  Integrability conditions for systems of bosons or fermions with seniority
conserving hamiltonians are derived. The conditions are shown to be invariant
under a large class of transformations of the interaction matrix elements.
Previously published integrable models are shown to satisfy these conditions
and the existence of a new class of integrable models is demonstrated. The
number of free parameters in the interaction in these models equals the number
of single particle levels plus 3 . Equations for the energy eigenstates and
eigenvalues are derived and the eigenvalues of the complete set of two-body
integrals of the motion are given for the new class. Some two-body correlations
in these eigenstates are derived from the integrals of the motion.
