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On the basis of the eikonal approximation of quantum scattering theory, theproblem of fast charged particles scattering in a thin crystal when particlesfall along one its plane of atoms and in a thin layer of amorphous matter isconsidered. It is shown that the scattering cross section in this problem, forparameters, which are beyond the scope of application of the Born perturbationtheory, differs significantly from the corresponding result of the Bornapproximation. In this case, the scattering in the transverse to the planedirection is determined mainly by a continuous plane potential, which is widelyused in the theory of the channeling phenomenon. The scattering of a particlein the longitudinal direction has features of scattering in a two-dimensionalamorphous medium with inhomogeneous density of atoms. The concept of acontinuous potential of the crystal plane of atoms in the considered approachappears automatically.

The Eikonal Approximation of the Scattering Theory for Fast Charged Particles in a Thin Layer of Crystalline and Amorphous Media