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Near field and exit wave computations for electron microscopy.

A Howie1

  • 1Department of Physics, University of Cambridge, J.J. Thomson Avenue, Cambridge CB3 0HE, UK.

Ultramicroscopy
|June 4, 2013
PubMed
Summary

This study applies atomic scattering phase shifts to calculate electron exit waves for gold and silicon atoms. The method clarifies wave behavior and offers a new way to test electron microscopy scattering theories.

Keywords:
Atomic exit wavesFar field and near fieldScattering and phase shifts

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Area of Science:

  • Atomic Physics
  • Electron Microscopy
  • Quantum Scattering Theory

Background:

  • The partial wave phase shift formalism is a key tool in atomic scattering theory.
  • Understanding electron wave functions is crucial for interpreting electron microscopy data.
  • Accurate modeling of electron-atom interactions is essential for advanced microscopy techniques.

Purpose of the Study:

  • To compute exit wave functions for isolated gold (Au) and silicon (Si) atoms using the partial wave phase shift formalism.
  • To clarify the relationship between far-field and near-field (exit) waves in atomic scattering.
  • To explore the potential of this formalism for testing traditional scattering theories in electron microscopy.

Main Methods:

  • Application of the partial wave phase shift formalism to atomic scattering.
  • Computation of exit wave functions for isolated Au and Si atoms.
  • Analysis under both plane wave and focused probe illumination conditions.
  • Proper treatment of the Coulomb singularity in the scattering potential.

Main Results:

  • Exit wave functions were computed for isolated Au and Si atoms.
  • Connections between far-field and near-field waves were elucidated.
  • The approach correctly handles the Coulomb singularity, though requiring many phase shifts at 100 keV.
  • The formalism was shown to be adaptable to various incident wave forms and embedded atomic potentials.

Conclusions:

  • The partial wave phase shift method provides a robust framework for calculating atomic scattering exit waves.
  • This formalism offers a valuable tool for validating existing electron microscopy scattering theories.
  • The approach can be extended to more complex scenarios, including atoms in a constant potential.