Here, I plotted the ratio between E’ and E so we can see how a photon’s energy impacts how
the scattered photon’s energy falls off more intensely as a function of theta, the scattering angle.
I also have the exact specified graph below.
The scattered energy is greatest at theta=0.
The scattered energy is the least at theta=pi or 180 degrees.
Right now there is no symmetry in the plot, but if I plotting theta from 0 to 2pi, there would have
been an axis of symmetry across theta=pi. This symmetry comes from cos(theta) =
cos(pi-theta), and from the presence of cos in the denominator of the compton scattering
equation.
The scattered energy never goes to 0. However, there is an notable limit case where as the
photon’s energy goes to infinity, the expression for the scattered photon becomes
2
𝑚𝑐
1−𝑐𝑜𝑠(θ)