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I would like to make a scattering toy simulation as a computational physics project. I'm having issues visualizing which parameter of the scattering function I need to compare with the randomly generated number to consider that the event was scattered or not.

Using $$ \frac{d\sigma}{d\Omega} = \frac{1}{\rho_n t \Delta \Omega} \frac{\mathrm{Flux_{scattered}}}{\mathrm{Flux_{incident}}} $$ where $\rho_n$ is the nuclear density of the material that will scatter, $t$ is the thickness, and $\Delta \Omega$ = $4\pi$ since in this toy model the detector will be a sphere around the scattering (and then I won't need to integrate). If I know the total cross-section $\sigma_{tot}$, is it ok to do something like this:

  • Generate $N$ random numbers $n_i$

  • If $n_i \le 4\pi \sigma_{tot} $ then I had a particle scattered

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  • $\begingroup$ Note that $n_i$ is just a unitless number whereas $\sigma$ has units of area, so you can't directly compare them. Try to think about what unitless number you could write down that you'd want to compare with your random numbers. $\endgroup$
    – kaylimekay
    Commented Dec 29, 2020 at 5:54
  • $\begingroup$ Hi @kaylimekay, in this case, in addition to the $4\pi$ multiplication, I would need to multiply the total cross-section by $\rho_n t$ for this comparison hight? Thank you for your help! $\endgroup$
    – jaspior
    Commented Dec 29, 2020 at 6:44

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