  We investigate a quantum non-relativistic system describing the interaction
of two particles with spin 1/2 and spin 0, respectively. Assuming that the
Hamiltonian is rotationally invariant and parity conserving we identify all
such systems which allow additional (pseudo)tensor integrals of motion that are
second order matrix polynomials in the momenta. Previously we found all the
(pseudo)scalar and (axial)vector integrals of motion. No non-obvious tensor
integrals exist. However, nontrivial pseudo-tensor integrals do exist. Together
with our earlier results we give a complete list of such superintegrable
Hamiltonian systems allowing second-order integrals of motion.
