Number of Events Detected (Neutrino Collisions)

[gradivcurl]

Homework Statement

Hi everyone,

So I am asked to detect the number of neutrino events that occur from them entering 3000 metric tonnes of pure water. I am given that t=10s , E(neutrino)=10MeV and that the electron cross section is 10^-47 m^2 . This was the famous neutrino experiment at Kamiokande for the explosion of SN 1987a. I also know the neutrino flux on Earth due to this event ~ 4x10^13 s^-1m^-2.

Any help starting off this problem is appreciated!

Homework Equations

The Attempt at a Solution

I know I need to find the rate at which electrons are scattered by neutrino collisions in the water . So the reaction is just ν+e^-→v+e^-.

I'm guessing that the number of events E detected will be E = collisional frequency * elapsed time

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[mfb]

I'm guessing that the number of events E detected will be E = collisional frequency * elapsed time

Right.

How are event rates and cross-sections related?
Can you calculate the probability that a single electrons takes part in a reaction, and the total number of electrons in the detector?

 

[gradivcurl]

So the number of events will be N = σLt , where σ is the neutrino-electron cross section , L is the integrated luminosity, and t =10s ? The total number of electrons in one molecule of h20 is 10. So in 3,000,000,000g of water we have # electrons = (mass of water * Avogadro's number* 10 electrons) / molar mass of H20

 

[mfb]

If you take L as integrated luminosity, then it includes the 10 seconds already.
N is the number of events per electron?
Looks good.