The question is in the title: How is the cross section related to the probability of a process?
If I have the total cross section $\sigma$ of a process how is this related to the probability of this process? What about the differential cross section?
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I have to build a MonteCarlo from scratch and I find myself stuck.
I have to simulate a proton losing energy into an absorber and producing delta-rays.
If it were a photon I could use the formula $p=\mu \exp(-\mu s)$ were $\mu$ is the macroscopic cross section $s$ is the space between two collisions a nd $p$ is the probability of a collision. In this case I could generate a random number $p$ and invert the formula to get $s$.
In the case of the proton, I can use the Bethe-Block to simulate the loss of energy between two collisions.
But my problem is: which is the probability that a proton collide with an electron of the absorber? It should be proportional to the cross section of the process, but which is the cross section and how is it actually connected with the probability of a collision?