Show that the creation of an electronpositron pair or any ma

Show that the creation of an electron-positron pair (or any matter anti-matter pair) by a single photon is not isolation

Solution

At first the electron and positron pair is possible to create by photon beam if the energy of the beam is of ~50 -110 GeV (you can go to the research article published in PHYSICS LETTER in 1985).

Now, it is not possible with the single photon since it does not have enogh energy to create it.

itr can be understand with momentum conservation

Pe- + Pe+ =Pphoton

At threshold, all the energy of the photon becomes the mass of the electron and positron so the electron and positron have KE=0.

h/lambda =Pe- + Pe+ 2me x c = mexu- + mexu+

2c= u- + u+

So, there must be two outgoing photons in opposite direction for the process.

Therefore,it is not possible with single photon