  We derive the cross section for the diffractive gluon production in high
energy onium-nucleus collisions that includes the low-x evolution effects in
the rapidity interval between the onium and the produced gluon and in the
rapidity interval between the gluon and the target nucleus. We analyze our
result in two limiting cases: when the onium size is much smaller than the
saturation scale and when its size is much larger than the saturation scale. In
the later case the gluon multiplicity is very small in the quasi-classical case
and increases when the low-x evolution effects in onium become significant. We
discuss the implications of our result for the RHIC, LHC and EIC phenomenology.
