Possibility of a diffracted beam in the absence of the corresponding Fourier component of potential in gas-surface scattering

It is shown, with a simple analytical example, that the intensity of a diffracted beam in atom-surface scattering is not necessarily small if the corresponding Fourier component of potential is small. This result contradicts the predictions of the existing first-order theory. An experimental result that higher-order diffracted beams can dominate the scattering while the specular and other lower-order beams can be relatively small, combined with a theoretical result that the Fourier components of potential decrease strongly with increasing order, leads to the conclusion that first-order theory is invalid in general for an interpretation of gas-surface diffraction.