Neutrino Excitation of the Giant Resonance inC12

The differential and total cross sections of the neutrino excitation of the giant resonance (gi. res.) in ${\mathrm{C}}^{12}$ are calculated using the Brown one-particle—one-hole theory. We find that the total cross section levels out at 1.5×${10}^{-39\mathrm{}}$ ${\mathrm{cm}}^2$ above 500 MeV. We also calculate the $\mathrm{N}_{}^{12}{}_{\mathrm{gi}.\mathrm{res}.\mathrm{}}{}^{}\to {\mathrm{C}}^{11}+p$ spectrum using Boeker's method, because this decay can identify the neutrino reaction in a bubble chamber. To check our programs we recalculated muon-capture matrix elements for transitions to the $\mathrm{B}_{}^{12}{}_{\mathrm{gi}.\mathrm{res}.\mathrm{}}{}^{}$ state and found that some published numerical values should be changed.