Charged-current single-pion production in scattering off ${}^{12}\text{C}$ is investigated for neutrino energies up to 1 GeV. A model of Nieves et al. [Phys. Rev. C 83, 045501 (2011)] is further developed by performing exact integration and avoiding several approximations. The effect of exact integration is investigated both for double-differential and total neutrino-nucleus cross sections. The impact of nuclear effects with in-medium modifications of the $\Delta \left(1232\right)$ resonance properties as well as an effective field theory nonresonant background contribution are discussed. The dependence of the fraction of $\Delta \left(1232\right)$ decays into $n$-particle–$n$-hole states on incident neutrino energy is estimated. The impact of various ingredients of the model on the ratio of muon to electron neutrino cross sections is investigated in detail.

• Received 5 November 2012

DOI:https://doi.org/10.1103/PhysRevC.87.065503