I have a problem in understanding the dependence by isospin of strong interaction.(adsbygoogle = window.adsbygoogle || []).push({});

In this potential one have a lot of operatorial terms wich include central, spin-spin, tensor force, spin-orbit terms, and all this four terms multiply by a factor isospin-dependent (tau_i dot tau_j).

I don't understand the last term.

What does it mean (tau_i dot tau_j)? If I have two nucleon, they can have tau_z=1/2 or -1/2. Dot product involves tau_x, tau_y and tau_z and why there are a dependence of other coordinates?

Because strong interaction is invariant for a system composed by neutron-neutron or proton-proton, one would have the same interaction if tau_iz=tau_jz=1/2 (proton-proton) or tau_iz=tau_jz=-1/2 (neutron-neutron). So I don't understand why strong interaction contains (tau_i dot tau_j) terms, instead (tau_zi tau_zj).

Thanks a lot.

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# Strong interaction and isospin

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