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

## TL;DR

This paper develops an eikonal approximation approach to analyze the scattering of fast charged particles in thin crystalline and amorphous layers, revealing significant deviations from the Born approximation and highlighting the role of continuous potentials.

## Contribution

It introduces an eikonal approximation method for scattering in thin media, capturing effects beyond the Born approximation and naturally deriving the continuous potential concept.

## Key findings

- Scattering cross section differs significantly from the Born approximation in certain parameters.
- Transverse scattering is mainly influenced by a continuous plane potential.
- Longitudinal scattering resembles scattering in a two-dimensional amorphous medium.

## Abstract

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.