  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}.
