# Pair production: photon collides with an electron

During pair production, a high energy photon collides with an electron which then creates an electron–positron pair, but what happens to the electron that the photon collides with?

I am asking because I am trying to set up the laws of conversation of energy but I am not sure what happens to the electron after the collision.

Suppose the high energy photon collides with the electron which then produces the electron-positron pair, will the conversation of energy look like the following:

$$E_{photon} + E_{initial \ electron} = E_{electron \ pair} + E_{positron \ pair} + \frac{1}{2}KE_{electron \ pair} + \frac{1}{2}KE_{positron \ pair}$$

$$\therefore E_{\lambda} + mc^2 = 3E$$

Nothing happens to it.

The electron - or the nucleus or whatever other object that interacts with the photon to make pair production possible - just participates for momentum conservation, since a single photon producing two massive particles is kinematically forbidden. The usual pair production reaction is $$\gamma + Z \to f^+ + f^- + Z,$$ where $$Z$$ is e.g. an electron or a nucleus and $$f$$ is some charged particle being produced.

• So suppose the high energy photon collides with the electron which then creates the electron-positron pair, what will the conservation of energy look like? Will it look the following: $$E_{photon} + E_{initial electron} = E_{electron} + E_{positron} + \frac{1}{2}KE_{electron} + \frac{1}{2}KE_{positron}$$ $$E_{\lambda} + mc^2 = 3E$$ Apr 4, 2020 at 22:11

An electron does not create an electron-positron pair. A photon creates an electron-positron pair. For a photon to do this it must be "off mass shell". It must be a high energy product of an earlier collision.

• Yes, that part I am aware of, that the photon is what creates the pair but when the high energy photon collides with the electron, what happens to the electron afterwards? Apr 4, 2020 at 21:49
• The photon does not collide with an electron. It spontaneously creates the pair, given only that it was itself created in a suitable process, which could have involved electrons or other particles. Those other particles either just wander off, or they may also decay, depending on the process, but they no longer have anything to do with pair production from the photon. Apr 4, 2020 at 21:54
• But my books explicitly says it does. Apr 4, 2020 at 22:02
• I can't comment on what your book says without reading it myself, but I can tell you that any collisions are prior to the creation of the photon which decays into a pair. Apr 4, 2020 at 22:05
• It may be that your book is describing a process in which a high energy photon collides with, and is absorbed by, an electron but this is only one possible collision which can result in pair production. The electron recoils and emits an off mass-shell photon, which then decays to a pair. Apr 4, 2020 at 22:36

A photon does not need to collide with an electron to have pair production.

During pair production, a high energy photon (near a nucleus) ceases to exist, and the photon's energy is transformed into a electron-positron pair. Energy needs to be conserved, thus, the energy of the incoming photon needs to be at least the energy (rest masses) of the electron-positron pair.

For pair production to occur, the incoming energy of the interaction must be above a threshold of at least the total rest mass energy of the two particles, and the situation must conserve both energy and momentum.[1]

https://en.wikipedia.org/wiki/Pair_production

Now momentum needs to be conserved too, that is why the incoming photon needs to be near a nucleus, which receives a recoil.

• But what happens when the photon does collide with an electron which then creates an electron-positron pair? What happens to the electron. Apr 4, 2020 at 22:02
• @Robben if it is an electron then it receives a recoil. Apr 4, 2020 at 22:09
• Why the downvote? Apr 4, 2020 at 22:09
• I didn't downvote, not sure who did. Apr 4, 2020 at 22:12