Scattering of neutral particles by an exponential corrugated potential: A solution for high corrugation amplitude

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Abstract
For a two-dimensional exponential corrugated potential the scattering equation is solved to any desired accuracy. A distorted wave formalism is used in which the distorted (exponential) potential can be translated with respect to the corrugated potential. The integral-equation set is solved by the Neumann iterative process. It is shown that a suitable potential translation allows the extension of the convergence domain to high corrugation amplitudes. Thus the different particle-crystal systems encountered in experimental studies can now be analyzed with this soft potential. Compared to the hard corrugated wall potential the finite potential slope yields the following: (1) For small corrugation amplitude an enhancement of the specular intensity and a reduction of diffracted beam intensities. This reduction varies like the wave penetration. (2) For higher corrugation amplitude a shift of the rainbow maxima towards higher corrugation amplitude. The intensity maximum is enhanced or lowered according to whether the wave penetration of the diffracted beam is smaller or greater than that of the specular beam. In the case of the He-LiF system the emergence of the 01 beam is studied. With a potential sufficiently soft the singularities which appear around emerging conditions are smoothed. The measurement of their shape and amplitude could give an approximate value of the potential slope.