Classification of States in O(8) Proton-Neutron Pairing Model

Abstract

Isoscalar (T=0) plus isovector (T=1) pairing hamiltonian in LS-coupling, which is important for heavy N=Z nuclei, is solvable in terms of a O(8) algebra for some special values of the mixing parameter that measures the competition between T=0 and T=1 pairing. The O(8) algebra is generated, amongst others, by the $S=1,T=0$ and $S=0,T=1$ pair creation and annihilation operators . Shell model algebras, with only number conserving operators, that are complementary to the $O(8)\supset O_{ST}(6)\supset O_S(3)\otimes O_T(3)$, $O(8)\supset [O_S(5)\supset O_S(3)]\otimes O_T(3)$ and $O(8)\supset [O_T(5)\supset O_T(3)]\otimes O_S(3)$ sub-algebras are identified. The problem of classification of states for a given number of nucleons (called `plethysm' problem in group theory), for these group chains is solved explicitly for states with O(8) seniority $v=0,1,2,3$ and 4. Using them, band structures in isospin space are identified for states with $v=0,1,2$ and 3.

Comments: 52 pages, 12 tables