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On fast charged particles scattering on zigzag nanotube

Viktoriia Omelchenko

TL;DR

This work analyzes fast charged particle scattering on zigzag carbon nanotubes using the $eikonal$-approximation of quantum electrodynamics and the continuous-potential approach to obtain orientation-dependent differential cross sections for straight and tilted nanotubes. It develops a formalism that averages over thermal atomic displacements and employs a structure-factor framework to relate multi-string scattering to single-structure outcomes, with explicit treatment of tilted geometries via averaged χ0-functions. The authors derive analytical and numerical expressions for the χ0-functions of straight and tilted strings and perform detailed numerical calculations for a $(5,0)$ nanotube, revealing orientation-sensitive scattering features and elucidating the regime of applicability for the eikonal method. The results have potential implications for nanotube diagnostics and beam steering, as rainbow-like scattering patterns encode information about nanotube orientation and structure. The study provides a pathway to exploit high-energy scattering as a probe of nanoscale targets and their geometrical configurations.

Abstract

A fast charged particle scattering on a single-wall carbon nanotube of zigzag type was considered. The differential cross sections of scattering on nanotubes of different spatial orientation with respect to the incident particles were obtained. The eikonal approximation of quantum electrodynamics and the continuous potential approximation were used.

On fast charged particles scattering on zigzag nanotube

TL;DR

This work analyzes fast charged particle scattering on zigzag carbon nanotubes using the -approximation of quantum electrodynamics and the continuous-potential approach to obtain orientation-dependent differential cross sections for straight and tilted nanotubes. It develops a formalism that averages over thermal atomic displacements and employs a structure-factor framework to relate multi-string scattering to single-structure outcomes, with explicit treatment of tilted geometries via averaged χ0-functions. The authors derive analytical and numerical expressions for the χ0-functions of straight and tilted strings and perform detailed numerical calculations for a nanotube, revealing orientation-sensitive scattering features and elucidating the regime of applicability for the eikonal method. The results have potential implications for nanotube diagnostics and beam steering, as rainbow-like scattering patterns encode information about nanotube orientation and structure. The study provides a pathway to exploit high-energy scattering as a probe of nanoscale targets and their geometrical configurations.

Abstract

A fast charged particle scattering on a single-wall carbon nanotube of zigzag type was considered. The differential cross sections of scattering on nanotubes of different spatial orientation with respect to the incident particles were obtained. The eikonal approximation of quantum electrodynamics and the continuous potential approximation were used.

Paper Structure

This paper contains 5 sections, 37 equations, 10 figures.

Table of Contents

  1. Introduction
  2. Problem formulation
  3. Differential scattering cross section
  4. Pontential-dependent functions
  5. Results and Discussion

Figures (10)

  • Figure 1: Fast charged particle scattering on zigzag nanotubes
  • Figure 2: "Unfolded" zigzag nanotube: dashed lines denote atomic strings
  • Figure 3: Tilted nanotube projection on the $(x,y)$-plane for $A=10$: black dots denote projection of atoms positions of the tilted nanotube, grey dots denote projection of atoms positions of the straight nanotube
  • Figure 4: Differential cross section of a fast charged particle scattering on a straight nanotube
  • Figure 5: Differential cross section of a fast charged particle scattering on a tilted nanotube, $L_x=0.4R$
  • ...and 5 more figures