Components of the force and isospin

The nuclear forces are almost charge independent. If we assume they are, we can introduce a new quantum number which is conserved. For nucleons only, that is a proton and neutron, we can limit ourselves to two possible values which allow us to distinguish between the two particles. If we assign an isospin value of \( \tau=1/2 \) for protons and neutrons (they belong to an isospin doublet, in the same way as we discussed the spin \( 1/2 \) multiplet), we can define the neutron to have isospin projection \( \tau_z=+1/2 \) and a proton to have \( \tau_z=-1/2 \). These assignements are the standard choices in low-energy nuclear physics.