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What is the case when a positron electron annihilation gives two photons and one of the photons has as small frequency as possible? I guess it is when the electron and positron are at rest before they annihilate. But what if doppler effect or conservation of momentum can cause smaller frequency for one of the photons?

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    $\begingroup$ The energy of a photon is not an intrinsic property as it depends on the frame of reference from which it is observed. $\endgroup$ Jun 21, 2016 at 22:57
  • $\begingroup$ So if the positron and electron is at rest in one frame, in another frame one of the photons will have smaller frequency because of the doppler effect. So least frequency is achieved with maximum doppler effect? $\endgroup$
    – Rasmus
    Jun 21, 2016 at 23:03
  • $\begingroup$ You can make the energy/frequency of one almost zero... just not both at the same time. Is that what you are asking? $\endgroup$
    – CuriousOne
    Jun 21, 2016 at 23:04
  • $\begingroup$ I've got it now. Yes that was what I was asking for. $\endgroup$
    – Rasmus
    Jun 21, 2016 at 23:07

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The annihilation of an electron positron pair most commonly creates either two or three photons in the final state (depending on the original angular momentum of the pair).

In each case both energy and momentum must be conserved so there are kinematic limits on the energies of the photons as measured in the center of momentum frame of the original pair.

You are presumably being asked to examine these two cases and find the highest energy that any single photon can have in that frame.

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