We consider the relationship between several different formalisms for treating the multiphonon inelastic scattering of atomic projectiles from surfaces. Starting from general principles of formal scattering theory, the trajectory approximation to the scattering intensity is obtained. From the trajectory approximation, the conditions leading to the fast-collision approximation for multiquantum inelastic scattering are systematically derived.
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Manson et al. (1994) studied this question.
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