  We consider electron-deuteron deep-inelastic scattering (DIS) with detection
of a proton in the nuclear fragmentation region ("spectator tagging") as a
method for extracting the free neutron structure functions and studying their
nuclear modifications. Such measurements could be performed at a future
Electron-Ion Collider (EIC) with suitable forward detectors. The measured
proton recoil momentum (~< 100 MeV in the deuteron rest frame) specifies the
deuteron configuration during the high-energy process and permits a controlled
theoretical treatment of nuclear effects. Nuclear and nucleonic structure are
separated using methods of light-front quantum mechanics. The impulse
approximation (IA) to the tagged DIS cross section contains the free neutron
pole, which can be reached by on-shell extrapolation in the recoil momentum.
Final-state interactions (FSI) distort the recoil momentum distribution away
from the pole. In the intermediate-x region 0.1 < x < 0.5 FSI arise
predominantly from interactions of the spectator proton with slow hadrons
produced in the DIS process on the neutron (rest frame momenta ~< 1 GeV, target
fragmentation region). We construct a schematic model describing this effect,
using final-state hadron distributions measured in nucleon DIS experiments and
low-energy hadron scattering amplitudes. We investigate the magnitude of FSI,
their dependence on the recoil momentum (angular dependence, forward/backward
regions), their analytic properties, and their effect on the on-shell
extrapolation. We comment on the prospects for neutron structure extraction in
tagged DIS with EIC. We discuss possible extensions of the FSI model to other
kinematic regions (large/small x). In tagged DIS at x << 0.1 FSI resulting from
diffractive scattering on the nucleons become important and require separate
treatment.
