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Relativity energy question

  1. Nov 14, 2007 #1
    1. The problem statement, all variables and given/known data
    5. A pi0 meson whose rest mass is 135 MeV/c^2 is moving with a kinetic energy of 1 GeV.
    It decays in flight into two photons whose paths are along the direction of motion of the
    meson. Find the energies of the two photons.
    [Ans: 4 and 1131 MeV.]


    2. Relevant equations



    3. The attempt at a solution
    Working in the CM frame (the rest frame of the pion) and conserving energy in that frame:

    mc^2 = 2E*, where E* are the energies of the photons in the CM frame


    I then thought I could use a lorentz transformation Ea=gamma(E* + betaE*) where Ea is the energy of one photon in lab frame and gamma and beta are the gamma and beta for the pion moving in lab frame, with gamma = (energy of pion)/mc^2 and beta = (pc)/E

    But first i was checking something, and i cannot get the simple conservation of energy to work with the answers given. So in the lab frame, i thought the energy of the pion must equal the sum of the energies of the photons, given as 1135? And the energy of the pion

    = sqrt[(pc)^2 + m^2c^4]
    i thought this
    =sqrt[1000^2 + 135^2]
    as the kinetic energy is given as 1GeV=1000MeV and the mass is given in units of MeV/c^2. Clearly I'm misunderstanding something, but what?!? Will my method work once this misunderstanding is resolved (and is there a better method or different method just for future reference)?

    Thanks
     
  2. jcsd
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