  We describe a QCD motivated model for total cross-sections which uses the
eikonal representation and incorporates QCD mini-jets to drive the rise with
energy of the cross-section, while the impact parameter distribution is
obtained through the Fourier transform of the transverse momentum distribution
of soft gluons emitted in the parton-parton interactions giving rise to
mini-jets in the final state. A singular but integral expression for the
running coupling constant in the infrared region is part of this model.
