  A simple method to calculate Wigner coupling coefficients and Racah
recoupling coefficients for U(3) in two group-subgroup chains is presented.
While the canonical U(3)->U(2)->U(1) coupling and recoupling coefficients are
applicable to any system that respects U(3) symmetry, the U(3)->SO(3) coupling
coefficients are more specific to nuclear structure studies. This new procedure
precludes the use of binomial coefficients and alternating sums which were used
in the 1973 formulation of Draayer and Akiyama, and hence provides faster and
more accurate output of requested results. The resolution of the outer
multiplicity is based on the null space concept of the U(3) generators proposed
by Arne Alex et al., whereas the inner multiplicity in the angular momentum
subgroup chain is obtained from the dimension of the null space of the SO(3)
raising operator. A C++ library built on this new methodology will be published
in a complementary journal that specializes in the management and distribution
of such programs.
