Why does the cross section for Compton scattered photons decrease with increasing energy of incident photon? The cross section is independent of energy for energies less than electron's mass, but for greater energies the cross section of compton scattered electrons decreases, why?
 A: Think about what happens as you increase the photon energy, you begin to move away from merely dislodging  an electron to an energy regime in which pair production becomes more predominant. 
As you probably know, in the pair-production reaction, we need  a third body for momentum conservation. Not surprisingly, that  heavy body is
 one of the nuclei in the surface of the metal. It recoils just a little, due to it's  relatively high mass, so that leaves the majority of the incident photon's energy available for pair production.
We can also discover pair production in the region of an atomic, as opposed to free, electron within the metal. Obviously in this situation, much more energy is absorbed by recoil effects. In fact,  the normal cutoff turns out to be  $4mc^2$. 

So the combined cross section required for pair production is the sum of the cross sections associated with the above two reaction pathways. The total pair-production cross section is the sum of the two components, nuclear and electronic. These cross sections depend on the energy of the incoming photon.  At high energies, approximately equal to or greater than 100 MeV, pair production is the dominant mechanism of radiation interaction with matter.
So as you increase the incident energy, you begin to see less of the Compton effect and more pair production,   Compton scattering is still a factor, at low energy it can be related to the   photoelectric effect and when you increase the energy, it competes with pair production.

Energy Dependent Photoelectric Effect, Compton Scattering & Pair Production
A good example of this is incident photon energy on lead. Below 0.1 MeV, we find almost totally photoelectric processes occurring , then between  between 0.1 MeV and 2.5 MeV we can detect both  photoelectric and Compton processes  and finally, as the energy level rises above to between  2.5 MeV and 100 MeV, we can observe both Compton scattering and pair production. 
