Isospin relations for four nucleons in a single j shell

We had previously used techniques involving isospin to count the number of states for three identical fermions in a single j shell with total angular momentum I=j. We generalize this to all I, but the main thrust of this work is to consider now a four-fermion system. As before, one evaluates the eigenvalues of the Hamiltonian â i<j[a+bt(i)•t(j)] from both an isospin point of view and an angular momentum point of view. In the four-particle case, we get a more limited result than in the three-particle case, namely the number of T=0 states minus twice the number of T=2 states, all of a given angular momentum I.