• The cross-section of the interaction of a high-energy neutrino and a hadron (proton or neutron) is roughly \(\sigma = 10^{-34} \text{ cm}^2\) for neutrinos with 10 TeV energy. For higher energy neutrinos, this cross-section grows proportionally with \(E^{1/2}\), where E is the neutrino energy.
• The fraction of neutrinos that cross some material with thickness z, in which the number density of hadrons is n, is \(e^{-n\sigma z}\).
• What is the highest neutrino energy for which the majority of neutrinos cross the Earth and therefore can reach neutrino observatories like IceCube?
• At this energy, what fraction of the neutrinos that cross the IceCube neutrino observatory (assume its size is a cube with each side being 1km long)?