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In this article we can read that energy of high energy gamma rays which have an astronomical source (for example gamma ray bursts) is about $10(TeV)$. This is more than enough for the creation of an electron anti-electron pair because the electron has a tiny rest energy [of about ${0,511}(MeV)$]. Also, the rest energies of the muon and the tau are small compared with the high energy of the photon. Then why aren't all the gamma photons (by means of the Feynman diagram, depicted below, where two real gamma photons go in and a real electron and a real anti-electron go out) converted to pairs of particle anti-particle pairs, so we can't receive the gamma photons on earth?

Are the electrons and anti- electron recombining again to produce a gamma ray?

enter image description here

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The two gammas in your diagram have to interact, i.e. coincide at a volume within the heisenberg uncertainty so as to have a measurable probability of interaction.

gamma rays which have an astronomical source (for example gamma ray bursts) is about 10(TeV).

The crux here is the word "source". If it is a point source , or an approximately point source, the paths of the rays will diverge due to the geometrical nature of a point source:

point source

Thus those ten GeV gammas will not cross each other's path so as to interact.

It is true that astronomical sources will not be point sources, except approximately, but the arguments hold, maybe gammas from an extended source might cross paths, but the ones at the edges will follow the law above, and those will be the gammas that survive and reach us.

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  • $\begingroup$ +1 off course...I f the photons are far apart they can't interact (via a virtual lepton), to produce a lepton anti-lepton pair. If that were the case all gamma photons would react with each other to produce such a pair. The chance exists that this happens does exist, but it is very very small. $\endgroup$ – descheleschilder Apr 18 '17 at 12:56
  • $\begingroup$ The gamma rays can of course interact with anything they meet along the way - photons from the cosmic microwave background for instance. $\endgroup$ – Rob Jeffries Apr 18 '17 at 13:12
  • $\begingroup$ @RobJeffries sure, but the density of matter in intergalactic space is not large "Estimates put the average energy density of the Universe at the equivalent of 5.9 protons per cubic meter, including dark energy, dark matter, and baryonic matter en.wikipedia.org/wiki/Outer_space. Limits on the source's intensity can be derived by this. $\endgroup$ – anna v Apr 18 '17 at 15:55
  • $\begingroup$ photon photon interaction has four em vertices and is small for a 10 GeV gamma to a CMB photon $\endgroup$ – anna v Apr 18 '17 at 15:58

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