Electron antineutrinos from natural or artificial sources have typical energies E of a few MeV. They

Electron antineutrinos from natural or artificial sources have typical energies E_ν of a few MeV. They can be detected by observing the reaction ν̅_e + p → e⁺ + n in a detector medium containing free protons. The process is immediately followed by the positron annihilation e⁺ + e^- → 2γ and by the deposit of the energy of the gammas. The medium is surrounded by photo multipliers and this energy, called visible energy E_vis, is measured and the neutrino energy is inferred.

a) State the dominating process(es) of gamma energy deposit.

b) Calculate the maximum kinetic energy of the recoiling neutron (neglect proton neutron mass difference) for the typical value E_ν = 3 MeV.

c) Taking into account the answer to (b), find the relation between E_ν and E_vis(neglect the neutron recoil energy).

d) Which is the minimum detectable neutrino energy?