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Pair production

  1. Apr 30, 2008 #1
    why can't a gamma ray photon -->positron+electron? My notes simply say this would violate momentum conservation (you need a recoiling nucleus), but why? I mean, the photon WOULD have momentum (=E/c), so the sum of momentums of the positron and electron would just have be E/c..
     
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  3. Apr 30, 2008 #2

    nrqed

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    there are several to prove that. The most intuitive and quick way is to consider the center of mass frame of the electron-positron pair. In that frame, the total three-momentum is zero. But it's impossible for a single photon to have zero three-momentum. Therefore the reaction is impossible, in that frame three-momentum can't be conserved.
     
  4. Apr 30, 2008 #3
    "But it's impossible for a single photon to have zero three-momentum"

    well, the photon COULD have zero three momentum if the CMF was travelling at a speed 'c'. I take it this isn't allowed? My knowledge of SR isn't amazing shall we say:(

    thanks for your reply, again nrqed.
     
  5. Apr 30, 2008 #4

    nrqed

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    No problem.

    The point is that if you have two massive particles, it is always possible to find a physical center of mass frame (in the sense that it is moving at a speed less than c so you can actually boost yourself to that frame).
     
  6. Apr 30, 2008 #5
    just did a little recap on SR:

    from wikipedia:

    # The Principle of Invariant Light Speed - Light in vacuum propagates with the speed c (a fixed constant) in terms of any system of inertial coordinates, regardless of the state of motion of the light source.

    SO you can pick a reference frame in which the photon IS at rest, thus having ZERO momentum (ie. travelling at c relative to the lab frame, if you will). This IS also the CMF for e+ and e-.

    What am I not understanding clearly?
     
  7. Apr 30, 2008 #6

    nrqed

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    The point is that if you have pair production, you can find a physical frame (moving below the speed of light) where the total three-momentum of the electron and positron is zero.

    If you have a single photon, you can NOT find a frame where the three-momentum of the single photon is zero. I mean a physical frame, one which travels at a speed smaller than c.

    Therefore, it's impossible for for a single photon to convert into an electron-positron pair.
    QED

    The point is to show that a single photon cannot convert into an electron positron pair , right?
     
  8. Apr 30, 2008 #7
    yeah I totally understand what you've said and it makes sense intuitivly.

    I was just wondering why you can't have a frame travelling AT c (probably a silly question)
     
  9. Apr 30, 2008 #8

    nrqed

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    Ah, ok.
    Well, you can define a frame travelling at c. It's just irrelevant to the question you asked here.

    As long as you don't ask questions like "If I am in that frame, what will the photon look like" and so on. So yes, you can define a frame moving at c but there is nothing you can do with it, no application, no gedanken experiment. So it's pretty much useless.
     
  10. Apr 30, 2008 #9
    i see what you're talking about:)
     
  11. Apr 30, 2008 #10

    nrqed

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    Iknow you said that you had understood my point but the second paragraph seemed to say that you had not. My point was that the CMF of the e+e- pair was NOT a frame travelling at c.


    Just to make sure things are clear.

    Regards
     
  12. May 2, 2008 #11

    pam

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    Without worrying about frames, E^2-p^2 is an invariant that must be the same before and after an interaction. E^2-p^2>0 for the electron+positron, while E^2-p^2=0 for a photon.
     
  13. May 2, 2008 #12
    thanks pam - that's a good explanation.
     
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