  The exclusive $Z^0$ photoproduction at high energies in $\gamma p (A)$, $p p$
and $AA$ collisions is investigate within the color dipole formalism. We
generalize the description of the deeply virtual compton scattering (DVCS)
process, which describe quite well the HERA data, for the production of $Z^0$
bosons and estimate the total cross section for the exclusive process $\gamma^*
h\to Z^0 h$ ($h=p,A$) for different energies, photon virtualities and atomic
numbers. As hadrons at collider energies are a source of Weizs\"{a}cker -
Williams photons, we consider electromagnetic interactions in hadron-hadron
collisions at Tevatron and LHC energies and estimate the rapidity distribution
and total cross section for $Z^0$ production in the $h h\to h Z^0 h$ process.
This is the first estimation for such a process in literature. It can allow us
to study, for instance, the physics of hadronic $Z^0$ decays in a clean
environment characterized by two rapidity gaps. Our results indicate that the
experimental analyzes of this process could be feasible in $pp$ but the physics
scenario for $AA$ collisions is not promising.
