# Calculate minimum beam energy

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1. May 2, 2015

### J_M_R

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

Calculate the minimum beam energy in a proton-proton collider to initiate the p+p→p+p+n0 reaction. The rest energy of the no is 547.3MeV.

2. Relevant equations

For a head on collision between particles a and b, from conservation of total energy: Ex = Ep + Ep' = 2Ep

so that mx^2c^4 = Ex^2 - px^2c^2 = (2Ep)^2

3. The attempt at a solution

Rearranging the above, gives mx = 2Ep/c^2

So using the values I have been provided: Ep = (547.3MeV)/2 = 0.2737Gev

I am not sure if my method is correct?

2. May 2, 2015

### Staff: Mentor

I guess "beam energy" means the total energy, including the rest energy of the protons.
For the additional energy: yes it is correct. The lab frame is also the center of mass frame, so both protons simply contribute half of the n0 energy plus their rest energy.

3. May 3, 2015

### J_M_R

So to get Ep, I am also required to add the rest energy of the two protons?:

Ep = (547.3MeV + 2(938.3MeV))/2 = 1.212GeV

If rest energy of a proton is 938.3Mev.

4. May 3, 2015

### Staff: Mentor

Right.

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