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

الأصل · EN

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) ⊃ OST(6) ⊃ Oₛ(3) ⊗ Oₜ(3), O(8) ⊃ [Oₛ(5) ⊃ Oₛ(3)] ⊗ Oₜ(3) and O(8) ⊃ [Oₜ(5) ⊃ Oₜ(3)] ⊗ Oₛ(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.