Low-lying dipole response: isospin character and collectivity in ${}^{68}$Ni, ${}^{132}$Sn and ${}^{208}$Pb

TL;DR

This study investigates the isospin character and collectivity of low-energy dipole responses in ${}^{68}$Ni, ${}^{132}$Sn, and ${}^{208}$Pb using Skyrme Hartree-Fock plus RPA, revealing differences in collectivity depending on the probe and symmetry energy slope.

Contribution

It provides a comprehensive analysis of the collectivity and isospin nature of pygmy dipole resonances across three nuclei using multiple Skyrme parameter sets within a self-consistent mean field approach.

Findings

Low-energy peaks increase with the slope of the symmetry energy.

Collectivity varies with the type of external probe (isoscalar vs. isovector).

Isoscalar responses show clear collectivity, isovector responses do not.

Abstract

The isospin character, the collective or single-particle nature, and the sensitivity to the slope of the nuclear symmetry energy of the low-energy isovector dipole response (known as pygmy dipole resonance) are nowadays under debate. In the present work we study, within the fully self-consistent non-relativistic mean field (MF) approach based on Skyrme Hartree-Fock plus Random Phase Approximation (RPA), the measured even-even nuclei ${}^{68}$Ni, ${}^{132}$Sn and ${}^{208}$Pb. To analyze the model dependence in the predictions of the pygmy dipole strength, we employ three different Skyrme parameter sets. We find that both the isoscalar and the isovector dipole responses of all three nuclei show a low-energy peak that increases in magnitude, and is shifted to larger excitation energies, with increasing values of the slope of the symmetry energy at saturation. We highlight the fact that the collectivity associated with the RPA state(s) contributing to this peak is different in the isoscalar and isovector case, or in other words it depends on the external probe. While the response of these RPA states to an isovector operator does not show a clear collective nature, the response to an isoscalar operator is recognizably collective, for {\it all} analyzed nuclei and {\it all} studied interactions.