There is formula for luminosity of fixed-target experiments: $$L = \Phi\rho l$$ $\Phi$ is the flux of incoming beam (particles per second), $\rho$ - density of target, $l$ - lenght of target. We can see that if we increase $l$ up to infinity luminosity will increase to infinity as well. For me it doesnt seem right. As I understood flux in material is a function of depth $\Phi(d)$. This mean that luminosity should be something like this: $$L = \int_{0}^{l} \rho \Phi(x) \text dx$$ Like this luminosity should be finite value even if lenght is infinite. Am I wrong somewhere?

  • $\begingroup$ The first formula is for thin targets. $\endgroup$ Jun 7, 2021 at 3:37
  • $\begingroup$ @KeithMcClary i see. Have you encountered formula for thick targets? $\endgroup$ Jun 7, 2021 at 9:13
  • $\begingroup$ You would have to take in to account the decrease in flux with depth due to interactions. $\endgroup$ Jun 7, 2021 at 14:11
  • $\begingroup$ With simplifying assumptions, the decrease in $\Phi(x)$ over $dx$ should be proportional to $\Phi(x)$. $\endgroup$ Jun 7, 2021 at 14:55


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