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I understood why a single photon can't be released from the annihilation of an electron and positron and that the common cases are 2 and 3 photons. I have two thing's I'm unsure of:

  1. why is the probability to let say 5 photons is less the let say 3? why is the probability go down as we increase the number of photons?

  2. how come we can have 2 and 3 photon emissions and still conserve the energy. is the energy gap between singlet and triplet states in positron sufficient to produce more photons?

Qmechanic
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Tomer Gigi
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  • Only the 2 photon decay (of an electron & positron initially at rest) produces 511 keV photons, so energy conservation isn't an issue. – PM 2Ring Mar 23 '22 at 13:00
  • i understood that the physics allows the system to be split into any number of photons just that the probability for more then 3 is small. even though it it's small if it happens does each photon has less energy then ? – Tomer Gigi Mar 23 '22 at 13:26
  • https://en.wikipedia.org/wiki/Positronium#Formation_and_decay_in_materials lists the various ways that the annihilation can happen, with rough probability estimates. Decays of Positronium by Czarnecki & Karshenboim gives some useful details. The (4 photon / 2 photon) branching ratio of para-positronium is ~$1.49×10^{-6}$, the (5 photon / 3 photon) branching ratio of ortho-positronium is ~$1.0×10^{-6}$. – PM 2Ring Mar 23 '22 at 14:19
  • Energy conservation must be obeyed, so the total photon energy must equal the original energy of the electron + positron system, that is, their rest mass-energies, plus their kinetic energies and potential energy. – PM 2Ring Mar 23 '22 at 14:25
  • why the fact that there are more photons means less probability ? – Tomer Gigi Apr 01 '22 at 16:54
  • We can model a simple decay by tossing a coin. Annihilation is a bit like tossing multiple coins or dice at once. Here's a crude model. We have 3 dice, and rolling a six means the annihilation decay occurs. If we roll 1 six we get 1 pair of photons, if we roll 2 sixes the decay releases 2 pairs of photons, and if we roll 3 sixes the decay releases 3 pairs of photons. Actual annihilation is a little more complicated, but hopefully that gives you the general idea. – PM 2Ring Apr 01 '22 at 20:34

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