Fermionic symmetries: Extension of the two to one relationship between the spectra of even-even and neighboring odd mass nuclei

In the single j shell there is a two to one relationship between the spectra of certain even-even and neighboring odd mass nuclei; e.g., the calculated energy levels of J = 0⁺ states in ⁴⁴Ti are at twice the energies of corresponding levels in ⁴³Ti(⁴³Sc) with J = j = 7/2. Here an approximate extension of the relationship is made by adopting a truncated seniority scheme; i.e., for ⁴⁶Ti and ⁴⁵Sc we get the relationship if we do not allow the seniority v = 4 states to mix with the v = 0 and v = 2 states. Better than that, we get very close to the two to one relationship if seniority v = 4 states are admixed perturbatively. In addition, it is shown that for the J = 0 T = 3 state in ⁴⁶Ti and for the J = j T= 5/2 state in ⁴⁵Sc (i.e., the states of higher isospin) there are no admixtures in which the neutrons have seniority 4.