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

In the single j shelf 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 Ti-44 are at twice the energies of corresponding levels in Ti-43(Sc-43) With J = j = 7/2. Here an approximate extension of the relationship is made by adopting a truncated seniority scheme; i.e., for Ti-46 and Sc-45 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 admired perturbatively. In addition, it is shown that for the J = 0 T = 3 state in Ti-46 and for the J = j T = 5/2 state in Sc-45 (i.e., the states of higher isospin) there are no admixtures in which the neutrons have seniority 4. [S0556-2813(99)03811-X].