If isospin is a good quantum number for individual nucleons, then the total isospin I of a 2-nucleon system must be consistent with the other quantum numbers of the system and with the Pauli exclusion principle (identical Fermions).
a) for a state of 2 neutrons, with symmetric (L=0) space wave function, work out the allowed quantum numbers for total angular momentum J and isospin I.
b) for a state consisting of 1 neutron and 1 proton, with symmetric (L=0) space wave function, work out the allowed quantum numbers for total angular momentum J and isospin I.
c) repeat the above analysis for a state consisting of 2 deuterons, assuming each deuteron has isospin 0 and intrinsic angular momentum J = 1. What nucleus would this system correspond to?