MULTIBODY OPERATOR MATRIX-ELEMENTS AND SUBDUCTION COEFFICIENTS IN U(N) .2.

Matrix elements of multibody operators in Gel'fand and similar bases o f irreducible representations of U(n) are evaluated algebraically to a rbitrary order. It is shown that in all cases the matrix element expre ssions consist of products of terms, each a matrix factor associated o nly with subgroup labels at step U(k)superset of U(k-1) in the group c hain U(n)superset of ...superset of U(k)superset of ...superset of U(1 ). Further, the matrices at step k occurring in the product are diagon alizable according to the irreps of SN, which signifies also for N the number of one-body operators contained in the multibody operator at t he level. The results extend previous work that was directed at specia l cases of multibody operators. Attention has been focused recently on such operators in connection with spin-dependent and higher-order mul tipole spin-independent interactions as arise in the unitary group app roach. Explicit phase relations are incorporated throughout the treatm ent. (C) 1997 American Institute of Physics.