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
$$(k+E_p)^2-(k-p)^2=(M_\Lambda+m_k)^2$$.