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M Lentzen1

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This study refutes claims that electron scattering theory is flawed. The research confirms the validity of the far-field expansion and the conservation of electron wave intensity in the first Born approximation.

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Area of Science:

  • Physics
  • Materials Science
  • Quantum Mechanics

Background:

  • A recent article questioned the validity of the far-field expansion in electron scattering theory.
  • The article proposed a "mystery of the missing phase" and suggested a standing spherical electron wave to resolve perceived flaws.
  • This work directly addresses and refutes these specific claims.

Purpose of the Study:

  • To rigorously re-examine and validate the fundamental principles of electron scattering theory.
  • To demonstrate the correctness of the far-field expansion and the conservation of wave intensity in the first Born approximation.
  • To clarify misconceptions regarding phase and intensity in high-energy electron scattering.

Main Methods:

  • A detailed review of the core assumptions and limitations of high-energy electron scattering theory.
  • Wave-mechanical calculations were performed to model electron scattering phenomena.
  • Specific target models, including a Gaussian phase object and a Silicon (Si) atom, were utilized.

Main Results:

  • The traditional far-field expansion, featuring a propagating spherical wave, is confirmed to be correct.
  • The investigation found no evidence for a "missing phase" in electron scattering.
  • Wave intensity is conserved to the first order in the scattering potential within the first Born approximation.

Conclusions:

  • The foundational principles of electron scattering theory, particularly the far-field expansion and first Born approximation, are robust and accurate.
  • The arguments presented in the prior work are shown to be incorrect.
  • Wave-mechanical calculations support the validated theoretical framework, offering insights into high-resolution transmission electron microscopy.