On the toroidal nature of the low-energy E1 mode

TL;DR

This paper investigates the low-energy E1 strength in lead-208, revealing that it exhibits a toroidal flow pattern and is not simply a pygmy mode, challenging previous simplistic models.

Contribution

It provides a detailed analysis of the toroidal nature of the low-energy E1 mode using self-consistent RPA calculations with Skyrme forces.

Findings

Clear isoscalar toroidal flow in 6.0-8.8 MeV range

Mixed flow patterns in 8.8-10.5 MeV range

Contradicts the simple pygmy mode picture

Abstract

The nature of E1 low-energy strength (LES), often denoted as a "pygmy dipole resonance", is analyzed within the random-phase-approximation (RPA) in $^{208}$Pb using Skyrme forces in fully self-consistent manner. A first overview is given by the strength functions for the dipole, compressional and toroidal operators. More detailed insight is gained by averaged transition densities and currents where the latter provide very illustrative flow pattern. The analysis reveals clear isoscalar toroidal flow in the low-energy bin 6.0-8.8 MeV of the LES and a mixed isoscalar/isovector toroidal/compression flow in the higher bin 8.8-10.5 MeV. Thus the modes covered by LES embrace both vortical and irrotational motion. The simple collective picture of the LES as a "pygmy" mode (oscillations of the neutron excess against the nuclear core) is not confirmed.