A cluster calculation for Cu(111), Ag(111), and Au(111) shows that the lateral Fourier transform of the charge deformation due to a displacement of a single surface atom is a Gaussian exp(-Q²2Qc²). This is proportional to the scattering amplitude for one-phonon exchange atom-surface scattering and produces a cutoff in the cross section. The values of Qc are evaluated for the above-mentioned surfaces, explaining very well the experimental observations. We also find a simple formula that should be useful to experimentalists in calculating the cutoff.
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Bortolani et al. (1983) studied this question.
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