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

Abstract

With nucleons occupying several shell model j orbits, the isovector pair creation operator A 1 µ (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(2Ω) algebra [2Ω = 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.