{"paper":{"title":"Simple formula for leading $SU(3)$ irreducible representation for nucleons in an oscillator shell","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nucl-th","authors_text":"V.K.B. Kota","submitted_at":"2018-12-05T04:21:12Z","abstract_excerpt":"Applications of rotational $SU(3)$ symmetry in nuclei, using Elliott's $SU(3)$ or pseudo-$SU(3)$ or proxy-$SU(3)$ model, often need just the lowest or leading $SU(3)$ irreducible representation (irrep) $(\\lambda_H, \\mu_H)$. For nucleons in an oscillator shell $\\eta$, with ${\\cal N}=(\\eta +1)(\\eta +2)/2$, we have the algebra $U(r{\\cal N}) \\supset [U({\\cal N}) \\supset SU(3)] \\otimes SU(r)$; $r=2$ when there are only valence protons or neutrons and $r=4$ for nucleons with isospin $T$. Presented in this paper is a simple general formula for the leading $SU(3)$ irrep $(\\lambda_H, \\mu_H)$ in any giv"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.01810","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}