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

Abstract

With nucleons occupying several shell model $j$ orbits, the isovector pair creation operator $A_{\mu }^1$ (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.

Comments: 10 pages, 1 table, 1 figure, to appear in Bulgarian Journal of Physics