Summing all the eikonal graphs. II

Abstract.A physically reasonable model is introduced in order to estimate, in a functional way, the vast number of distinct graphs which are conventionally neglected in eikonal scattering models that lead to total cross sections increasing with energy in the form of the Froissart bound. A range of estimates of non-leading-log effects on the conventional, leading-log, ladder-tower graphs is also attempted. Upon summing all the eikonal graphs of this model, one finds significant cancellations away from the conventional, tower-graph result, with total cross sections tending to constant values at extreme scattering energies on the order of 103-106 TeV.