Scattering of neutral particles by a two-dimensional exponential corrugated potential

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Abstract
The integral equation for the scattering is solved exactly for a two-dimensional exponential corrugated potential. An infinite set of coupled integral equations involving a function proportional to the wave amplitude has been found. This set is numerically solved by a Neumann iterative process. For a surface square unit cell and a sinusoidal corrugation profile, the convergence domain is determined and numerical results are obtained which are compared to those given by the hard corrugated wall potential. The finite slope of the potential yields an enhancement of the specular intensity and a reduction of all the others. This is qualitatively explained by considering of wave penetration. The singularities which appear in the different beam intensities when a beam is emerging are analysed. They are of two types depending on whether the beam is strongly coupled or not to the emerging one. As their shape and amplitude depend strongly upon the damping coefficient of the exponential, their measurement could allow the determination of this quantity