Reactor antineutrinos
Nuclear reactors of power plants are intense sources of antineutrinos. A reactor emits isotropically about \(2\cdot 10^{20}\) antineutrinos per second for every GW of thermal power. Consider a project of experiments with reactor neutrinos.
(i) Compute the cross section of the interaction \(\bar{\nu}_e + p \to e^+ + n\).
(ii) Estimate the number of such interactions per year for \(E_{\bar{\nu}}=4\) MeV from a typical reactor of 3 GW. The target is water of mass 20 t. The distance between the detector and the reactor is 2 km.
(iii) Estimate the detector mass needed to detect \(10^5\) events \(\bar{\nu}_e + p \to e^+ + n\) at a distance \(L=50\) km from reactors with a total power of 30 GW. Take neutrino oscillations into account.