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No pair production with light alone

  1. Jul 26, 2005 #1
    Hi,

    I have heard someplace in my graduation course that two gamma photons are not allowed to yield a pair of particle anti-particle unless there is some material agent nearby. I remember also that this result was told to be very easy to demonstrate. Unfortunatelly there is no room for that in this page (recalling Fermat..).

    Is there anyone who knows this proof ?

    Thankx
     
  2. jcsd
  3. Jul 26, 2005 #2
    Try writing a S-matrix and drawing a Feynman diagram for such a process.
     
    Last edited: Jul 26, 2005
  4. Jul 27, 2005 #3
    But as I remember one can derive this result from conservation laws, using Lorentz invariants or related things.
     
  5. Jul 27, 2005 #4

    ZapperZ

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    This is a very naive explanation, but it'll do for now.

    Take a photon with energy exactly equal to the rest mass energy of an electron-positron pair. It has energy JUST enough to create that pair. So conservation energy is fine.

    However, the photon had a MOMENTUM before. If it has exactly just enough energy to create an electron-positron pair, there's nothing leftover to be converted into a net momentum for the electron-positron. So there's violation of conservation of momentum.

    It requires a coupling to another "massive" entity to provide the necessary recoil momentum.

    Zz.
     
  6. Jul 27, 2005 #5
    you will find everything in here
    http://laser.phys.ualberta.ca/~egerton/pair-p&a.htm

    marlon
     
  7. Jul 27, 2005 #6
    Well, I didn't really understand which process you were describing. Is it two photons decaying into two electrons and two positrons, or something else?
    I thought that maybe the S-matrix would show that there is a violation of 4-momentum. Or that a Feynman diagram would reveal an open internal vertix.

    EDIT: Oops. I'm too late.
     
  8. Jul 27, 2005 #7

    EL

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    The question was about two photons producing a electron-positron pair.
    If the photons collide heads on, momentum can be conserved...why do we need some other material then?
     
  9. Jul 27, 2005 #8

    It is quite like that, I can remember the outlines. But if the incoming photon had more energy? Wouldn't it be sufficient to guarantee the extra kinetic energy which would be noticeable also in the form of momentum (recoil momentum) ?


    Best Regards

    DaTario
     
  10. Jul 27, 2005 #9

    ZapperZ

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    You may or may not. But when was the last time we had a "photon collider", and how often does this happen? Yet, we HAVE generated antimatter via pair production.

    This means that there is an inherent and more universal conservation consideration that should work for one, two, three, four, etc... photon conversion into matter. ALL electron-positron pair production, for example, are produce via gamma rays going through a crystal, where the crystal is the medium that supply the necessary momentum conservation. And unless I missed something, the feynman diagram for matter-antimatter pair production in general always seem to have an extra coupling to a nearby object [Someone doing high energy physics can correct me on this].

    Zz.
     
  11. Jul 27, 2005 #10

    EL

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    Sure, but in principle it is possible to create electron-positrons pairs out of two colliding photons. (In fact the collision need not be heads on, but that's the case when it's most effective.)
    However, we do not have sufficently good lasers at the moment.
    But at least it may soon be possible to detect photon-photon scattering by colliding laser beams.
     
  12. Jul 27, 2005 #11

    ZapperZ

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    I think that for any appreciable cross-section, gamma-gamma is the only choice currently. If that is the case, then I know for sure we don't have gamma lasers as of yet. :)

    I believe this is one type of collision that is being considered for LHC as one of its many functions.

    Zz.
     
  13. Jul 27, 2005 #12
  14. Jul 27, 2005 #13

    EL

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    Appreciable cross-section for what: Pair production or photon-photon scattering?
     
  15. Jul 27, 2005 #14

    ZapperZ

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    Photon-photon collision cross-section.

    Zz.
     
  16. Jul 27, 2005 #15
    I don't know that the LHC can work in gamma-gamma mode. However, one of the operating modes of the proposed International Linear Collider (which accelerates electrons and positrons) is as a photon collider. Since this machine works in the TeV region there is certainly enough energy to produce all kinds of interesting particles, and the cross-sections are comparable to the cross-section for e+ e- annihilation at those energies.
     
  17. Jul 27, 2005 #16
    You can show using Lorentz invariance that a massless particle can not decay into any two particles. There is no such restriction on two massless particles colliding. So, as long as there is enough center-of-mass energy, two photons can collide to produce an electron-positron pair.

    If you like, you can think of pair production by a single photon in a medium as a two photon collision, where the second photon is provided by an electrically charged particle in the medium. After that, the physics is exactly the same as in any other gamma-gamma collision.
     
  18. Jul 27, 2005 #17

    EL

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    Well that depends on what comes out after the collision. For pair production the photons surely must have a large frequency. (A minimum frequency is easy to work out, just equal to the electron mass, but I don't have the numbers right now. Anyway to get any cross-section to talk about we would probably need more photon energy than that).
    However, in photon-photon scattering you need not have that large photon energy since the fermions are only virtual.

    In fact by using three incoming laser beams, it will probably soon be possible to generate scattered photons, even with wavelengths as large as in the visible spectrum. We just need lasers with somewhat better power than the existing ones. Well in fact it could be enough if we just had three of todays most powerful lasers at the same place...
     
    Last edited: Jul 27, 2005
  19. Jul 28, 2005 #18

    reilly

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    One photon can convert to a pair only if there is some stuff around, with which to interact. That's a result of standard energy and momentum conservation laws.

    But, these conservation laws do not preclude a direct conversion of 2 gammas into a pair, or vice versa. What's to prevent the process?

    Note: Rotate Compton scattering diagrams (by 90 degrees with the usual convention that "going up" means increasing time.) and, lo and behold, you have the diagrams for 2 gamma -> one pair.

    Regards,
    Reilly Atkinson
     
  20. Jul 28, 2005 #19

    EL

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    Nothing, but as ZZ noted, there exist no lasers with high enough frequency today.
     
  21. Jul 28, 2005 #20
    A sub - question on this subject: does photon - photon scattering contradict superpostition principle and / or independent luminal path principle ?
     
    Last edited: Jul 28, 2005
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