Why do photons/electrons scatter at angles in compton scattering?

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Discussion Overview

The discussion centers on the phenomenon of photon scattering at angles other than 0 or 180 degrees during Compton scattering. Participants explore the underlying reasons for this behavior, touching on concepts from quantum mechanics and classical scattering theory.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant expresses confusion about why photons scatter at various angles, suggesting it might be a complex issue not covered in standard textbooks.
  • Another participant explains that the uncertainty principle implies that while a photon has a defined momentum, its position is uncertain, leading to a range of possible scattering angles based on different impact parameters.
  • A further reply acknowledges the connection between the uncertainty principle and classical scattering, particularly the role of the impact parameter in determining scattering angles.
  • Another participant describes the classical and relativistic treatments of photon scattering, noting that Thomson scattering and Compton scattering provide consistent results for photon energies up to about 100 keV, and emphasizes the importance of conservation laws in the kinematics of the scattering process.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the complexity of the reasons behind scattering angles, with some focusing on the uncertainty principle while others highlight classical and relativistic frameworks. The discussion remains unresolved regarding the depth of explanation needed.

Contextual Notes

Participants reference classical and relativistic models without fully resolving the implications of the uncertainty principle or the specifics of scattering kinematics. There may be limitations in the assumptions made regarding the applicability of classical concepts to quantum phenomena.

nlsherrill
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This is something that I always just took for granted, but I have no idea how a photon scatters off of an electron at an angle other than 0 or 180 degrees. I haven't seen this mentioned in a modern physics or nuclear engineering textbook either, so I assuming its a pretty complicated reason?
 
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An incident photon has a well-defined momentum. According to the Heisenberg's Uncertainty principle, its position is unknown. Particularly, the impact parameter, as defined in classical scattering theory, is not defined and may take any value. But, different impact parameters correspond to different scattering angles, so you get a whole spectrum of scattering angles.

More formally, the scattering matrix element between two plane-wave states is non-zero. The square of the modulus, multiplied by the available phase space around the final state, gives the scattering cross section.
 
Dickfore,

Thanks for the quick reply! So essentially all comes down to the uncertainty principle? I understand classical scattering and understood the connection you made to an impact parameter.
 
The inelastic scattering of a photon off of a free stationary electron is described classically by Thomson scattering, and relativistically by Compton scattering. The two solutions agree for photon energies up to roughly 100 keV.
The kinematics requires conservation of energy, and conservation of momentum in both longitudinal and transverse planes (3 unknowns, and 3 equations total). This is very similar to billiard ball kinematics.

See Section 4 in http://farside.ph.utexas.edu/teaching/em/lectures/node92.html for a discussion of Thomson scattering.
 

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