  Certain Hamiltonians based on two coupled quantum mechanical spins exhibit
degenerate eigenvalues despite having no obvious non-abelian symmetries.
Operators acting to permute the degenerate states do not have a simple form
when expressed as polynomials of the generators of rotations for the respective
spins. As observed in [1], one such Hamiltonian helps explain resonances in the
spin relaxation rate of optically pumped Rb_2, as a function of applied
magnetic field. We give an explanation of why the degeneracies exist, based on
properties of the commutator and anti-commutator of the Hamiltonian and its
image under magnetic field reversal.
