Neutrino-nucleus interactions and nuclear giant resonances

We present new theoretical results of the flux averaged ¹²C(v_e,e^-)¹²N and ¹²C(v_μ,μ^-)¹²N cross sections with v_μ (v_e) coming from the decay-in-flight (decay-at-rest) of π⁺ (μ⁺). The microscopic approaches used are charge-exchange RPA, charge-exchange RPA among quasi-particles (QRPA) and the Shell Model. We show that the exclusive cross sections are in nice agreement with the experimental values for both reactions when a large-scale shell model calculation is performed. Concerning the v_μ inclusive cross section the calculated values overestimate the experimental ones by 20 - 30%, while the v_e inclusive cross sections are in agreement within experimental error bars with the measured values. The shell model prediction for the decay-in-flight neutrino cross section is reduced compared to the RPA one because of the different kind of correlations in the calculation of the spin modes (in particular, the quenching of the 1⁺) and also because of the limited shell-model space.