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Positron annihilation

  1. Feb 18, 2009 #1
    Imagine you have electron and positron (leptons) falling towards each other. The interaction between these two is electromagnetic at long distances. It is well established that this reaction eventually leads to annihilation of these two particles. Now consider electron and proton(hadron) falling towards each other. Now, the interaction between these two is again electromagnetic at long distances. However, this process does not lead to annhilation, but a stable compound is formed instead (Hydrogen).

    Which force (in the framework of the standard model) is responsible for the difference between these two cases ?

  2. jcsd
  3. Feb 19, 2009 #2


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    The electron and the positron are each others antiparticles, whereas the protons antiparticle partner is the antiproton.

    In the interaction, all quantum numbers must be conserved, and a proton, which is build up by quarks, have more quantum numbers such as flavour and colour, so in the final state you can't get a photon which is an elementary particle with just spin as quantum number.

    So it is a conservation law consideration.
  4. Feb 19, 2009 #3

    to me, a conservation law, is the expression of some underlying symmetry of the governing equations (e.g. in classical physics, the consevation of the angular momentum corresponds
    to invariance of the Hamiltonian wrt to rotations, compare Noether theorem).

    Now you state that the necessity of conservation of the "special" proton quantum numbers as "flavour and colour" forbids the creation of a photon out of the interaction between electron and proton (this would be annihilation) . To me, positron/electron is a compatible pair of particles (being antiparticlea) whereas the system proton/electron obviously is less symmetric. Why there are then more conservation laws ?
    Last edited by a moderator: Feb 19, 2009
  5. Feb 19, 2009 #4


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    conservation of flavour and colour, on the quark level. And strong isopsin on the nucleon level.

    Why there are more conservation laws? Well you have more symmetries than U(1) - gauge symmetry, that is the obvious answer.
  6. Feb 19, 2009 #5
    if you look at the nucleon alone , then I agree, it has on its own additional symmetries. But I prefer to look at the compound system, which contains two particles: for this you gain additional (nucleus) symmetries but of course you lose the particle/antiparticle symmetry when you go from positron/electron to proton/electron. To me , it sounds like a trade-off ;-).

    But actually I would like to repeat my original question: Which force (in the framework of the standard model) is responsible for the difference between these two cases ? Naively speaking: if it is the electromagnetic interaction which is responsible that opposite charges are falling against each other, which force (or if you prefer interaction) counteracts the falling and prohibits annihilation in case of proton/electron.
  7. Feb 19, 2009 #6


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    Protons aren't fundamental. Quarks are. How do you annihilate a charge -1 electron with a charge +1/3 or -2/3 quark?
  8. Feb 19, 2009 #7


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    The proton has isospin symmetry quantum number, so since the proton also interact with the strong force, you can't get e^- + p -> Gamma

    Also you need to forget about the picture that particles are tiny balls which "falls into each other". There is no force that acts as something "repulsive" in the e^- + proton system. In the analogous way, there is no force acting repulsive in the Pauli exclusion principle in degenerate matter. The thing is simply that there are no available states to go into. In the same way, the electron can't annithilate with a proton to make a photn since in that interaction symmetry of isospin will be violated. (however this invokes the z-component of isospin. The total isospin can be violated, e.g in decay pion0 -> gamma gamma )

    An electron and a proton can interact with the Weak force, which CAN violate isospin and other symmetries, that is the peculiarity of the weak interaction.
    electron + proton -> Neutron + neutrino
    That is an ok interaction.

    But I have to stress again that you have to forget about the picture of particles as tiny balls and the interaction as a physical collision of such.
  9. Feb 19, 2009 #8
    I never mentioned that I consider the particles as tiny balls.
    I used the picture of "falling things" because the idea of electromagnetic interaction
    was developed from macroscopic observations, where you always observe that opposite charges are attracting each other
    via a certain force (simply consider the case of electrostatic discharge or any electric circuit). This idea of interaction was then extrapolated to the
    microscopical world, and it is still used in any QM/QFT calculations (this is at least my impression, please correct me if I'm wrong)

    Of course, you can argue that there is makes no sense to use classical notions in microscopic world, but then you might allow the question, whether it is the "same" electromagnetic interaction which we observe at macroscopic or microscopic scales.

    Do you suggest to consider this sentence as a basic postulate ? Or can it be derived
    from some more fundamental ?
  10. Feb 19, 2009 #9
    I let the electron collide with a suitable number of quarks, which might need to be in a specially prepared state.
  11. Feb 19, 2009 #10


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    Since you used that language, I argued against it - I read what I read.

    You are asking about the Pauli Principle now? Since that sentence was connected to my excursion to the P principle that there are no "force" that prevents things to happen, and in the case of the pauli principle it is from the postulate that identical fermions can not occupy the same quantum state.
  12. Feb 19, 2009 #11


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    So what you need is a many body interaction, or an effective interaction.

    If you want reading tips, we are more than helpful to assist. This is quite often asked question.
  13. Feb 19, 2009 #12
    this is sometimes the drawback of written communication ;-)

    No, I guess this is something for another thread, many topics inside one thread too easily lead to a kind of divergence (at least without moderator)

    Yes, a good readable, not too formal review article covering both theoretical and experimental aspects of this "many body interaction" would be surely helpful. In addition, are you aware of any good reference to experimental data on "spectral lines" of positronium ?
  14. Feb 19, 2009 #13


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    That statement was done for the pauli principle, so that's why I aksed. You asked about a sentence for the pauli principle, but now you didn't wanted an answer.. strange :P

    The statement "if there is no state to

    I think Griffiths book on elementary particle physics will suite you well, check out the newest edition. The thing is simple, there is no such coupling between the electron and the proton to make an electron and a proton make a photon.

