  In the energy range of present and future accelerator-based
neutrino-oscillation experiments, single-pion production (SPP) is one of the
main contributions to the neutrino-nucleus scattering cross section. For these
neutrino energies, ranging from several hundreds of MeV to a few GeV, the SPP
on the nucleus is usually described by the reaction in which the incoming
lepton couples to one bound nucleon in the nucleus, producing a pion and the
knock-out nucleon, along with the residual system and the scattered lepton in
the final state. Here, the kinematics and cross section formula for this
process are discussed, although the formalism can be applied to other
$2\rightarrow4$ processes.
