Threshold energy of a photoproduction

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SUMMARY

The discussion centers on calculating the threshold energy required for the photoproduction reaction (photon + proton → neutron + pion+). Participants emphasize the importance of using invariant mass and quadrimomentum conservation to determine the minimum energy of the photon. The center of mass frame is recommended for simplifying calculations. The conversation highlights that understanding 4-momentum is crucial for solving the problem effectively.

PREREQUISITES
  • Understanding of photoproduction reactions
  • Familiarity with invariant mass in particle physics
  • Knowledge of quadrimomentum conservation
  • Ability to work in the center of mass frame
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  • Research the concept of invariant mass in particle collisions
  • Study quadrimomentum conservation principles in relativistic physics
  • Learn how to perform calculations in the center of mass frame
  • Explore threshold conditions for various particle interactions
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Physicists, students of particle physics, and anyone involved in high-energy physics research will benefit from this discussion.

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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