High resolution measurements of the angular distributions for the elastic and inelastic scattering of helium atoms from the translational vibrations (T modes) of single CO molecules on Pt(111) agree quantitatively with a simple transformation which predicts the inelastic cross section from the measured elastic cross section. The new theory predicts not only the inelastic interference structures and their correlations with the elastic channel, but also the individual state-to-state transitions. (C) 2001 American Institute of Physics.