# Thread: relativity - particle collision

1. A Proton, m_{1} with Kinetic energy T = 200MeV strikes a stationary proton in the lab frame.
p + p -> p + p + X

what is the maximum mass of X, which can be produced.

I think I need to make use of E^2 - P^2 c^2 is invariant.
and
In S: E = (m_{1} + m_{0}c^2 , p = p_{1]
In S ' :

E^2 - P^2 c^2 = E^2_{1} + 2m_{0}E_{1}c^2 + m^2_{0}c^4 - T^2 (1)

where E_{1} = T + m_{0}c^2
I'm not sure what is happening in the centre of mass frame, I thought that the particle would have maximum mass when there was zero K.E i.e E' = (2m_{0} + m_{x})c^2, p' = 0 in the lab frame but I got lost when I tried to equate this with (1). This violates conservation of momentum so its pretty clearly wrong, but I'm not sure where to go any help would be appreciated.

2.

3. Why cant you just convert all the kinetic energy of the moving proton into mass after the collision and then just balance the new masses velocity to conserve momentum and energy?

The equations arent pretty but it seems to work, just two relatively easy simulaneous equations.

4. E = 2Moc^2 + T Initial state
= 2Moc^2 + (Mx)c^2 Final state (protons are at rest)
p = (Moc^2 + T)/ c Initial state
=

I tried the Book says the answer is 17.6GeV.