Why Can't a Lower Energy Photon Remain After Pair Production?

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Discussion Overview

The discussion revolves around the phenomenon of pair production, specifically addressing why a lower energy photon cannot remain after the creation of an electron-positron pair when a high-energy photon interacts with a nucleus. The scope includes theoretical considerations and conceptual clarifications related to particle interactions in quantum physics.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant questions why, after pair production from a 10 MeV photon interacting with a carbon nucleus, a lower energy photon (between 0 and 8.98 MeV) cannot remain as a product of the interaction.
  • Another participant suggests that while there is no fundamental prohibition against a lower energy photon remaining, the occurrence of this is suppressed by the fine structure constant and certain phase space factors.
  • A request is made for resources or explanations that discuss the calculations involved and the reasons for the suppression of this process.
  • Another participant asserts that the situation should be clear at an A level understanding, noting that the Feynman diagram requires an additional electromagnetic vertex, indicating a three-body final state.

Areas of Agreement / Disagreement

Participants express differing views on the likelihood of a lower energy photon remaining after pair production. While some acknowledge the theoretical possibility, others emphasize the suppression factors that make it unlikely. The discussion does not reach a consensus on the implications of these factors.

Contextual Notes

The discussion highlights the dependence on specific calculations related to the fine structure constant and phase space, which remain unresolved. There is also an assumption that participants have a certain level of understanding of quantum mechanics and Feynman diagrams.

TheCanadian
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In pair production, if the photon has an energy greater than 1.02 MeV, why can't a lower energy photon remain after creation of the electron-positron pair? For example, if you have a 10 MeV photon interacting with a carbon nucleus, why are the stated products of pair production the carbon nucleus, positron, and electron? Why can't a final photon with energy between ## 0 < E_\gamma < 8.98## MeV exist afterwards from this interaction with the carbon nucleus?
 
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In principle, there is nothing forbidding this. However, the rate of this occurring is going to be suppressed by the fine structure constant and some phase space factor.
 
Orodruin said:
In principle, there is nothing forbidding this. However, the rate of this occurring is going to be suppressed by the fine structure constant and some phase space factor.

Do you mind providing a resource/explanation discussing this calculation and why it's unlikely by a factor of the fine structure constant/phase space difference?
 
It should be pretty obvious at A level. The Feynman diagram needs an extra electromagnetic vertex and it is a 3-body final state.
 
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