The reaction \bar { \nu } _ { e } + p \rightarrow e ^ { + } + n is very important for low-energy ( E _ { \nu } \lesssim 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 well-understood analytically for E _ { \nu } \lesssim 60 MeV by calculating to { \cal O } ( 1 / M ) , where M is the nucleon mass .
The correct angular distribution is useful for separating \bar { \nu } _ { e } + p \rightarrow 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 \bar { \nu } _ { e } + d \rightarrow e ^ { + } + n + n and \nu _ { e } + d \rightarrow e ^ { - } + p + p .
Finally , in the reaction \bar { \nu } _ { e } + p \rightarrow 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 .