Determining the proximity of [Formula Presented] scattering to the black body limit using deep inelastic scattering and [Formula Presented] production

We use information about DIS and [Formula Presented] production on hydrogen to model the t dependence of the [Formula Presented] scattering amplitude. We investigate the profile function for elastic scattering of hadronic components of the virtual photon off both a nucleon and heavy nuclear target, and we estimate the value of the impact parameter where the blackbody limit is reached. We also estimate the fraction of the cross section that is due to hadronic configurations in the virtual photon wave function that approach the unitarity limit. We extract, from these considerations, approximate lower limits on the values of x where the leading twist approximation in DIS is violated. We observe that the blackbody limit may be approached within DESY HERA kinematics with [Formula Presented] equal to a few [Formula Presented] and [Formula Presented] Comparisons are made with earlier predictions by Munier et al., and the longitudinal structure function is compared with preliminary HERA data. The principle advantage of our method is that we do not rely solely on the t dependence of ρ-meson production data. This allows us to extend our analysis down to very small impact parameters and dipole sizes. Finally, we perform a similar calculation with a [Formula Presented] target, and we demonstrate that the blackbody limit is already approached at [Formula Presented] and [Formula Presented].