ABSTRACT
In Section 23 it was pointed out that if the coefficients in the pair creation operator S+ are unequal it is not possible to define a complete scheme of generalized seniority. Unlike the case of the quasispin scheme, there is no set of J = 0 states with generalized seniority ν = 2 (or ν = 4,…). Among all J = 0 states of the system of identical valence nucleons, it is possible to pick out one state which shares important features with the seniority ν = 0 state in the quasi-spin scheme. That state, with generalized seniority ν = 0, has been the subject of the preceding section. Here, we shall consider states of such two nucleon systems with J = 2,4,…. It turns out that it is possible to define one state for each spin which is the analog of a ν = 2 state in the quasi-spin scheme. These states may be assigned generalized seniority ν = 2. In the following, we focus our attention on J = 2 states which are better known and are of greater interest. Similar results may be obtained also for J = 4 and higher even values of J.
