  We perform Time Dependent Hartree-Fock (TDHF) calculations to investigate the
small amplitude dipole response of selected neutron-rich nuclei and Sn
isotopes. A detailed comparison with the dipole strength predicted by
Random-Phase Approximation (RPA) calculations is presented for the first time.
TDHF results are also confronted to Vlasov calculations, to explore up to which
extent a semi-classical picture can explain the properties of the nuclear
response. The focus is on the low-energy response, below the Giant Dipole
Resonance region, where different modes of non negligible strength are
identified. We show that the relative weight of these excitations evolves with
nuclear global features, such as density profile and neutron skin, which in
turn reflect impor tant properties of the nuclear effective interaction. A
thorough analysis of the associated transition densities turns out to be quite
useful to better characterize the mixed isoscalar(IS)/isovector(IV) nature of
the different modes and their surface/volume components. In particular, we show
that the dipole response in the so-called Pygmy Dipole Resonance region
corresponds to isoscalar-like surface oscillations, of larger strength in
nuclei with a more diffuse surface. The ratio between the IV and IS Energy
Weighted Sum Rule fractions exhausted in this region is shown to almost
linearly increase with the neutron skin thickness in Sn isotopes.
