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Name: Margaret
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This is about particle-antiparticle annihilation. What is seen in a frame of reference in which the total momentum of the annihilating pair is not zero? (e.g. moving e+ hits stationary e- in the lab frame). Can the 2 gammas still be the same frequency but not in opposite directions? Or will there be two unequal gammas? If so will they be in opposite directions? Hope this is intelligible.

Dear Margaret,

Yes, if the total momentum of the annihilating pair is not zero, in general the momenta of the two gammas will be different. That means, of course, that the two gammas will in general have different frequencies.

Overall momentum (and energy) is, of course, always conserved (unchanged).

Best, Dick Plano, Professor of Physics emeritus, Rutgers University


Photons of light have both energy and momentum. The directions and wavelengths will be such that both momentum and energy balance. Remember that energy includes mass energy (mc^2). One way to find the values is to adjust the reference frame with relativity so that total momentum equals zero. Determine the resulting photons, and then shift back to the original reference frame.

Dr. Ken Mellendorf
Illinois Central College

Momentum will be conserved in the annihilation. In other words, in any inertial reference frame from which you observe the interaction, the total momentum of the photons after the annihilation will be equal to the total momentum of the electron and positron before the annihilation.

If you look at the interaction in the center-of-mass reference frame, the total momentum is zero throughout: the electron and positron have opposite velocities (equal speed but opposite direction), and the produced photons have equal frequencies and move in opposite directions.

You are correct to suppose that things are different in another reference frame. If the electron and positron do not have exactly opposite velocities, the net momentum of the system will not be zero. The photons produced will preserve this non-zero net momentum. For this to happen, they must have different frequencies, they must move in directions that are not exactly opposite to each other, or both. The restrictions on the system are:

1. The total momentum of the two photons after the annihilation equals the total momentum of the electron + positron after the annihilation.

2. The total energy of the two photons after the annihilation equals the total energy (rest energy + kinetic energy) of the electron + positron.

3. The photons both move at the speed of light.

Richard Barrans, Ph.D., M.Ed.

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