# Intensity of Compton scattering photons

In various sources (1, 2, 3, 4, to name a few) I have seen this graph shown below, that shows how intensity depends on the wavelength of the scattered photon $$\lambda'$$.

Now, I do understand what this graph shows conceptually: front-scattered photons preserve most of it's energy, so $$\lambda'=\lambda_0$$, and as the scattering angle increases from 0°to 180° (back-scattering), photon loses part of it's original energy so the energy of scattered photon is smaller (i.e. wavelength is larger $$\lambda'>\lambda_0$$).

What I don't understand is: how is intensity found analytically in this case? My guess is that these graphs are a depiction of experimental results, and intensity is being measured by detectors placed at certain angles.

But, also, I guess that there must be an analytical way to express this intensity, so that when it is graphed for certain $$\theta$$, it shows a pattern as seen in the picture above.

I tried using Planck's radiation intensity formula combined with $$\Delta\lambda=\frac{h}{mc}(1-\cos\theta)$$, but it didn't meet with the graphs above.

So my question is: how is intensity expressed analytically as a function of $$\theta$$ and $$\lambda'$$ in the case of Compton scattering?