  We analyse pp elastic scattering data at the highest accelerator energy
region (between 10 and 63 GeV) through a multiple diffraction approach. The use
of Martin's formula in a model developed earlier is substituted by the
introduction of a complex elementary (parton-parton) amplitude. With this the
total cross section and the real part of the hadronic amplitude may be
simultaneously investigated and, with the exception of the diffraction minimum
at some ISR energies, a satisfactory description of all experimental data is
obtained. Total cross sections extrapolations to cosmic-ray energies (above 6
TeV) show agreement with the reanalysis of the Akeno data performed by N. N.
Nikolaev and also with Gaisser, Sukhatme and Yodh results, leading to the
prediction 147 mb for the total cross section at 16 TeV. Physical
interpretations and critical remarks concerning our parametrizations and
results are also presented and discussed.
