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arXiv · 2111.03521

Multiple $SO(5)$ isovector pairing and seniority $Sp(2\Omega)$ multi-$j$ algebras with isospin

V. K. B. Kota·R. Sahu
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Abstract

With nucleons occupying several shell model $j$ orbits, the isovector pair creation operator $A^1_\mu$ (creates a two particle state with angular momentum $J=0$ and isospin $T=1$) is no longer unique. Choosing it to be a sum of single-$j$ isovector pair creation operators each with a phase, there will be multiple pair $SO(5)$ algebras with isospin; with $r$ number of $j$ orbits, there will be $2^{r-1}$ $SO(5)$ algebras each with a corresponding complementary $Sp(2\Omega)$ algebra [$2\Omega = \sum_j (2j+1)$] that gives seniority and reduced isospin quantum numbers. Three applications of multiple $SO(5)$ algebras are presented demonstrating the usefulness of considering $SO(5)$ pairing algebras with general sign factors.

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V. K. B. Kota, R. Sahu. 2021-11-05. Multiple $SO(5)$ isovector pairing and seniority $Sp(2\Omega)$ multi-$j$ algebras with isospin. https://arxiv.org/abs/2111.03521

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