1. (12 pts) In 1987, a supernovae occurred in the Large Magellanic Cloud, a dwarf galaxy about 50 kilo-parsecs from the Earth. Eleven antineutrinos were detected by the Kamiokande- 13 second interval just before the arrival of visible light from the II experiment, in a supernovae. The detected antineutrinos had energies of about 15 MeV. These events are believed to be due to thermal emission of antineutrinos from the supernovae. The Kamiokande-ll detector measured Cerenkov light produced by antineutrino-proton scatter- ing, + p+ + n + e+, or antineutrino-electron scattering, D + e + D + e , in about 700 tons of water. The produced positron (or scattered electron) has sufficient energy so that its velocity is greater than the speed of light in water. Charged particles moving faster than light in a medium emit light (Cerenkov radiation) in a characteristic pattern which can be detected. The rate 17 of scattering events is given by the flux of projectiles times the number of = (flux) N targets times the cross section, 17 targets o, where the flux is the number of incident particles per unit area per unit time. The cross section for antineutrino-proton scattering is approximately 1047 m2 E 2 , where Ev is 1 MeV the antineutrino energy and Q = 1.3 MeV is the neutron-proton mass difference. (The cross section for antineutrino-electron scattering is about 100 times smaller at these energies.) Use the above information to estimate the total energy emitted by the supernovae in an- tineutrinos, assuming that this emission is nearly isotropic. Hints: Evaluate the number of protons in 700 tons of water. Then find the time-integrated flux (or total number of antineu- trinos per unit area) which, when combined with the cross section and number of protons, would yield the observed number of events. Assuming that this flux is emitted isotropically from the supernovae, find the total number of emitted antineutrinos and convert this to a total neutrino energy assuming that 15 MeV is the typical antineutrino energy.