wigner 12j · recoupling

a b c d e f g h j₁₃₅ j₁₂₅ j₆ j₅ j₃₄ j₁₂ j₄ j₃ j₂ j₁ j₂₄ j₁₃
j₁5.0
5.0
j₂5.0
5.0
j₃5.0
5.0
j₄5.0
5.0
j₅5.0
5.0
j₆5.0
5.0
j₁₂5.0
5.0
j₃₄5.0
5.0
j₁₂₅5.0
5.0
j₁₃₅5.0
5.0
j₁₃5.0
5.0
j₂₄5.0
5.0
12j symbol 0.0000 (zero) ⚪ zero
12j = sum over x,y of (-1)^{...} (2x+1)(2y+1) * { ... } (sum over 6j and 9j symbols)
what does 12j mean? it appears in the quantum mechanics of angular momentum when four angular momenta are coupled. the 12j symbol is a recoupling coefficient that transforms between different coupling schemes of four angular momenta. it is used in advanced atomic and nuclear physics, particularly in the theory of complex spectra and in the description of systems with four independent angular momenta.