Neutrino and antineutrino charge-exchange reactions on 12C

Understand

We extend the formalism of weak interaction processes, obtaining new expressions for the transition rates, which greatly facilitate numerical calculations, both for neutrino-nucleus reactions and muon capture.

• Explicit violation of CVC hypothesis by the Coulomb field, as well as development of a sum rule approach for the inclusive cross sections have been worked out.
• We have done a thorough study of exclusive (ground state) properties of $^{12}$B and $^{12}$N within the projected quasiparticle random phase approximation (PQRPA).
• Good agreement with experimental data achieved in this way put in evidence the limitations of standard RPA and the QRPA models, which come from the inability of the RPA in opening the $p_{3/2}$ shell, and from the non-conservation of the number of particles in the QRPA.