Neutrino and antineutrino cross sections in 12C

Abstract. We extend our formalism of weak interaction processes, obtaining new expressions for the transition rates, which greatly facilitate numerical calculations, of neutrino (휈) and antineutrino (휈̃)-nucleus reactions and the muon capture. We have done a thorough study of exclusive (ground state) properties of 12B and 12N within the Projected Quasiparticle Random Phase Approximation (PQRPA). Good agreement with experimental data is achieved in this way. The inclusive 휈/휈̃-nucleus reactions 12C(휈, 푒−)12N and 12C(휈̃, 푒+)12B are calculated within both the PQRPA, and the Relativistic QRPA (RQRPA). It is found that the magnitudes of the resulting cross-sections: i) are close to the sum-rule limit at low energy, but significantly smaller than this limit at high energies both for 휈 and 휈̃, ii) steadily increase when the size of the configuration space is augmented, and particulary for 휈/휈 ̃ energies> 200 MeV, and iii) converge for sufficiently large configuration spaces and final state angular momenta. 1