In this paper we present calculations of nucleon structure functions in the three-dimensional MIT bag model. The nucleon wave functions are modified by the Peierls Yoccoz projection in order to give eigenstates of the total momentum operator. Pair creation by the probe is taken into account. Without this the quark distributions would not obey normalization requirements. The quark distributions have vanishing support for $x>\mathrm{}1\mathrm{}$. The effect of one-gluon exchange, yielding the $N-\Delta$ mass splitting, is incorporated. This has significant effects on the $\frac{d}{u}$ ratio as well as the spin-dependent $g_1\mathrm{}\left(x\right)\mathrm{}$ of the neutron. Finally, the results are compared to data after allowing for perturbative QCD evolution.

• Received 5 June 1991

DOI:https://doi.org/10.1103/PhysRevD.44.2653