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

Abstract

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.

arXiv commentRevTex4, 17 pages; added Appendix A, with proof for the new relation; corrected Eqs.(26),(38), and (39)

References in corpus (8)

• Number of states with fixed angular momentum for identical fermions and bosons
• Alternate Derivation of Ginocchio-Haxton relation [(2j+3)/6]
• Classification of states of single-$j$ fermions with $J$-pairing interaction
• Degeneracies when T=0 Two Body Matrix Elements are Set Equal to Zero and Regge's 6j Symmetry Relations
• Degeneracies when T=0 Two Body Interacting Matrix Elements are Set Equal to Zero : Talmi's method of calculating coefficients of fractional parentage to states forbidden by the Pauli principle
• Companion problems in quasispin and isospin
• Expressions for the number of J=0 pairs in even-even Ti isotopes
• Fermionic Symmetries: Extension of the two to one Relationship Between the Spectra of Even-Even and Neighbouring Odd mass Nuclei

Cited by in corpus (6)

• Seniority conservation and seniority violation in the g_{9/2} shell
• Partial Dynamical Symmetries in the g9/2 Shell-Progress and Puzzles
• Relations Between Coefficients of Fractional Parentage
• Analytic proof of partial conservation of seniority in $j=9/2$ shells
• Total number of $J$ levels for identical particles in a single-$j$ shell using coefficients of fractional parentage
• Exact expressions for the number of levels in single-\textit{j} orbits for three, four and five fermions