Unitary-group approach to spin-dependent operators

General, closed-form expressions are presented for the matrix elements of ${\mathit{ssS}}_{\mathit{K}}$(${\mathbf{s}}_{\mathit{i}}$,${\mathbf{s}}_{\mathit{j}}$) (rank K=0,1,2), tensors in the single-particle spin operators ${\mathbf{s}}_{\mathit{i}}$, in the unitary-group approach. Factorization of the matrix elements in terms of 6-j and 9-j coefficients is achieved through methods of spin-graphical analysis. Results are also obtained for the rank-2 spin-spin operator.