Theory of Direct Scattering, Trapping and Desorption in Atom-Surface   Collisions
  When gas atoms or molecules collide with clean and ordered surfaces, under many circumstances the energy-resolved scattering spectra exhibit two clearly distinct features due to direct scattering and to trapping in the physisorption well with subsequent desorption. James Clerk Maxwell is credited with being the first to describe this situation by invoking the simple assumption that when an impinging gas beam is scattered from a surface it can be divided into a part that exchanges no energy and specularly reflects and another part that equilibrates or accommodates completely and then desorbs with an equilibrium distribution. In this paper a scattering theory is developed, using an iterative algorithm and classical mechanics for the collision process, that describes both direct scattering and trapping-desorption of the incident beam. The initially trapped fraction of particles can be followed as they continue to make further interactions with the surface until they are all eventually promoted back into the positive energy continuum and leave the surface region. Consequently, this theory allows a rigorous test of the Maxwell assumption and determines the conditions under which it is valid. The theory also gives quantitative explanations of recent experimental measurements which exhibit both a direct scattering contribution and a trapping-desorption fraction in the energy-resolved spectra. 
Guoqing Fan, J. R. Manson