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During particle-antiparticle annihilation, are the photons expelled perfectly perpendicular to the original direction of the particle-antiparticle pair?

There is very little information on the web about this topic, though I read a book awhile ago that stated that the photons are emitted from an angle, not perfectly perpendicular to the particles. Is this true? If so why?

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  • $\begingroup$ Remember that the energy and momentum of the process need to be conserved. $\endgroup$ – SchrodingersCat May 30 at 14:55
  • $\begingroup$ @SchrodingersCat Yes, but this doesnt explain why they are emitted at an angle. $\endgroup$ – Lochlan Crawley May 30 at 15:05
  • $\begingroup$ Maybe you can write down some equations and show your working. $\endgroup$ – SchrodingersCat May 30 at 15:07
  • $\begingroup$ Do the particle and antiparticle have definite trajectories before they annihilate? $\endgroup$ – Alfred Centauri May 30 at 15:29
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During particle-antiparticle annihilation, are the photons expelled perfectly perpendicular to the original direction of the particle-antiparticle pair?

No.

In the center-of-momentum frame, the two photons can come out back-to-back in various directions, with a probability distribution. Any direction is consistent with energy-momentum conservation.

When non-relativistic electrons and positrons annihilate, all directions are equally likely for the photons; the differential cross section is isotropic. When the electron and positron are ultra-relativistic, the photons strongly tend to be along the direction of motion the annihilating particles. (This is for unpolarized beams.)

The calculation of the differential cross section for any energy may be found here.

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  • $\begingroup$ Thank you very much for the inciteful response! $\endgroup$ – Lochlan Crawley May 30 at 23:47

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