[en] We present an application of the hybrid anti-symmetrized coupled channels approach to compute static field ionization rates for multi-electron atoms (He, Ne, Ar) and small molecules (H_2, N_2, CO). While inert gas atoms behave as effective single electron systems, molecules exhibit multi-electron effects in the form of core polarization. It is shown that at moderate field strengths, these effects can be modeled to about 10% accuracy using a few (5–6) channel ansatz. In the case of the CO molecule, description of core polarization is essential for the correct prediction of the maximum ionization direction and our converged results are in good agreement with the experimental measurements. (paper)