The nature of scattering from composite systems in the case where the constituent cross sections saturate the Froissart bound is discussed. The questions of whether or not all cross sections approach the same limit and whether the ratio of the elastic to total cross section approaches ½ are discussed. The answers to these questions depend crucially on the form of the profile functions of the constituents.

• Received 2 April 1974

DOI:https://doi.org/10.1103/PhysRevD.10.3022