Racah coefficient

The Racah W-coefficients, sometimes simply called the Racah coefficients, are quantities introduced by Racah that are related to the Clebsch-Gordan coefficients by (J_1 J_2[J'] J_3|J_1, J_2 J_3[J'']) = sqrt((2J' + 1)(2J'' + 1))W(J_1 J_2 J J_3 ;J' J'') and (J_1 J_2[J'] J_3|J_1 J_3[J''] J_2) = sqrt((2J' + 1)(2J'' + 1))W(J_1^, J_3 J_2 J'' ;J J_1). The Racah W-coefficients are related to the Wigner 6j-symbols by (-1)^(a + b + c + d) W(a b c d;e f) = {a | b | c d | e | f} (Messiah 1962, p. 1062, p. 279).

Clebsch-Gordan coefficient | Racah V-coefficient | Wigner 3j-symbol | Wigner 6j-symbol | Wigner 9j-symbol