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Solving for Momentum in Pion Decay

  1. Jan 17, 2014 #1
    1. The problem statement, all variables and given/known data

    We are the given the rare decay:

    π+ → e+ + ve

    Also, we are given mπ = 139.6 MeV/c2, mv ≈ 0, me+ = 0.511 MeV/c2

    And we are given that the decay starts with the pion at rest, so I took that to mean that pπ = 0

    Solve for the momentum of the positron.

    2. Relevant equations

    Conservation of Momentum
    Conservation of Energy
    E2 = (pc)2 + (mc)2
    E = mc2


    3. The attempt at a solution

    I started with the fact that since the pion was at rest before decay, pπ = 0 so pe + pv = 0.

    Then, also using the fact that the pion was at rest before decay I solved for its energy using the formula E = mc2, substituting mπ = 139.6 MeV/c2 getting that Ebefore = 139.6 MeV.

    Ebefore = Eafter = Ee + Ev

    (Ee)2 = (pec)2 + (mec2)2

    And because the neutrino is massless:
    Ev = pv*c

    From before, since Ee + Ev = 139.6 MeV, I solved for Ee to get Ee =139.6 MeV - Ev.

    Then I substituted pvc for Ev to get the equation:

    (139.6 MeV - pvc)2 = (pec)2 + (mec2)2

    The (pc)2 would cancel each other out, leaving:

    -279.2pvc = -19487.8 MeV

    So, pv = 69.799 MeV/c leaving pe = -69.799 MeV/c

    My question is, is this right, or have I made some glaring mistakes in my method?
     
  2. jcsd
  3. Jan 17, 2014 #2

    TSny

    User Avatar
    Homework Helper
    Gold Member

    Looks good to me.
     
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