Coupling of Angular Momenta Isospin Nucleon-Nucleon Interaction

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Wigner 3-j 3 j symbols Relation of Clebsch-Gordon-coefficients to Wigner 3-j (or 3-jm) symbols: Symmetry properties: • 3j symbol is invariant under an even permutation of its columns: •An odd permutation of the columns gives a phase factor: • Changing the sign of the m quantum numbers also gives a phase factor: • Selection rules The Wigner 3-j is zero unless all these conditions are satisfied:
Wigner 3-j 3 j symbols • Scalar invariant The contraction of the product of three rotational states with a 3j symbol: is invariant under rotations. • Orthogonality relations: • Relation to spherical harmonics: The 3jm symbols give the integral of the products of three spherical harmonics:
Page 1 and 2: Lecture 5 Coupling of Angular Momen
Page 3 and 4: Angular Momenta Cartesian coordina
Page 5 and 6: Coupling of Angular Momenta A fully
Page 7: Properties of Clebsch-Gordon coeffi
Page 11 and 12: Table of Clebsch-Gordon coefficient
Page 13 and 14: Isospin Formally: The isospin symme
Page 15 and 16: Isospin The proton and neutron must
Page 17 and 18: III. Nucleon-nucleon nucleon intera
Page 19 and 20: Nucleon-nucleon nucleon interaction
Page 21 and 22: Nucleon-nucleon nucleon interaction
Page 23 and 24: Interactions from Nucleon-Nucleon S
Page 25 and 26: Interactions from Nucleon-Nucleon S

Coupling of Angular Momenta Isospin Nucleon-Nucleon Interaction

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