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

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

2005-03-30

arxiv.org/abs/nucl-th/0503081v5

Annals Phys. 321 (2006) 987-998

Physics

Nuclear Physics

Nuclear Theory

RevTex4, 17 pages; added Appendix A, with proof for the new relation; corrected Eqs.(26),(38), and (39)

Scientific paper

10.1016/j.aop.2005.08.006

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.

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