Neutrino Excitation of the Giant Resonance in C 12

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\char22{}one-hole theory. We find that the total cross section levels out at 1.5\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}39}$ ${\mathrm{cm}}^{2}$ above 500 MeV. We also calculate the $\mathrm{N}_{}^{12}{}_{\mathrm{gi}.\mathrm{res}.}{}^{}\ensuremath{\rightarrow}{\mathrm{C}}^{11}+p$ 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 $\mathrm{B}_{}^{12}{}_{\mathrm{gi}.\mathrm{res}.}{}^{}$ state and found that some published numerical values should be changed.