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Cross section of pair production with interaction of photon increases with energy. But why does that happen? I want a non mathematical answer on this.

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A photon, no matter how much energy it has, will not turn into a pair of particles because of conservation of momentum and energy. The photon does not have a center of mass because it has no rest frame . Any pair of particle-antiparticle will have a rest frame, so there is a reductio ad absurdium.

In order for a pair to appear there must exist a target nucleus which will interact with the gamma and together with the pair obey energy and momentum conservation, the nucleus taking up momentum and energy.

So any cross section will depend on the nucleus, i.e. the target, that the gamma hits. There are tables on this, depending on the nucleus.

This is a simple Feynman diagram that also shows pictorially what is necessary to get a cross section to first order:

pairprod

Feynman Diagram of electron-positron pair production. One can calculate multiple diagrams to get the cross section

Thus the cross section will depend on the field of the particular nucleus. For example this plot (fig 2.2) has the cross sections calculated for pair production in carbon, for the specific needs of an experiment:

gammacross

The cross section rises with energy because the higher the energy of the gamma, the more it penetrates the nucleus, where the electric fields are stronger,(1/r^2). Higher frequencies probe smaller distances, and the probability of interacting with the electric field larger. There is a saturation when the gamma energy is high enough, it will scatter with the quarks which exist in the nuclei, and create jets. The specific pair production crossection reaches a plateau. Also as the energy rises, more pair production channels will open .

This is about non mathematical as I can get.

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