Reduced matrix elements of tensor operators

Of frequent interest is the need to evaluate matrix elements for a tensor product of two irreducible tensor operators 

The reduced matrix element (free of projections of angular momenta) is evaluable according to the following decoupling formula 

The matrix elements of a unit operator (of rank zero) are reduced as 

The reduced matrix elements of uncoupled angular momenta are collected in Table 1.15. 

Let us apply the decoupling formula to several important cases.  

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