  Two different nuclear-medium effects are isolated using a low three-momentum
transfer subsample of neutrino-carbon scattering data from the MINERvA neutrino
experiment. The observed hadronic energy in charged-current $\nu_\mu$
interactions is combined with muon kinematics to permit separation of the
quasielastic and $\Delta$(1232) resonance processes. First, we observe a small
cross section at very low energy transfer that matches the expected screening
effect of long-range nucleon correlations. Second, additions to the event rate
in the kinematic region between the quasielastic and $\Delta$ resonance
processes are needed to describe the data. The data in this kinematic region
also has an enhanced population of multi-proton final states. Contributions
predicted for scattering from a nucleon pair have both properties; the model
tested in this analysis is a significant improvement but does not fully
describe the data. We present the results as a double-differential cross
section to enable further investigation of nuclear models. Improved description
of the effects of the nuclear environment are required by current and future
neutrino oscillation experiments.
