Coupling of Angular Momenta Isospin Nucleon-Nucleon Interaction

Nucleon-nucleon nucleon interaction
The interaction between the nucleons can now be formulated also as a sum of a
singlet and a triplet potential:
(2)
A third formulation is based on isospin exchange. A two-particle wave
function with good isospin is
Using the symmetry of the Clebsch-Gordan coefficients
we see that an exchange of the two isospin projections t 3 and t 3 ' corresponds to a
change of sign for T = 0 and no change for T = 1. Because of (1.1), the isospin
exchange operator P τ - which produces the correct sign change - can be expressed as
and the isospin dependence of the nucleon-nucleon interaction may be
formulated in a third way as:
(3)