A unified approach for nucleon knock-out, coherent and incoherent pion production in neutrino interactions with nuclei

submitted to Phys. Rev. CWe present a theory of neutrino interactions with nuclei aimed at the description of the partial cross-sections, namely quasi-elastic and multi-nucleon emission, coherent and incoherent single pion production. For this purpose, we use the theory of nuclear responses treated in the random phase approximation, which allows a unified description of these channels. It is particularly suited for the coherent pion production where collective effects are important whereas they are moderate in the other channels. We also study the evolution of the neutrino cross-sections with the mass number from carbon to calcium. We compare our approach to the available neutrino experimental data on carbon. We put a particular emphasis on the multi-nucleon channel, which at present is not easily distinguishable from the quasi-elastic events. This component turns out to be quite relevant for the interpretation of experiments (K2K, MiniBooNE, SciBooNE). It can account in particular for the unexpected behavior of the quasi-elastic cross-section