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By considering different parameterizations with density of the symmetry energy is investigated
theoretically the emergence and the nature of the low energy dipole response evidenced experimentally for various systems. We analyze the consistency of the predictions provided
by a generalization of the Brown-Bolsterli schematic model with a density dependent particle-hole residual interaction and those
based on self-consistent microscopic transport approaches using the Vlasov equation. In both cases an additional collective mode is signaled whose energy centroid is closer to the distance between two major shells and exhaust few percentages of Energy Weighted Sum Rule.
From the sensitivity of EWSR to the density dependence of the symmetry energy is concluded that precise experimental determination of the
PDR properties can settle important constraints
on the behavior of the symmetry energy well below saturation.