  A semiclassical model based on the solution of the Vlasov equation for finite
systems with a sharp moving surface has been used to study the isoscalar
quadrupole and octupole collective modes in heavy spherical nuclei. Within this
model, a unified description of both low-energy surface modes and higher-energy
giant resonances has been achieved by introducing a coupling between surface
vibrations and the motion of single nucleons. Analytical expressions for the
collective response functions of different multipolarity can be derived by
using a separable approximation for the residual interaction between nucleons.
The response functions obtained in this way give a good qualitative description
of the quadrupole and octupole response in heavy nuclei. Although shell effects
are not explicitly included in the theory, our semiclassical response functions
are very similar to the quantum ones. This happens because of the well known
close relation between classical trajectories and shell structure. The role
played by particular nucleon trajectories and their connection with various
features of the nuclear response is displayed most clearly in the present
approach, we discuss in some detail the damping of low-energy octupole
vibrations and give an explicit expression showing that only nucleons moving on
triangular orbits can contribute to this damping.
