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

TL;DR

This paper explores multiple $SO(5)$ isovector pairing algebras in nuclear shell models with several orbits, revealing their structure and applications in understanding seniority and isospin quantum numbers.

Contribution

It introduces the concept of multiple $SO(5)$ algebras with phase choices in pairing operators and demonstrates their usefulness through three applications.

Findings

Multiple $SO(5)$ algebras exist with $2^{r-1}$ variants for $r$ orbits.

Each $SO(5)$ algebra has a complementary $Sp(2 extOmega)$ algebra.

Applications show the practical relevance of these algebraic structures in nuclear physics.

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.