I am trying to understand the difference between the 3 above mentioned terms but i have it hard to picture each of them. I know that the geometrical cross section would be the physical area for which we would have a collision (billiard spheres) and i know that the scattering cross section if we have a charged nucleus and an electron colliding with it, will be bigger then the physical cross section of the nucleus. But what i cannot understand are the following 3 things:
How does the total cross section in case of a scattering event looks like? Like how to visualize that.
How is it related to the differential cross section (geometrically). I assume if i integrated in spherical coordinates the diff. cross section I should get the total one.
And most importantly ,we were given the following formula without actually showing the logic of how it was derivated:
Total rate $W_r$ of scattering events $dN_s$ per unit of time:
$W_r = dN_s/dt = J \cdot N_t \cdot \sigma_{tot}$, where
J is the flux density, $N_t$ is the number of the nuclei of the target object and $\sigma_{tot}$ is the total cross section.
If there are links/ docs with detailed explanation to the above 3 questions (specially the last one) and about the Rutherford scattering, that would also help!
