  Energetic neutrons produced in $ep$ collisions at HERA have been studied with
the ZEUS detector in the photoproduction regime at a mean photon-proton
center-of-mass energy of 220 GeV. The neutrons carry a large fraction $0.64 <
x_L <0.925$ of the incoming proton energy, and the four-momentum-transfer
squared at the proton-neutron vertex is small, $|t|<0.425$ GeV$^2$. The $x_L$
distribution of the neutrons is measured in bins of $t$. The $(1-x_L)$
distributions in the $t$ bins studied satisfy a power law $dN/dx_L \propto
(1-x_L)^{a(t)}$, with the powers $a(t)$ following a linear function of $t$:
\mbox{$a(t)=0.88\pm 0.09 ({\rm stat.})^{+0.34}_{-0.39}({\rm syst.})-(2.81\pm
0.42({\rm stat.})^{+1.13}_{-0.62}({\rm syst.}) {\rm Ge V}^{-2})t$.} This result
is consistent with the expectations of pion-exchange models, in which the
incoming proton fluctuates to a neutron-pion state, and the electron interacts
with the pion.
