Interplay between low-lying isoscalar and isovector dipole modes: a comparative analysis between semi-classical and quantum approaches

Abstract: 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.