According to this Wikipedia article, the Electron–positron annihilation forms two gamma photons from an electron and a positron collision. However, according to this other article from Wikipedia, pair production can yield the positron and electron from a single gamma photon. How come this be the case? Why would two particles collide and form 2 photons and then each one of these photons would make 4 particles?

Annihilation: enter image description here

Pair production: enter image description here

This behavior is reversible, so we would generate more and more electrons and positrons implying an increase in both energy and mass as time progresses. In other words:

enter image description hereenter image description here+enter image description here

This is wrong because of conservation laws.

Now, this diagram shows a somewhat more understandable process, however, I do not understand what exactly does the line in between both circles represents. And what do the red arrow heads mean? Wikipedia article for the image. enter image description here


3 Answers 3


A single photon can pair produce only in the presence of some other body like an atomic nucleus. This extra body is required to conserve momentum. In the case of pair production from a single photon the photon has to have enough energy to produce both the particle and antiparticle e.g. to produce an electron positron pair it would need an energy of 1022keV.

When an electron and positron annihilate they produce two 511keV photons, so neither of these two photons has enough energy to go on to create another electron positron pair.

In principle two 511keV photons can interact with each other to produce an electron positron pair, but it turns out the probability for this process is vanishingly small so in practice it is never observed.

Re the Feynman diagram: it is very, very important to understand that a Feynman diagram is not a depiction of what happens to the particles. It is a pictorial representation of an integral called the propagator. You should not attempt to interpret it as some physically occurring process as this will mislead you.


Note the Feynman diagram that describes how a single photon can give a pair of electron positron in the link you give:


The gamma coming out of the Z (a nucleus with an electric field) is called virtual and the two particles are the effect of the gamma hitting a nucleus which allows for momentum conservation of the pair creation. A single photon has no center of mass and moves always with velocity c. The electron positron have a center of mass, and can be created with the pair momentum zero, (one can always go to the inertial frame where the pair is at rest) so a single photon from conservation laws cannot create a pair.

Your proposal at the end of the question would violate energy conservation too.

From the Feynman diagram you show one can calculate the probability for annihilation when positron scatters of an electron. At the center of mass frame the two photons leave in equal and opposite directions and momentum and energy is conserved. The line joining the vertices is a virtual electron . One has to study quantum field theory to understand the mathematics.

  • $\begingroup$ I see. So, how many photons would be needed to make the pair? My guess would be two. By the way, I know the proposal is wrong. But it illustrates my understanding from the equations in the Wikipedia articles. $\endgroup$ Jul 22, 2021 at 5:04
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    $\begingroup$ Two are enough, for momentum conservation at the center of mass, which is what assuming the nucleus field does. Scattering of three particles of any type, photon or not is very improbable, due to the nature of particle interactions. $\endgroup$
    – anna v
    Jul 22, 2021 at 5:12
  • $\begingroup$ Now, my issue with the diagram is that I do not understand it. From top-down, it shows a gamma photon interacting with a positron somewhere. This interaction produces a neutrino. The neutrino then spontaneously splits into another gamma photon and an electron. The diagram doesn't show where this occurs. How is this similar to the equations? Please check the question, I've added more info. $\endgroup$ Jul 22, 2021 at 5:26
  • $\begingroup$ There are no neutrinos. In feynman diagrams moving against the arrows meansan antiparticle. so the line is an electron line moving downwarsds becomes virtual and exits as electron. hyperphysics.phy-astr.gsu.edu/hbase/Particles/expar.html see page three for "virtua. You need mathamatics of physics to be able to understand. Lets stop this here. $\endgroup$
    – anna v
    Jul 22, 2021 at 5:38

Electron-positron annihilation requires the production of two photons to conserve momentum (the two photons must move in opposite directions).

For pair production, a single incoming photon will not produce an electron-positron pair since momentum conservation would not hold.

But momentum conservation will occur and this process will be allowed if you have some other charged particle close by that will take care of the photon momentum (such an interaction will usually occur near a nucleus).

You have also added a Feynman diagram and ask what the line in between means. This line is called a propagator and mathematically expresses the probability amplitude that a particle interaction happens between two spacetime points. You seem to imply that the particles follow paths described by these diagrams. The particles do not have classical trajectories as the diagrams seem to imply. Rather, they are pictorial descriptions of mathematical objects.


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