The angular distribution of the reaction ν̄ e + p → e + + n

The reaction ν̄e + p → e+ + n is very important for low-energy (Eν ∼ 60 MeV) antineutrino experiments. In this paper we calculate the positron angular distribution, which at low energies is slightly backward. We show that weak magnetism and recoil corrections have a large effect on the angular distribution, making it isotropic at about 15 MeV and slightly forward at higher energies. We also show that the behavior of the cross section and the angular distribution can be wellunderstood analytically for Eν ∼ 60 MeV by calculating to O(1/M), where M is the nucleon mass. The correct angular distribution is useful for separating ν̄e + p → e+ + n events from other reactions and detector backgrounds, as well as for possible localization of the source (e.g., a supernova) direction. We comment on how similar corrections appear for the lepton angular distributions in the deuteron breakup reactions ν̄e + d → e+ + n + n and νe + d → e− + p + p. Finally, in the reaction ν̄e+p→ e+ +n, the angular distribution of the outgoing neutrons is strongly forward-peaked, leading to a measurable separation in positron and neutron detection points, also potentially useful for rejecting backgrounds or locating the source direction.