Consider a possible experiment looking for neutrino oscillations using as a source a nuclear reactor complex of 3 GW, producing 6 x 10²⁰ s^-1 electron antineutrinos. You are planning a detector containing free protons (such as a liquid scintillator) to observe the reaction ν̅_e + p → e⁺ + n. In the MeV energy range the cross section of the process varies strongly with energy, but for a rough calculation assume the value σ = 10^–47 m². You want to measure the νe flux at two distances, L₁ = 100 m and L₂ = 2 km. Calculate the proton masses necessary in the two detectors to have 100 counts per day.