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Threshold energy of proton beam?

  1. Oct 26, 2013 #1
    1. The problem statement, all variables and given/known data
    I am trying to find the minimum energy for a proton beam to make pions that have 100Gev of momentum. The proton beam is hitting a fixed target.

    2. Relevant equations

    p + n -> n + n + ##π^{+}##

    3. The attempt at a solution

    In the centre of mass frame, there is zero initial momentum. But the pion has 100GeV of momentum on the other side, so I gave the neutrons the same amount in the opposite direction to cancel it out.

    Then I used E=2m##c^2## for the initial energy and got the relativistic mass. (I wasn't sure about this)
    The velocity was very close to the speed of light, and I then used relativistic velocity addition to find gamma. (this is for the proton colliding with the neutron)

    I had gamma ~ 9000
    In the end I had an answer of ##E_{proton beam}## ~ 8.5 TeV

    Is this the right sort of value to be looking at? If necessary I can write up all my working.
  2. jcsd
  3. Oct 26, 2013 #2


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    Isn't the 100 GeV momentum of the pion measured in the lab frame? If so, that's not the momentum of the pion in the center-of-mass frame.
  4. Oct 27, 2013 #3
    How can I find out what the momentum is in the CoM frame? Do I still need the CoM frame?
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