Small-$x$ Nuclear shadowing from Diffractive Scattering

We calculate nuclear shadowing ratio at small Bjorken-$x$ for a wide range of nuclei in the framework of the Gribov theory. The diffractive dissociation cross sections, which are inputs, are taken from the FNAL and HERA experiments. We investigate the effects of the inclusion of subleading reggeons on shadowing. We compare our result with experimental data from the NMC and E665 experiments.