I was visiting the Australian Synchrotron earlier today as part of a tour group; as the guide was going over the booster and storage rings I was reminded of something I learnt of quantum.
If I know my quantum well enough, every so often, there are spontaneous pairs of electrons and positrons created and destroyed everywhere. Now I know that they don't last very long, but I got to thinking, what would happen if a pair was created at just the right instant for the positron to collide with one of the super-high-energy electrons in the booster or storage ring of a synchrotron?
When I asked our guide he said that the probability was pretty low since there were only 1x10^6 electrons in there and naturally the pair would have to generate at just the right spot at just the right time. Ultimately he wasn't quite sure what would happen if the circumstances were correct for it though.
I have been doing some further thinking, if I remember correctly, these pairs form as an electron spiralling in towards a central positron. I think that therefore at ordinary energies any nearby electrons would be repelled by the electron around the positron (which is a little reminiscent of the atomic stuff of first year chemistry).
Question is, could an electron, at the sorts of energy levels of the order of giga-electron-volts, get past the spiralling electron and collide with the positron instead of its paired electron doing so? As this energy could not simply vanish, would you then get a lonely (now unpaired) electron and an explosion? or would the energy somehow transfer itself to the other electron?
My interest here is towards what would actually happen if all circumstances were just right; also appreciated would be anyone who might be able to tell me the theoretical frequency of electron-positron pairs being spontaneously generated, as well as helping me to think up a way of determining the probability of finding an electron within one of the rings (for instance, perhaps if electrons can be considered to have an effective 'volume' within which they are most likely to appear and comparing that to the volume of the ring?)
Thanks for your time, I really appreciate it.