Pygmy dipole resonance: Collective features and symmetry energy effects

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. PACS numbers: 25.70.Pq, 25.70.Mn, 21.65.Ef, 24.10.Cn Keywords:One of the important tasks in many-body physics is to understand the emergence of the collective features as well as their structure in terms of the individual motion of the constituents. The steady progress of experimental methods of investigation opens now the possibility to study very neutron rich nuclei, beyond the limits of stability. The goal is to have a unified picture of the evolution of various nuclear properties with mass and isospin and to test the validity of our theoretical understanding over an extended domain of analysis.New exotic collective excitations show up when one moves away from the valley of stability [1]. Their experimental characterization and theoretical description is a challenge for modern nuclear physics. Recent experiments provided several evidences about their existence but the available information is still incomplete and their nature is a matter of debate.An interesting exotic mode is the Pygmy Dipole Resonance (PDR) which was observed as an unusually large concentration of the dipole response at energies clearly below the values associated with the GDR. The latter is one of the most prominent and robust collective motions, present in all nuclei, whose centroid position varies, for medium-heavy nuclei, as 80A −1/3 M eV . Adrich et al. [2] reported the observation of a resonant-like shape distribution with a pronounced peak around 10M eV in 130 Sn and 132 Sn isotopes. A concentration of dipole excitations near and below the particle emission threshold was also observed in stable Sn nuclei, a systematics of PDR in these systems being presented in [3]. It was concluded that the strongest transitions locate at energies between 5 and 8.5M eV and a sizable fraction of the Energy-Weighted Sum Rule (EWSR) is exhausted by these states. From a comparison of the available data for stable and unstable Sn isotopes a correlation between the fraction of pygmy strength and isospin asymmetry was noted [4]. In general t...

Dipole response in neutron-rich nuclei with new Skyrme interactions

“…While the model is unable to account for effects associated with the shell structure, this selfconsistent approach is suitable to describe robust quantum modes, of zero-sound type, in both nuclear matter and finite nuclei [26,35,38,40]. One has essentially to solve the two coupled Vlasov kinetic equations for the neutron and proton distribution functions f q (r, p, t), with q = n, p [26]:…”

Constraining simultaneously nuclear symmetry energy and neutron-proton effective mass splitting with nucleus giant resonances using a dynamical approach

“…As a breathing oscillation mode in the radial direction of a nucleus, the isoscalar giant monopole resonance (GMR) is a good probe of the incompressibility of nuclear matter [24][25][26][27][28], while the isoscalar giant quadruple resonance (IS-GQR), an oscillation mode with quadruple deformation of a nucleus, has been found to be much affected by the isoscalar nucleon effective mass m * s [29][30][31][32][33][34]. On the other hand, the isovector giant dipole resonance (IVGDR) and the pygmy dipole resonance (PDR), with the former an oscillation mode between the centers of mass of neutrons and protons and the latter that between the neutron skin and the nucleus core, are valuable probes of the nuclear symmetry energy at subsaturation densities [35][36][37][38][39][40][41][42][43][44][45][46][47][48][49]. Since the nuclear symmetry energy acts as a restoring force for the IVGDR, the main frequency of the IVGDR oscillation, i.e., the centroid energy E −1 , is related to E sym at subsaturation densities or its slope parameter L at the saturation density [36,45,49].…”

Mass and isospin dependence of the dipole response in a microscopic transport approach

“…We performed a systematic analysis by considering all systems indicated above. The results indicate a position of the peak not much influenced by the symmetry energy [19] and quite well described by the parametrization E PDR = 41A − 1 3 , see Fig. 4 (a).…”

“…A close inspection evidences the emergence of an additional peak of the strength function, situated below the main E GDR peak, more pronounced for greater number of excess neutrons. We interpret it as corresponding to a new collective mode describing the PDR [19].…”