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Coupling of Angular Momenta Isospin Nucleon-Nucleon Interaction

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Wigner 3-j 3 j symbols<br />

Relation <strong>of</strong> Clebsch-Gordon-coefficients to Wigner 3-j (or 3-jm) symbols:<br />

Symmetry properties:<br />

• 3j symbol is invariant under an even permutation <strong>of</strong> its columns:<br />

•An odd permutation <strong>of</strong> the columns gives a phase factor:<br />

• Changing the sign <strong>of</strong> the m quantum numbers also gives a phase factor:<br />

• Selection rules<br />

The Wigner 3-j is zero unless all<br />

these conditions are satisfied:

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