§34.10 Zeros

In a $\mathit{3}j$ symbol, if the three angular momenta $j_1,j_2,j_3$ do not satisfy the triangle conditions (34.2.1), or if the projective quantum numbers do not satisfy (34.2.3), then the $\mathit{3}j$ symbol is zero. Similarly the $\mathit{6}j$ symbol (34.4.1) vanishes when the triangle conditions are not satisfied by any of the four $\mathit{3}j$ symbols in the summation. Such zeros are called trivial zeros. However, the $\mathit{3}j$ and $\mathit{6}j$ symbols may vanish for certain combinations of the angular momenta and projective quantum numbers even when the triangle conditions are fulfilled. Such zeros are called nontrivial zeros.

For further information, including examples of nontrivial zeros and extensions to $\mathit{9}j$ symbols, see Srinivasa Rao and Rajeswari (1993, pp. 133–215, 294–295, 299–310).