  Obtaining cross sections for nuclear reactions at intermediate energies based
on the Glauber formulation has a long tradition. Only recently the energy
regime of a few hundred MeV has become accessible to ab-initio Faddeev
calculations of three-body scattering. In order to go to higher energies, the
Faddeev equation for three-body scattering is formulated and directly solved
without employing a partial wave decomposition. In the simplest form the
Faddeev equation for interacting scalar particles is a three-dimensional
integral equation in five variables, from which the total cross section, the
cross sections for elastic scattering and breakup reactions, as well as
differential cross sections are obtained. The same observables are calculated
based on the Glauber formulation. The first order Glauber calculation and the
Glauber rescattering corrections are compared in detail with the corresponding
terms of the Faddeev multiple scattering series for projectile energies between
100 MeV and 2 GeV.
