Nonsinglet structure function of the ³He-³H system and divergence of the Gottfried integral

We study shadowing and antishadowing corrections to the flavor nonsinglet structure function F₂^3He-F₂^3H and show that the difference between the one-particle density distributions of ³He and ³H plays an important role at very small x. We find that the flavor nonsinglet structure function in these mirror nuclei is enhanced at small x by nuclear shadowing, which increases the nuclear Gottfried integral, integrated from 10^-4 to 3, by 15-41 %. When integrated from zero, the Gottfried integral is divergent for these mirror nuclei. It seems likely that, as a consequence of charge symmetry breaking, this may also apply to the proton-neutron system.