VECTOR COHERENT STATE CONSTRUCTIONS OF U(3) SYMMETRICAL TENSORS AND THEIR SU(3)-SUPERSET-OF-SU(2)XU(1) WIGNER COEFFICIENTS

Generalized vector coherent state constructions of totally symmetric U(3) tensors are used to gain new expressions for the SU(3)⊃SU(2)xU(1) Wigner coefficients for the coupling (λ1μ1) x (λ20) → (λ3μ3). These expressions show how the extremely simple formulas of Le Blanc and Biedenharn, involving a single 9-j coefficient, arise as special cases of a general result that involves 12-j coefficients. A simpler general result involving only 9-j coefficients and K-normalization factors is derived in a way that can, in principle, be generalized to the generic coupling with multiplicity. © 1990 American Institute of Physics.