The ionization of He atoms, prepared in a well-defined (n=14)
1P Rydberg state, in collisions with electron-attaching molecules like
SF6 and
NO2, is studied in a crossed-beam experiment at thermal energies. The ionization cross section is observed to be large for
SF6, reaching 4.2\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}13}$
cm2, and to be smaller for
NO2, close to ${10}^{\mathrm{\ensuremath{-}}15}$
cm2. The dependence of these two cross sections on the relative velocity of the reactants exhibits a characteristic behavior with a saturation at low velocities, a dependence that is completely different from that obtained with polar molecules. The observation of such a dependence for
NO2 indicates that, for this molecule, the reaction product is an ion pair, as for
SF6, and that ionization is not due to rotational energy transfer even though
NO2 has a dipole moment. This dependence cannot be explained by the ``free-electron model'' usually used in Rydberg-atom--molecule collisions; it clearly shows that the interaction of the molecule with the ion core cannot be neglected.