We consider the effect of the transitions $n \to \Delta^{ 0}$ and $p \to \Delta^{ +}$ in deep inelastic scattering on polarized $^3$He on the extraction of the neutron spin structure function $g_{ 1}^{ n}(x,Q^2)$. Making the natural assumption that these transitions are the dominant non-nucleonic contributions to the renormalization of the axial vector coupling constant in the A=3 system, we find that the effect of $\Delta$ increases $g_{ 1}^{ n}(x,Q^2)$ by $10 \div 40$% in the range $0.05 \le x \le 0.6$, where our considerations are applicable and most of the data for $g_{ 1}^{ n}(x,Q^2)$ exist.
Categories: hep-ph hep-ex nucl-th