Threshold energy of a photoproduction

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Discussion Overview

The discussion revolves around determining the minimum energy of a photon required for the photoproduction reaction involving a proton, neutron, and pion. Participants explore the implications of energy conservation and quadrimomentum in both lab and center of mass frames, while addressing the complexities involved in the calculations.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested, Homework-related, Mathematical reasoning

Main Points Raised

  • One participant suggests that the total energy of the photon and proton must meet or exceed the mass energy of the neutron and pion produced, but expresses doubt about this being a satisfactory solution.
  • Another participant hints at using the center of mass frame to determine the threshold condition for the final state, indicating a potential simplification.
  • There is a discussion about the term "quadrimomentum," with participants confirming it refers to 4-momentum.
  • One participant recommends searching for "invariant mass" as a relevant concept that is both Lorentz invariant and conserved, suggesting it may aid in the calculations.
  • Another participant acknowledges the complexity of the problem despite it being described as a straightforward task and requests to see the work done by the original poster.
  • There is a repeated emphasis on the threshold condition for the final state as a key aspect of the discussion.

Areas of Agreement / Disagreement

Participants express varying levels of confidence in their approaches, with some finding the calculations complex and others suggesting simpler methods. No consensus is reached on the best approach or solution to the problem.

Contextual Notes

Participants note the complexity of the calculations involved and the potential need for clearer definitions or assumptions regarding the threshold conditions and the use of invariant mass.

kknull
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hi,
I have the reaction:

(photon) + (proton) ---> (neutron) + (pion+)

I have to find the minimum energy of the photon.
A first condition can be that total energy of photon and proton has to be at least the mass energy of the output, but I don't think this can be a satisfying solution...

When I try to include quadrimomentum conservation, calculus becomes very complex and I cannot find a solution...
Suggestions?

Thanks.
 
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what is "quadrimomentum " ?

Hint: work in center of mass frame -> what is the threshold condition for the final state?
 
malawi_glenn said:
what is "quadrimomentum " ?

4-momentum, I suspect. :smile:
 
George Jones said:
4-momentum, I suspect. :smile:

yeah, I also suspected that hehe

OP: search for "invariant mass", that is all you need, that quantity is both lorentz invariant and conserved. Also look at the hint I gave you earlier.
 
yeah, It is 4-momentum
I have tried both in lab and in center of mass frame, but it is too much complex...
 
kknull said:
yeah, It is 4-momentum
I have tried both in lab and in center of mass frame, but it is too much complex...

This is infact a super easy task, can you show work done?

Can you try to answer my hint-question, "what is the threshold condition for the final state?"
 

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