A unified description of the N-P symmetry states and non-symmetry states in the fermion dynamical symmetry model

In the S-D truncated subspace, the low-lying collective quadrupole states are classifed in terms of proton-neutron symmetry states and proton-neutron non-symmetry states. It is shown that the driving force for the splitting of the proton-neutron symmetry states and proton-neutron non-symmetry states are multiple proton-neutron interactions. When realistic strengths of the effective interactions are taken, both the above N-P symmetry states and non-symmetry states can be described in a unified manner and are in good agreement with experimental spectroscopy. It is futher shown that in fact no analogous Majorana interaction as in IBM-2 is required in a fermionic truncation space to reproduce this splitting. The description is applied to the discussion of 1+ states in rare-earth region