Stimulated by the He-beam diffraction experiment on metal surfaces, the interaction between an atom and surface is considered [1,2]. This is a typical problem to make a first-principles calculation on an interaction between two systems each of which has internal structure. Thus it is very difficult in general, but Takada and Kohn have made an exact formulation by introducing the S matrix for evanescent waves [3].    Takada has also proposed a new formalism to treat atom-surface inelastic scatterings [4].