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Pozitron-Electron interaction(anihilation)

  1. Jan 30, 2013 #1
    1. The problem statement, all variables and given/known data
    A given pozitron with T kinetic energy is approaching an electron bound to a hard nucleus(in the K energy level, and the ionization energy for this level, Ek(>0), is given).
    The energy of the two resulting photons is to be determined.


    2. Relevant equations
    Conservation of energy.

    3. The attempt at a solution
    So I wrote the conservation of energy as follows:
    2m0c2 + T = 2ε + Ek ( ε is the energy of one photon )
    Let me explain my way of thinking: After the anihilation, the electron has vanished, so the atom has become a ion(so it's energy has increased by Ek).

    However, the proposers of the problem consider the conservation of energy as follows:
    2m0c2 + T + Ek = 2ε;

    So who is right?
     
  2. jcsd
  3. Jan 30, 2013 #2

    mfb

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    Staff: Mentor

    If Ek is defined to be positive, it should be subtracted on the left side (or added on the right side).
    Otherwise you can violate energy conservation: Take a free electron, let it get caught by a nucleus (emitting energy). Add a free positron, and get more than 2*511keV as energy => you gained the binding energy two times.
     
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