  Basing on the thickness (profile) function, previously obtained for the
realistic Fermi type distribution of nucleons in nuclei, calculations are made
of the microscopic eikonal phases of the nucleus-nucleus scattering and the
total reaction cross- sections. In so doing, the phase is deduced to the
one-dimensional integral provided that the Gaussian density distribution for
the projectile nucleus and an arbitrary shape of the thickness density for the
target nucleus are used. The problems of obtaining parameters of the "point"
nucleon density are considered. A possibility of approximating the realistic
densities by the "surface-matched" Gaussian functions and the dependence of
cross-sections on the nucleon-nucleon interaction radius are discussed. The
in-medium effects and the role of the trajectory distortion are studied.
Conclusions are made on physics of the process, and comparison with
experimental data is made with cross sections calculated by using the developed
method where no free parameters are introduced.
