  The single diffractive cross section for heavy quarks production is
calculated in next-no-leading order (NLO) in nucleus-nucleus collisions. Such
processes are expected to occur at the LHC. We start using the hard diffractive
factorization formalism, taking into account the recent experimental
parameterization for the Pomeron Structure Function (DPDF). Absorptive
corrections are accounted by the multiple Pomeron contributions considering a
gap survival probability, where its theoretical uncertainty for nuclear
collisions is discussed. We estimate the diffractive ratios for single
diffraction process in nuclear coherent/incoherent collisions at the LHC.
