Wigner 6-j symbol

The symbol W is called a Racah coefficient. Quite often, instead of the Racah coefficient W, one uses a Wigner 6 - j symbol... 

The coefficient in bracket is called a Wigner 6 - j symbol. Tables of these coefficients exist (Rotenberg et al., 1959). 

Coupling of three or more angular momenta Racah algebra, Wigner 6-j and 9-j symbols... 

A formula relating Wigner 3-j and 6-j symbols [73] is the following, where the right hand side may be evaluated for any M in the range... 

Note that the Wigner 3-j, 6-j and 9-j symbols are simply numbers when evaluated for particular values of the angular momentum symbols. There are numerous tabulations and programs available which allow their evaluation and the program Mathematica can handle 3-j and 6-j symbols analytically. 

A general theorem, known as the Wigner-Eckart theorem (see, for example, Schiff, p. 222 see the Further reading section), states that the expectation value of any vector operator in the space of the JLSJ ) states is proportional to the expectation value of J itself and does not depend on (in the following we use bold symbols with a hat, 6, to denote vector operators and bold symbols, O, to denote their expectation values). Let us consider as an example a vector operator which is a linear combination of L and S,... 

---