The Laue equation for atom diffraction by crystal surfaces is generalized to include the effects of the atom-phonon interactions exactly. An intensity formula near resonance is derived on the basis of the generalized Laue equation. The diffraction amplitude T is written as the sum of the amplitude T p due to the potential scattering and the amplitude T r due to the resonance scattering. The resonance width and the shift of the resonance energy are involved in the expression for T . Provided that near resonance the variation of T r with the incident conditions are much more larger than that of T p , it is predicted from the intensity formula that the resonance minima and resonance maxima appear in the intensity curves for the specular and non-specular beams, respectively. The intensity formula is applied to the analysis of intensity profiles near resonance for the H+NaF(001)system.
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Yoshihiro Hamauzu (1977) studied this question.
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