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

We study shadowing and antishadowing corrections to the flavor non-singlet structure function F_2(3He)-F_2(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 non-singlet 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 1, by 11-36 %. 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.