    In the same way, an electron and a positive muon can't combine to make a photon. Then we have an interaction of 2 leptons, so we can totally forget about that "many body problem" of the proton. The leptons carry lepton family number, which would be violated in that interaction.

    And speak about divergences, why asking about positronium levels now? :S
  15. Feb 20, 2009 #14
    This is not strange, actually, when I posed my question about positronium, I was expecting some discussion about positronium. You brought PP into play, we could discuss this too but not in this thread.

    Why not, when speaking about positronium all aspects need to be considered, stereotyped thinking too often results in missing important points,

    Finally, after about 50 posts I realized, that I obviously chose the wrong forum for debating about advanced topics in physics. At least I do not have the impression, that my questions are taken seriously here.

    Nevertheless, thank you for your efforts and good luck


  16. Feb 20, 2009 #15


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    Well the thing is that I brought up the Pauli principle was to discuss the general feature of forbibben processes - that there is no "force" involved - since you seemed to have an impression that there is a "force" that prevails proton and electron to form a photon.

    When you later commented on a statement I did about the Pauli Principle, and asked for an elaboration, I was suprised, since that was just a side remark done by me. Therefore I asked if you really wanted an answer on that, and you said "no". That was strange I think.

    Your question was why eletctron + proton is stable and does not annihilate.

    I don't think this is an advanved question, we have quite more advanced things going on. The thing is perhaps that this question is asked by a person who does not have a strong background in particle phy
  17. Feb 20, 2009 #16
    You are, perhaps, making too many assumptions but this is always easy when one is sitting in an ivory tower. If you are not willing to answer my question in a polite and assumptionless way, you do not need to. I will survive this.
  18. Feb 20, 2009 #17


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    It is hard to help a person who does not explicit state his background and current status.

    When one make statements such as particles falling into each other and asking "which force is responsible within the standard model to prevent the particles to falling into each other" it is hard to judge if the person asking have understood even the basic concepts of the standard model.

    As I said, I read what I read.

    I want to answer your questions, but it is hard since I don't know where you are.

    regarding positronium energy levels, I have a theoretical paper which is quite recent who has a lot of references to experimental studies. Asking that question in a new thread would be more fruitful however.

    So, you came back, why?
  19. Feb 20, 2009 #18
    For me it does not matter (at least in a forum) what the background of a person is. If somebody is asking me a question in his "language", I first try to answer him in the same "language". Otherwise, he might get the impression, that his question is not taken seriously. I consider answering in a different "language" as bad style (but this is of course everyones free choice, how he answers).

    I used the provocative formulation with this "things falling against each other" to check the general reaction. I'm often surprised how dogmatic physics became: if one is trying to describe microscopic things and uses classical terminology for this purpose, he is too often immediately labelled (in best case) as "antiquated". Where there is written which language I shall use to describe something ? If I would work mainly with macroscopic things, say, lenght scale 28nm and above, I would maybe say (the following is not to be taken personally) : "what is all that advanced particle physics stuff about ? If you ask the particle guys to explain in their "language" how "Ohmic law works", they say, oh no, you need to use another formalism". But does it not mean, that the particle formalism is also somehow limited ? So why give that particle formalism a preference when discussing positronium ? Just because you can better calculate at the expense of understanding ?

    I'll give that some thought.

    Maybe I simply want to have the final say in this thread ;)
  20. Feb 20, 2009 #19


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    I more concerned to teach "the real deal" then by invoking false analogies. If someone thinks that there is some kind of repulsive force or similar that prevents electron and proton going into a photon, I must respond. The question was "which force within the standard model", and since the question tells quite much about the person who asked it one might easy suggest that there is a misunderstanding going one. The question is related to "which women is the president of the United states of America?". The answer is "none".

    If one knows basic quantum physics and something about the standard model of elementary particle physics want to know why a certain reaction is not possible, why not saying so? If I want to understand something at the level I am now, I don't use language so the guys I am asking think that I am a totally newbie and first needs to be taught the basics...

    If you ask particle physicists about particle physics, you should not be too surprised if you get particle physics answers and descriptions of physical processes. Since you seemed to have some disbeliefs in particle physics, we (I) tried to sort things up for you.

    Understanding and calculation abilities goes hand in hand. Believing that one understands something is not the same as actually understanding it. I can think that I understand what supersymmetry is since I know that it is a symmetry between bosons and fermions, but when I consult the Weinbergs QFT part 3, I am lost already on page 17.. so do I understand it or not?

    The experimental results are from the early 80's, but the paper I have is from 2008. Why are you interested in knowing these energy levels?
  21. Feb 20, 2009 #20
    Can I hijack this thread a little (since I don't see where it's going other than to argument and dispute over petty things like ego and pride) and ask, "Why, if this is a valid interaction, does this not take place on a daily basis?"

    I understand this interaction is due to the weak interaction, which is 10^-11 times as strong as the electomagnetic force. Is this what it means to be 10^-11 times as strong? That the interactions are 10^-11 times as likely to take place? Does anyone know why or is that just like asking why the fine structure constant is approx. 1/137?

    Does it make any sense to ask "how many virtual particles are exchanged between the proton and electron in one second of interaction in the hydrogen atom?"? Or is that just nonsense?
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