suppose you have a proton beam ($E=500MeV)$with a current of$$6 \cdot 10^{-12} A $$that is colliding with a gaseous hydrogen target which is $3 cm $ thick. The total cross section is $ 20 mb$. (Further suppose $p=1013hPa$ and $T=273K$)

Now I want to calculate the Luminosity which is defined as proton flux times number of target elements.

I tried to calculate the number of target elements $N$ by using the law of ideal gas: $$p \cdot V = N \cdot k_B \cdot T $$

But my Problem is that I don’t know how to find the Volume of the gas target? Can someone help?

Thanks! :)

Suppose you have a proton beam ($E=500\,\textrm{MeV})$ with a current of $$6 \cdot 10^{-12}\,\textrm{A} $$ that is colliding with a gaseous hydrogen target which is $3\,\textrm{cm}$ thick. The total cross section is $ 20\,\textrm{mb}$. (Further suppose the target pressure and temperature are $p=1013\,\textrm{hPa}$ and $T=273\,\textrm{K}$.)

Now I want to calculate the Luminosity which is defined as proton flux times number of target elements.

I tried to calculate the number of target elements $N$ by using the law of ideal gas: $$p \cdot V = N \cdot k_B \cdot T $$

But my Problem is that I don’t know how to find the Volume of the gas target? Can someone help?

Thanks! :)