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The process of scattering of fast charged particles in thin crystals isconsidered in the transitional range of thicknesses, between those at which thechanneling phenomenon is not developed and those at which it is realized. Thepossibility is shown of application of the methods of geometrical optics fordescription of the scattering process. The dependence is studied of the totalscattering cross-section of ultrarelativistic positrons on target thickness inthis range of crystal thicknesses. In the case of ultrarelativistic particleschanneling the possibility is shown of the existence of an effect analogical tothe Ramsauer-Townsend effect of conversion into zero of the total scatteringcross-section at some values of crystal thickness. The important role isoutlined of the Morse-Maslov index that enters into the wave functionexpression in the geometrical optics method.

Geometrical optics method in the theory of channeling of high energy particles in crystals