Superintegrable systems with spin and second-order integrals of motion

We investigate a quantum nonrelativistic system describing the interaction of two particles with spin-1/2 and spin 0, respectively. We assume that the Hamiltonian is rotationally invariant and parity conserving and identify all such systems which allow additional integrals of motion that are second-order matrix polynomials in the momenta. These integrals are assumed to be scalars, pseudoscalars, vectors or axial vectors. Among the superintegrable systems obtained, we mention a deformation of the Coulomb potential with the scalar potential V-0 = alpha/r + 3 (h) over bar (2)/8r(2) and spin-orbital one V-1 = (h) over bar /2r(2).