  We calculate the inelastic scattering cross sections to populate one- and
two-phonon states in heavy ion collisions with both Coulomb and nuclear
excitations. Starting from a microscopic approach based on RPA, we go beyond it
in order to treat anharmonicities and non-linear terms in the exciting field.
These anharmonicities and non-linearities are shown to have important effects
on the cross sections both in the low energy part of the spectrum and in the
energy region of the Double Giant Quadrupole Resonance. By properly introducing
an optical potential the inelastic cross section is calculated semiclassically
by integrating the excitation probability over all impact parameters. A
satisfactory agreement with the experimental results is obtained.
