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Q & A: Electron-Positron annihilation

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Most recent answer: 10/22/2007
Q:
Does an electron-positron annihilation always creates 2 photons of 511 kev each? If so, what happens to the kinetic energies of the particles? (Since 511 kev is the rest mass of the electron, it seems that the total energy is not conserved.)
- David (age 26)
Montréal
A:
That's a very important question!

Your sense of what should be going on is exactly right- the energies of the particles that come out have to add up to be the same as the eenrgies of the ones that went in. The answer of course is no, you don't always get two photons of energy 511 KeV. That's what you (usually) get if the e+ and e- have no relative velocity. (Even then you can get a third photon,or more, to be produced.) If the e+ and e- are moving relative to each other, so they have nonvanishing kinetic energy in their common center-of-mass reference frame, then one possibility of the outcome is two photons which share equally the total energy of the collision. They each then have more than 511 keV of energy. If their center-of-mass is moving with respect to, say, some laboratory appratus which detects the outcome, then there is a well-defined procedure for predicting the energies and directions of these photons in the laboratory reference frame if you know it in the center-of-mass reference frame.

Studying what you get when you throw an electron and a positron at each other at high speeds has been the subject of high-energy physics research for the last 35 years or so, and a huge amount has been learned about the structure of matter and energy in the process. Some strange things can happen! If you throw the e+ at the e- at ever higher energies, different kinds of particles will get produced. At some energies, you get a resonance in the production of something new, a bit like tuning in a radio station on a dial. Get the energy too high or too low, and you see some level of background stuff. Get the energy of the collision just right, and the collision rate goes up, and a specific kind of thing gets produced very often. Specifically, you can make a quark and an antiquark together (matter and antimatter get produced in equal quantities in these interactions). If the energy is just right,the quark and antiquark will stick together and make a little bound-state system. These can be seen in a plot of the production cross-section of hadrons in e+e- collisions vs. the energy as the resonances rho, omega, phi, J/Psi, the rest of the Psi family, the Upsilon family, and the Z resonance. Here are some of the e+e- cross-section, showing these peaks in the production rate of hadrons. The rho and omega are excited resonances of light quarks, the phi is a bound state of a strange and antistrange quark, the J/Psi and other psi resonances are charm/anticharm quarks, the upsilon is a bottom/antibottom bound state, and the Z is the weak neutral force carrier. Crank the energy higher, and you'll find W pairs, pairs of top quarks, and maybe something new that hasn't been seen before.

If the energy's not tuned to one of the resonances, what's produced are quark pairs which are not bound states, but make other hadrons which fly from each other very rapidly, in sprays of particles. Two or more photons is possible, as are getting back e+e-, or other leptons, like mu+mu- and tau+tau-. You can even have a glancing blow where the e+ and e- do not annihilate but pass by each other, and their electromagnetic interaction is strong enough to produce some quarks -- e+e- -> e+e- q qbar, for example.

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Tom J. (w mike w)

(published on 10/22/2007)

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