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Homework Help: Maximum rest mass in particle collision

  1. Oct 21, 2014 #1
    1. The problem statement, all variables and given/known data

    Suppose that a certain accelerator can give protons a kinetic energy of 200 GeV. The rest mass of a proton is 0.938 Gev/c^2. Calculate the largest possible rest mass M0 of a particle that could be produced by the impact of one of the high-energy protons on a stationary proton in the following process: p+p --> p+p+x

    2. Relevant equations
    Ek = γmc^2
    E^2 - (pc)^2=(mc^2)^2
    Energy before = energy after
    P before = P after

    3. The attempt at a solution
    Ok, I am almost positive this has to do with conservation of energy and momentum, and that is how I would end up finding the rest mass of the particle, I am just unsure of how I would know when this is at a maximum. My initial thought is that it would be when both the protons after the collision are stationary, but I have no way of proving that.

    Energy before = 200 Gev +0.938 + 0.938 = 201.876 GeV
    Energy before = γmc^2 = 0.938 GeV / √(1-v^2/c^2)
    I solved for v and got 0.999989c, which I can use for momentum, so
    P before = (0.938 GeV * 0.999c)/ √(1-(0.999989)^2) = 199.998 GeV/c

    After that, I could just find equations for the energy and momentum after, but I want to know first when it would be at a maximum. My professor said it had something to do with the center of mass reference frame, but I'm not sure how that would come in to play. Help?
  2. jcsd
  3. Oct 22, 2014 #2


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    Stationary in what frame? As your professor suggested, analyze the interaction in the center-of-mass frame.

  4. Oct 22, 2014 #3


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    What would happen with energy and momentum if both protons were stationary after the collision?

    And just to check before making life unnecessarily complicated: Are you familiar with 4-vector notation?
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