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
PDF plots
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.
You can find out more about particle physics
here at particleadventure.org.
Tom J. (w mike w)
(published on 10/22/2007)
