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We review predictions of the theory of leading twist nuclear shadowing for inclusive unpolarized and polarized deuteron structure functions , and and for the tagged deuteron structure function . We analyze the possibility to extract the neutron structure function from electron–deuteron data and demonstrate that an account of leading twist nuclear shadowing leads to large corrections for the extraction of from the future deuteron collider data both in the inclusive and in the tagged structure function modes. We suggest several strategies to address the extraction of and to measure at the same time the effect of nuclear shadowing via the measurement of the distortion of the proton spectator spectrum in the semi-inclusive eD → e′NX process. We address the issue of the final state interactions in the eD → e′NX process and examine how they affect the extraction of .
We show that exclusive photoproduction of J/ψ in ultraperipheral collisions of heavy ions at the LHC constrains the nuclear gluon density at small x and gives evidence of large nuclear gluon shadowing.