Superintegrable systems with spin and second-order tensor and pseudo-tensor integrals of motion

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