In this paper we study leading neutron production in photon - hadron interactions which take place in $pp$ and $pA$ collisions at large impact parameters. Using a model that describes the recent leading neutron data at HERA, we consider exclusive vector meson production in association with a leading neutron in $pp/pA$ collisions at RHIC and LHC energies. The total cross sections and rapidity distributions of $rho$, $phi$ and $J/Psi$ produced together with a leading neutron are computed. Our results indicate that the study of these processes is feasible and that it can be used to improve the understanding of leading neutron processes and of exclusive vector meson production.
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