| Popis: |
The cross section for neutrino-induced nuclear reactions is presented in the form of a multipole expansion, appropriate for the excitation of nuclear levels of a definite spin and parity. The theory is then applied to the $T=1$ levels of $^{12}\mathrm{C}$, knowledge of their excitation cross sections being required for both low-energy ${E}_{\ensuremath{\nu}}\ensuremath{\le}53$ MeV, with neutrinos from stopped muons) and high-energy (${E}_{\ensuremath{\nu}}\ensuremath{\sim}\mathrm{GeV}$) neutrino experiments that use counters containing carbon. We take a phenomenological approach, determining the needed transition densities from fits to the measured form factors of these levels for the closely related electroexcitation process. While the low-energy cross section is dominated by the excitation of the ${1}^{+}$ ground state of $^{12}\mathrm{N}$, the high-energy cross sections receive their largest contributions from both positive-parity spin-flip states and especially from the ${1}^{\ensuremath{-}}$ giant-resonance levels, with additional strength from ${3}^{+}$ and ${2}^{\ensuremath{-}}$, ${4}^{\ensuremath{-}}$ levels. |
