Threshold energy of a photoproduction

[kknull]

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.

 

[malawi_glenn]

what is "quadrimomentum " ?

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

 

[George Jones]

what is "quadrimomentum " ?

4-momentum, I suspect.

 

[malawi_glenn]

4-momentum, I suspect.

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.

 

[kknull]

yeah, It is 4-momentum
I have tried both in lab and in center of mass frame, but it is too much complex...

 

[malawi_glenn]

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?"