No surprise in the first Born approximation for electron scattering

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.