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The hybrid model for electroweak single-pion production (SPP) off thenucleon, presented in [Gonz\'alez-Jim\'enez et al., Phys. Rev. D 95, 113007(2017)], is extended here to the case of incoherent pion-production on thenucleus. Combining a low-energy model with a Regge approach, this modelprovides valid predictions in the entire energy region of interest for currentand future accelerator-based neutrino-oscillation experiments. The RelativisticMean-Field model is used for the description of the bound nucleons while theoutgoing hadrons are considered as plane waves. This approach, known asRelativistic Plane-Wave Impulse Approximation (RPWIA), is a first step towardsthe development of more sophisticated models, it is also a test of our currentunderstanding of the elementary reaction. We focus on the charged-current$\nu$($\bar\nu$)-nucleus interaction at MiniBooNE and MINERvA kinematics. Theeffect on the cross sections of the final-state interactions, which affect theoutgoing hadrons on their way out of the nucleus, is judged by comparing ourresults with those from the NuWro Monte Carlo event generator. We find that thehybrid-RPWIA predictions largely underestimate the MiniBooNE data. In the caseof MINERvA, our results fall below the $\nu$-induced 1$\pi^0$ production data,while a better agreement is found for $\nu$-induced 1$\pi^+$ and$\bar\nu$-induced 1$\pi^0$ production.

Pion production within the hybrid relativistic plane wave impulse approximation model at MiniBooNE and MINERvA kinematics