We calculate the nuclear shadowing ratio for a wide range of nuclei at small Bjorken-x in the framework of Gribov theory. The coherent contribution to the (virtual) photon-nucleon cross section is obtained in terms of the diffractive dissociation cross section. Information on diffraction from FNAL and HERA is used. Our results are compared to available experimental data from the NMC and E665 experiments at x ~ 10^{-4}.
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