Racah W-Coefficient

Related to the Clebsch-Gordan Coefficients by

$$(J_1J_2[J']J_3\vert J_1,J_2J_3[J''])=\sqrt{(2J'+1)(2J''+1)}\, W(J_1J_2JJ_3;J'J'')$$

and

$$(J_1J_2[J']J_3\vert J_1J_3[J'']J_2)=\sqrt{(2J'+1)(2J''+1)}\, W(J_1'J_3J_2J'';JJ_1).$$

See also Clebsch-Gordan Coefficient, Racah V-Coefficient, Wigner 3j-Symbol, Wigner 6j-Symbol, Wigner 9j-Symbol

References

Messiah, A. ``Racah Coefficients and `$6j$' Symbols.'' Appendix C.II in Quantum Mechanics, Vol. 2. Amsterdam, Netherlands: North-Holland, pp. 1061-1066, 1962.

Sobel'man, I. I. ``Angular Momenta.'' Ch. 4 in Atomic Spectra and Radiative Transitions, 2nd ed. Berlin: Springer-Verlag, 1992.