Pygmy resonances: what’s in a name?

Abstract

The centroid, width and percentage of energy weighted sum rule of dipole resonances can be strongly affected by dynamical fluctuations and static deformations of the nuclear surface, deformations and fluctuations which, in turn, depend on pairing, and thus on Cooper pairs. Because of angular momentum conservation, such insight is restricted, to lowest order, to deformations of quadrupole and monopole arXiv:1806.09409v3 [nucl-th] 11 Apr 2019 type. The latter being closely connected with the neutron (excess) skin and thus with soft dipole modes. From the values (N − Z)/A ≈ 0.18, 0.21, and 0.45 for the nuclei 122 Sn, 208 Pb, and 11 Li, it is expected that the latter system, which is weakly bound by pairing effects (spatially extended single Cooper pair and odd proton acting as spectator), constitutes an attractive laboratory to study the properties of soft E1-modes and thus of isospin nuclear deformation. From the calculation of the full dipole response function in QRPA, discretizing the continuum in a spherical box of radius of 40 fm, one finds a GDR with centroid E x ≈ 24 MeV, width Γ ≈ 11 MeV and carrying 90% of the EWSR, and a low-lying collective resonance characterized by E X = 0.75 MeV, Γ = 0.5 MeV and 6.2% EWSR The wave function of the latter resonance is built out of about fifteen components (both protons and neutrons), typical of a collective mode. The transition densities indicate this soft E1-mode to be generated by surface density oscillation of the neutron skin (∆r np ≈ 1.71 fm)relative to an approximately isospin-saturated core. Through a detailed study of the full dipole response of 11 Li we will draw a comparison between the soft E1-mode of this halo nucleus and the PDR of heavy stable nuclei, pointing to the physical similarities and also to the basic differences.

Characterization of vorticity in pygmy resonances and soft-dipole modes with two-nucleon transfer reactions

“…The results lead to a soft mode of centroid 0.75 MeV and FWHM Γ = 0.5 MeV, and carrying 6.2 % of the EWSR, in overall agreement with the experimental findings. The associated r 2 −weighted transition densities are typical of a dipole LES of light halo systems: out-of-phase motion of the neutron (skin) halo against a core in which protons and neutrons oscillate in phase [16] (Fig. 2) .…”

Nuclear Josephson-like $γ$-emission

“…33. Transition density of the soft E1-mode (pygmy dipole resonance) of 11 Li (for details see [78]).…”

Indirect methods in nuclear astrophysics with relativistic radioactive beams

“…Following the first calculations on pygmy resonances based on two-and three-body models, it was soon realized that the the role of the continuum and of the nuclear contribution was crucial to explain the experimental data on the EM response obtained in breakup experiments [295,300,330,331,332,333,334,297,335,303,304,336,337,338,339,340]. Calculations based on effective field theories started to appear recently [341].…”