Longitudinal resolution in a large relativistic nucleus: Adding a dimension to the McLerran-Venugopalan model

We extend the McLerran-Venugopalan model for the gluon distribution functions of very large nuclei to larger values of the longitudinal momentum fraction $x_F.$ Because gluons with larger values of $x_F$ begin to resolve the longitudinal structure of the nucleus, we find that it is necessary to set up a fully three-dimensional formalism for performing the calculation. We obtain a relatively compact expression for the gluon number density provided that the nucleus is sufficiently large and consists of color-neutral nucleons. Our expressions for the gluon number density saturate at small transverse momenta. The nuclear dependence we obtain is such that the number of gluons increases more slowly than the number of nucleons as the size of the nucleus is increased.