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Low-energy electric dipole response of Sn isotopes

We study the low-energy dipole (LED) strength distribution along the Sn isotopic chain in both the isoscalar (IS) and the isovector (IV, or E1) electric channels, to provide testable predictions and guidance for new experiments with stable targets and radioactive beams. We use the self-consistent Quasi-particle Random-Phase Approximation (QRPA) with finite-range interactions and mainly the Gogny D1S force. We analyze also the performance of a realistic two-body interaction supplemented by a phenomenological three-body contact term. We find that from N=50 and up to the N=82 shell closure (132Sn) the lowest-energy part of the IS-LED spectrum is dominated by a collective transition whose properties vary smoothly with neutron number and which cannot be interpreted as a neutron-skin oscillation. For the neutron-rich species this state contributes to the E1 strength below particle threshold, but much more E1 strength is carried by other, weak but numerous transitions around or above threshold. We find that strong structural changes in the spectrum take effect beyond N=82, namely increased LED strength and lower excitation energies. Our results with the Gogny interaction are compatible with existing data. On this basis we predict that a) the summed IS strength below particle threshold shall be of the same order of magnitude for N=50-82, b) the summed E1 strength up to approximately 12 MeV shall be similar for N=50-82 MeV, while c) the summed E1 strength below threshold shall be of the same order of magnitude for N ~ 64 - 82 and much weaker for the lighter, more-symmetric isotopes. We point out a general agreement of our results with other non-relativistic studies, the absence of a collective IS mode in some of those studies, and a possibly radical disagreement with relativistic models.