Two-body-operator matrix-element factorization technique in U(n)↓SNunitary bases: Raising-raising operators

Abstract
A detailed exposition of explicit formulas used in the evaluation of raising-raising forms of two-body-operator matrix elements is presented. The methods are based on the use of the unitary-group distinct-row tabular-graphical representation of the many-particle basis. All matrix elements are expressible in the form of scalar and 2×2 matrix factors. In order to facilitate the derivations of simple, computationally efficient forms for the matrix factors we develop a calculus based on elementary graphs. The methods are applicable to systems of particles involving spins greater than (1/2 and reduce to previously known results for the case of spin (1/2.