  We report the discovery of a partial conservation law obeyed by a schematic
Hamiltonian of two protons and two neutrons in a j shell. In our Hamiltonian
the interaction matrix element of two nucleons with combined angular momentum J
is linear in J for even J and constant for odd J. It turns out that in some
stationary states the sum J_p + J_n of the angular momenta J_p and J_n of the
proton and neutron pairs is conserved. The energies of these states are given
by a linear function of J_p + J_n. The systematics of their occurrence is
described and explained.
