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

Larry Zamick·Alberto Escuderos
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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.

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Larry Zamick, Alberto Escuderos. 2006-06-05. New Relations for Coefficients of Fractional Parentage--the Redmond Recursion Formula with Seniority. https://doi.org/10.1016/j.aop.2005.08.006

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