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We present a microscopic model for neutrino induced one-pion production offthe nucleon and its implementation for the purpose of calculating coherent pionproduction in nuclei.  We further criticize the use of the Rein--Sehgal model for coherent pionproduction by low energy neutrinos. In particular, we show how theapproximations in that model give rise to a much flatter differential crosssection in the $\eta=E_\pi(1-\cos\theta_\pi)$ variable. We discuss thelimitations intrinsic to any approach based on the partial conservation of theaxial current hypothesis and the inability of such models to properly determinethe angular distribution of the outgoing pion with respect to the direction ofthe incoming neutrino. We show the effects of those limitation for the case ofthe $\frac{d\sigma}{d\eta}$ differential cross section.

Neutrino induced weak pion production off the nucleon and coherent pion production in nuclei at low energies