Cross section?
If we imagine a surface F with the thickness dx in which target particles are located, we can calculate the probability that an incident particle interacts with a target particle by
described with the target particle density n, because, so to speak, n*F*dx target particles are "in an area F." Each of these target particles then has a small area. Adding these together and dividing them by the total area yields the probability of interaction.
However, in some textbooks, I saw that the length wasn't specified as infinitesimal (they simply wrote x instead of dx). Am I correct in assuming that the length must be infinitesimal?
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depends on what is on the left side of your equation. if there is something infinitesimales on the right, there must also be something infinitesimales on the left. I don’t know what you want to express with your w.
Ok so dN = n * dx * σ * Φ would be the scattered particles per second, where Φ stands for particles per second impinging on the surface. But would ΔN = n * x * σ * Φ also vote? I mean, you can really say that the probability that a particle interacts with the target particles in volume F*x is n*x*σ? With an area I know how to calculate the likelihood, but with a volume, the target particles can be one behind the other and that’s a bit confused.
that does not work with the dinensionen. left dimensionless, right 1/time.