New Relations for Coefficients of Fractional Parentage--the Redmond Recursion Formula with Seniority

We find a relationship between coefficients of fractional parentage (cfp) obtained on the one hand from the principal parent method and on the other hand from a seniority classification. We apply this to the Redmond recursion formula which relates $n \to n+1$ cfp's to $n-1 \to n$ cfp's where the principal parent classification is used. We transform this to the seniority scheme. Our formula differs from the Redmond formula inasmuch as we have a sum over the possible seniorities for the $n \to n+1$ cfp's, whereas Redmond has only one term.Comment: RevTex4, 17 pages; added Appendix A, with proof for the new relation; corrected Eqs.(26),(38), and (39

A Linear Approximation for the Excitation Energies of single and double analog states in the f_{7/2} shell

We find that the excitation energies of single analog states for odd-even nuclei in the f$_{7/2}$ shell with J=j=7/2$^{-}$ and the J=0$^{+}$ double analog states in the even-even nuclei are well described by the formulas $E^{*}(j,T+1) = b (T+X)$ and $E^{*}(0^{+},T+2) = 2b (T+X+0.5)$,respectively, where $T=\mid N-Z\mid /2$ is usually the ground state isospin. It is remarkable to note that the parameter X accounts for the departures from the symmetry energy based predictions.Comment: 8 pages and no figure