Abstract
An explicit expression for the transformation brackets between the basis for an arbitrary irreducible representation of U(3) labeled in the U(3) ⊃ R(3) scheme introduced by Elliott and the Gel'fand U(3) ⊃ U(2) ⊗ U(1) scheme is obtained. The results are applied in deriving an expression for both the U(3) ⊃ R(3) coupling coefficients and projected tensor matrix elements.
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