Neutrino Induced Coherent Pion Production off Nuclei and PCAC

We review the Rein--Sehgal model and criticize its use for low energy neutrino induced coherent pion production. We have studied the validity of the main approximations implicit in that model, trying to compare with physical observables when that is possible and with microscopical calculations. Next, we have tried to elaborate a new improved model by removing the more problematic approximations, while keeping the model still reasonably simple. Last, we have discussed the limitations intrinsic to any approach based on the partial conservation of the axial current hypothesis. In particular, we have shown the inability of such models to determine the angular distribution of the outgoing pion with respect to the direction of the incoming neutrino, except for the $q^2= 0$ kinematical point.