Scattering of neutral atoms by a periodic potential : the Morse corrugated potential

2014 Within the two-potential formalism a general set of t matrix integral equations is obtained which describes the scattering of a neutral particle by a periodic potential. Furthermore a projection method is developed which allows us in the case of resonance, to get a new set of equations in which the resonance singularities do not appear. This formalism is applied to the Morse corrugated potential. The integral equation set is solved by an iterative process and in this way an exact solution is obtained. The convergence of the iterative expansion is studied and an approximate convergence criterion is found. Results are compared with those given by an equivalent exponential corrugated potential which demonstrates the influence of the well and potential slope on the distribution of the intensities among the different diffracted beams. In order to have a precise determination of the corrugation function it is shown that it is necessary to use a realistic potential and also to avoid approximate methods for the calculation of intensities. J. Physique 44 (1983) 473-487 AVRIL 1983, :