# Threshold energy for pion production

1. Sep 28, 2009

### bcjochim07

1. The problem statement, all variables and given/known data
When a beam of high energy protons collides with protons at rest in the laboratory, neutral pions are produced by the reaction p + p ---> p + p + pi^o. Compute the threshold energy of the protons in the beam for this reaction to occur.

2. Relevant equations

3. The attempt at a solution
I think that threshold energy means the energy required so that the pion is formed at rest, so:

E_0 + mc^2 = 2mc^2 + Ek + mpi*c^2
where E_0 is the energy of the incoming proton, m is the rest mass of a proton, Ek is the kinetic energy of one of the protons after collision, and mpi is the rest mass of the pion.
So, one of the protons is at rest to begin with and then in order for momentum to be conserved, I'm thinking that after the collision, one of the protons is at rest and the other is moving with kinetic energy Ek. Maybe this isn't right?

Previous examples say that recoil velocity is negligible, so I'll say Ek =0

E_0 = mc^2 + mpi*c^2 = 1073 MeV... this isn't right. Maybe I'm not understanding the process?

2. Sep 29, 2009