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:
$$E_{photon} + E_{initial \ electron} = E_{electron \ pair} + E_{positron \ pair} + \frac{1}{2}KE_{electron \ pair} + \frac{1}{2}KE_{positron \ pair}$$
$$\therefore E_{\lambda} + mc^2 = 3E$$