Neutrino and antineutrino cross sections in ¹²C

We extend our formalism of weak interaction processes, obtaining new expressions for the transition rates, which greatly facilitate numerical calculations, of neutrino (ν) and antineutrino ()-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 ν/-nucleus reactions ¹²C(ν, e⁻)¹²N and ¹²C(, e⁺)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 ν and , ii) steadily increase when the size of the configuration space is augmented, and particulary for ν/ energies > 200 MeV, and iii) converge for sufficiently large configuration spaces and final state angular momenta.