On the basis of the eikonal approximation of quantum scattering theory, the problem of fast charged particle scattering in a thin crystal when particles fall along one of its planes of atoms and in a thin layer of an 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 channeling theory. The scattering of a particle in the longitudinal direction has features of scattering in a two-dimensional amorphous medium with the inhomogeneous density of atoms. The concept of a continuous potential of the crystal plane of atoms in the suggested approach appears automatically.

根据量子散射理论的近似，考虑了当粒子沿其原子平面之一落下时以及非晶态物质薄层中时，带电粒子在薄晶体中快速散射的问题。结果表明，在此问题中，对于超出伯恩摄动理论应用范围的参数，其散射截面与伯恩逼近的相应结果有很大不同。在这种情况下，横向于平面方向的散射主要由在沟道理论中广泛使用的连续平面电势确定。颗粒在纵向上的散射具有在原子密度不均匀的二维非晶态介质中散射的特征。