Algebraic forms for the leading factor of the two-electron coefficients offractional parentage for the atomic l shell

The part of a one-electron coefficient of fractional parentage (cfp) depend ing, for the atomic l shell, on the spin S, seniority nu, and electron numb er n of the daughter state, is factored into two parts, the first with depe ndence on n and nu, and the second with dependence on nu and S. Various tec hniques are used to extend these results to the two-electron cfp. These ent ail deriving analogues of the 6-j symbols for the symplectic group sp(4l+2) and the special orthogonal group SO(2l+1). Explicit algebraic expressions are provided, and the choice of multiplicity indices and their circumventio n are discussed.