Fermionic Symmetries: Extension of the two to one Relationship Between the Spectra of Even-Even and Neighbouring Odd mass Nuclei

In the single j shell there is a two to one relationship between the spectra of certain even-even and neighbouring 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 the higher isospin states do not contain seniority four admixtures. Typeset using REVTEX 1