Propagation coefficients for fixed-isospin (T,T z) average and related spectroscopic sum rules

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Abstract
The reduction relation for the fixed‐isospin (T,Tz) average of a general operator in the model space of many fermions is described in two forms with and without recourse to factorization of isospin z components. Algebraic treatment is developed to deduce various types of expressions for each propagation coefficient that plays the role of the Green’s function in each form of the reduction relation. Propagation coefficients are described also in relation to sum rules as to fixed‐isospin spectroscopic factors. These results lead to novel identities among n‐j symbols and factorials.