  On the basis of the eikonal approximation of quantum scattering theory, the
problem of fast charged particles scattering in a thin crystal when particles
fall along one its plane of atoms and in a thin layer of amorphous matter is
considered. It is shown that the scattering cross section in this problem, for
parameters, which are beyond the scope of application of the Born perturbation
theory, differs significantly from the corresponding result of the Born
approximation. In this case, the scattering in the transverse to the plane
direction is determined mainly by a continuous plane potential, which is widely
used in the theory of the channeling phenomenon. The scattering of a particle
in the longitudinal direction has features of scattering in a two-dimensional
amorphous medium with inhomogeneous density of atoms. The concept of a
continuous potential of the crystal plane of atoms in the considered approach
appears automatically.
