# Photon and particle reaction

1. Apr 13, 2008

### faen

1. The problem statement, all variables and given/known data

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

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.

2. Relevant equations

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

3. The attempt at a solution

I cant find anywhere in my book explaining what fermi motion is. The binding energy depends on how big the nucleus is, which isnt specified unless fermi motion does so.

2. Apr 13, 2008

### 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.

3. Apr 13, 2008

### 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?

4. Apr 15, 2008

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

Last edited: Apr 15, 2008