# Luminosity of beamdump experiments

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?

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