How Does Fermi Motion Affect the Threshold Energy in Photon-Proton Reactions?

[faen]

Homework Statement

Consider the production of the K+ in the reaction: \gamma p --> Κ+ Λ

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What will be the minimal \gamma energy if the proton is not free but is bound in the nucleus? Take into account the Fermi motion with p=250 MeV/c.

Homework Equations

proton mass = 770 MeV
Kaon mass = 494 MeV
hyperon mass = 1100 MeV

The Attempt at a Solution

I can't find anywhere in my book explaining what fermi motion is. The binding energy depends on how big the nucleus is, which isn't specified unless fermi motion does so.

 

[pam]

Fermi motion means the proton can be heading toward the beam with p=250.
Put this into the total momentum for the initial gammas p state.

 

[faen]

Thank you the answer. Should i convert the fermi motion into energy units, and use the concept of conservation of energy to calculate the minimum \gamma energy? The task mentions something about the proton being bound to a nucleus. Do i somehow have to take that into account in the calculation?

 

[pam]

The proton being bound is taken care of b using the Fermi momentum given.
Everything is in MeV, with c=1. You have to calculate the Fermi energy, given by E_p^2=p^2+M^2.
The equation for the threshold gamma energy k is
(k+E_p)^2-(k-p)^2=(M_\Lambda+m_k)^2.