The vibrational structure of the Pygmy Dipole Resonance (PDR) is investigated within a quantum many-body treatment with extended separable interactions able to encode the dependence of nuclear symmetry energy on density. A new picture of PDR is unveiled in terms of a combined dynamics of the neutron skin and of the core isovector polarization, which determines the isoscalar features of PDR while reproducing the isovector properties of Giant Dipole Resonance. The key role played by the variation with density of the symmetry energy on shaping the low-lying dipole response and its isoscalar-isovector structure is underlined. Our results provide insights for the challenge of clarifying the transition from skin oscillation to a highly bulk collective dynamics.
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