  Deep Inelastic Scattering (DIS) experiments at the planned Electron-Ion
Collider will be affected by details of the hadron formation inside the nuclear
volume. Besides semi-inclusive particle production experiments decays of the
target nucleus via emission of neutrons provide an additional opportunity to
probe this domain. This paper reports on the hybrid dynamical+statistical
calculations of low-energy neutron production in muon- and virtual
photon-induced collisions with nuclei. We confirm the conclusion that the E665
data on neutron production in $\mu^-$ + Pb DIS at 470 GeV indicate a strong
suppression of the final state interaction for hadrons with momenta above $\sim
1$ GeV/c. Ultraperipheral heavy-ion collisions at the Large Hadron Collider
(LHC) and the Relativistic Heavy Ion Collider (RHIC) can be used to test this
suppression. The calculations of the neutron multiplicity distributions and
$p_t$-spectra in photon - nucleus collisions at the energies accessible at the
LHC and RHIC are presented for several models of hadron formation. We argue
that studies of neutron production in ultraperipheral heavy ion collisions open
a new window on the small-$x$ dynamics and hadron component of the photon wave
function.
