Homework Help: Scattering of neotrinos off an iron block

1. Feb 26, 2010

Gal Winer

1. The problem statement, all variables and given/known data

Consider a beam of neutrinos moving in the x direction at energy of 200 GeV, and passing through a block of iron.

(a) The density of iron is ρ = 7.9gcm−3. In the rest frame of the neutrino, what is the flux of iron nuclei which are moving in its direction (give the answer in term of the neutrino velocity, the iron density, and the iron nucleus mass)?

(b) The neutrino might scatter off a nucleus with cross section σν. What is the probability for a neutrino to scatter in an infinitesi- mal length element dx? If N(x) is the number of surviving neu- trinos, How many neutrino scatterings in total will occur in an infinitesimal length element dx?

2. The attempt at a solution

(a) i wrote to flux to be: $$\phi=-\frac{V_{\mu}\rho}{M_{Fe}}\hat{x}$$
where the quantities have obvious meanings

(b) the cross section $$\sigma_{\mu}$$ is in units of: $$\frac{\frac{scattering}{second}}{flux}$$
so i try to multiply $$\phi\sigma_{\mu}$$ and get $$\frac{scattering}{second}$$. i'm not sure how to move from here to get a probability.

thanks

2. Feb 26, 2010