  The current and near-future neutrino oscillation experiments require
significantly improved neutrino-nucleus reaction models. Neutrino-nucleon pion
production data play a crucial role to validate corresponding elementary
amplitudes that go into such neutrino-nucleus models. Thus the currently
available data extracted from charged-current neutrino-deuteron reaction data
($\nu_\mu d\to \mu^-\pi NN$) must be corrected for nuclear effects such as the
Fermi motion and final state interactions (FSI). We study $\nu_\mu d\to
\mu^-\pi NN$ with a theoretical model including the impulse mechanism
supplemented by FSI from $NN$ and $\pi N$ rescatterings. An analysis of the
spectator momentum distributions reveals that the FSI effects significantly
reduce the spectra over the quasi-free peak region, and leads to a useful
recipe to extract information of elementary $\nu_\mu N\to \mu^-\pi N$ processes
using $\nu_\mu d\to \mu^-\pi NN$ data, with the important FSI corrections taken
into account. We provide $\nu_\mu N\to \mu^-\pi N$ total cross sections by
correcting the deuterium bubble chamber data for the FSI and Fermi motion. The
results will bring a significant improvement on neutrino-nucleus reaction
models for the near-future neutrino-oscillation experiments.
