Classification of states in SO(8) proton–neutron pairing model

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 SO(8) Lie algebra for three special values of the mixing parameter that measures the competition between the T=0 and T=1 pairing. The SO(8) algebra is generated, amongst others, by the S=1, T=0 and S=0, T=1 pair creation and annihilation operators and corresponding to the three values of the mixing parameter, there are three chains of subalgebras: SO(8)⊃SOST(6)⊃SOS(3)⊗SOT(3), SO(8)⊃[SOS(5)⊃SOS(3)]⊗SOT(3) and SO(8)⊃[SOT(5)⊃SOT(3)]⊗SOS(3). Shell model Lie algebras, with only particle number conserving generators, that are complementary to these three chains of subalgebras are identified and they are used in the classification of states for a given number of nucleons. The classification problem is solved explicitly for states with SO(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.