Scattering of ultrarelativistic electrons in ultrathin crystals

TL;DR

This paper develops a quantum theory for high-energy electron scattering in ultrathin crystals, revealing sharp diffraction peaks and periodic variations in scattering cross-sections, which suggest new interference effects in radiation.

Contribution

It introduces a novel quantum scattering theory for ultrathin crystals, highlighting diffraction effects and periodic cross-section variations not captured by classical models.

Findings

Quantum scattering cross-section shows sharp peaks due to diffraction.

Cross-section peaks vary periodically with crystal thickness.

Quantum and classical cross-sections differ significantly in transitional thickness range.

Abstract

Quantum theory is proposed of high energy electrons scattering in ultrathin crystals. This theory is based upon a special representation of the scattering amplitude in the form of the integral over the surface surrounding the crystal, and on the spectral method of determination of the wave function. The comparison is performed of quantum and classical differential scattering cross-sections in the transitional range of crystal thicknesses, from those at which the channeling phenomenon is not developed up to those at which it is realized. It is shown that in this thickness range the quantum scattering cross-section, unlike the classical one, contains sharp peaks corresponding to some specific scattering angles, that is connected with the diffraction of the incident plane wave onto the periodically distributed crystal atomic strings. It is shown that the value of the scattering cross-section in the peaks varies periodically with the change of the target thickness. We note that this must lead to a new interference effect in radiation that is connected with the rearrangement of incident wave packet in transitional area of crystal thicknesses.