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Information content of the low-energy electric dipole strength: correlation analysis

We study the information content carried by the electric dipole strength with respect to isovector and isoscalar indicators characterizing bulk nuclear matter and finite nuclei. To separate isoscalar and isovector modes, and low-energy strength and giant resonances, we analyze the E1 strength as a function of excitation energy $E$ and momentum transfer $q$. We use the self-consistent nuclear density functional theory with Skyrme energy density functionals, augmented by the random phase, to compute the E1 strength, and covariance analysis to assess correlations between observables. Calculations are performed for spherical, doubly-magic nuclei $^{208}$Pb and $^{132}$Sn. We demonstrate that E1 transition densities in the low-energy region below the giant dipole resonance exhibit appreciable state dependence and multi-nodal structures, which are fingerprints of weak collectivity. The correlation between the accumulated low-energy strength and symmetry energy is weak, and dramatically depends on the energy cutoff assumed. On the other hand, a strong correlation is predicted between isovector indicators and the accumulated isovector strength at $E$ around 20 MeV and momentum transfer $q\sim 0.65$ fm$^{-1}$. Momentum- and coordinate-space pattern of the low-energy dipole modes indicate a strong fragmentation into individual particle-hole excitations. The global measure of low-energy dipole strength poorly correlates with the nuclear symmetry energy and other isovector characteristics. Consequently, our results do not support the suggestion that there exists a collective "pygmy dipole resonance," which is a strong indicator of nuclear isovector properties.