Background: Recent experiments on the electric dipole (E1) polarizability in heavy nuclei have stimulated theoretical interest in the low-energy electric dipole strength, both isovector and isoscalar.

Purpose: 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 the excitation energy $E$ and momentum transfer $q$.

Methods: We use the self-consistent nuclear density functional theory with Skyrme energy density functionals, augmented by the random phase approximation, to compute the E1 strength and covariance analysis to assess correlations between observables. Calculations are performed for the spherical, doubly magic nuclei ${}^{208}$Pb and ${}^{132}$Sn.

Results: We demonstrate that E1 transition densities in the low-energy region below the giant dipole resonance exhibit appreciable state dependence and multinodal structures, which are fingerprints of weak collectivity. The correlation between the accumulated low-energy strength and the 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${}^{-1}$.

Conclusions: Momentum- and coordinate-space patterns of the low-energy dipole modes indicate a strong fragmentation into individual particle-hole excitations. The global measure of low-energy dipole strength correlates poorly 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. By considering nonzero values of momentum transfer, one can isolate individual excitations and nicely separate low-energy excitations from the $T=1$ and $T=0$ giant collective modes. That is, measurements at $q>0$ may serve as a tool to correlate the E1 strength with certain bulk observables, such as incompressibility and symmetry energy.

• Received 7 November 2012

DOI:https://doi.org/10.1103/PhysRevC.87.014324