Pygmy dipole resonance: collective features and symmetry energy effects

TL;DR

This paper investigates the collective nature of pygmy dipole resonances in neutron-rich nuclei, analyzing their dependence on symmetry energy and identifying a distinctive isoscalar-like mode through theoretical models and kinetic equations.

Contribution

It introduces a generalized harmonic oscillator shell model approach and self-consistent kinetic equations to analyze the collective features and symmetry energy effects on pygmy dipole resonances.

Findings

Existence of a collective isoscalar-like mode below GDR energy

Weak dependence of mode energy on isovector interaction

Strength sensitivity to symmetry energy below saturation

Abstract

A very important open question related to the pygmy dipole resonance is about its quite elusive collective nature. In this paper, within a harmonic oscillator shell model, generalizing an approach introduced by Brink, we first identify the dipole normal modes in neutron rich nuclei and derive the energy weighted sum rule exhausted by the pygmy dipole resonance. Then solving numerically the self-consistent Landau-Vlasov kinetic equations for neutrons and protons with specific initial conditions, we explore the structure of the different dipole vibrations in the $^{132}Sn$ system and investigate their dependence on the symmetry energy. We evidence the existence of a distinctive collective isoscalar-like mode with an energy well below the Giant Dipole Resonance (GDR), very weakly dependent on the isovector part of the nuclear effective interaction. At variance the corresponding strength is rather sensitive to the behavior of the symmetry energy below saturation, which rules the number of excess neutrons in the nuclear surface.