless fermions in a given η shell. Using the codes developed, tables of SU(3) irreps are generated for identical nucleons (protons or neutrons) with a given total spin S. Similarly, the SU(3) irreps are generated for nucleons with a given spin-isospin SU(4) irrep. Some applications of these tables for η=4 shell for 52 ≤ Z,N ≤ 78 nuclei with proxy-SU(4) symmetry are presented. Also, the procedure used for the shell model SU(3) limits is easy to be extended for the SU(3) limit of various interacting boson models and some examples for these are also presented.
ER -