Symmetry energy from the nuclear collective motion: constraints from dipole, quadrupole, monopole and spin-dipole resonances

Abstract

Abstract. The experimental and theoretical studies of Giant Resonances, or more generally of the nuclear collective vibrations, are a well established domain in which sophisticated techniques have been introduced and firm conclusions reached after an effort of several decades. From it, information on the nuclear equation of state can be extracted, albeit not far from usual nuclear densities. In this contribution, which complements other contributions appearing in the current volume, we survey some of the constraints that have been extracted recently concerning the parameters of the nuclear symmetry energy. Isovector modes, in which neutrons and protons are in opposite phase, are a natural source of information and we illustrate the values of symmetry energy around saturation deduced from isovector dipole and isovector quadrupole states. The isotopic dependence of the isoscalar monopole energy has also been suggested to provide a connection to the symmetry energy: relevant theoretical arguments and experimental results are thoroughly discussed. Finally, we consider the case of the charge-exchange spin-dipole excitations in which the sum rule associated with the total strength gives in principle access to the neutron skin and thus, indirectly, to the symmetry energy.

Neutron skin thickness from the measured electric dipole polarizability inNi68,Sn120, andRoca-Maza1, Viñas2, Centelles3 et al. 2015Phys. Rev. CSelf Cite233322563View full textAdd to dashboardCite

“…The range for the slope of the symmetry energy L predicted by the subset of selected EDFs lies at the lower end of accepted values when compared to other analysis (see, e.g., Refs. [56][57][58]), yet it is consistent with studies involving giant resonances [59]. We emphasize that the limits deduced in the present work follow from the analysis of relatively clean electromagnetic experiments.…”

“…These estimates are consistent with other predictions of the neutron skin thickness, J, and L extracted from various experiments that include heavy-ion collisions, giant resonances, antiprotonic atoms, hadronic probes, polarized electron scattering, as well as astrophysical observations; see, e.g., Refs. [53,54,57,59,61]. Finally, the correlation between the electric dipole polarizabilities in 68 Ni, 120 Sn, and 208 Pb shows that almost all the EDFs that reproduce the measured polarizability in 208 Pb also reproduce the measured polarizabilities in 68 Ni and 120 Sn.…”

Nuclear Symmetry Energy Extracted from Laboratory Experiments

“…The latter refers to the phenomenon that in any density region where the symmetry energy is low/high, it is energetically more favorable for the region to be more/less isospin asymmetric at chemical equilibrium. In addition, for isovector collective modes of excited nuclei, the symmetry energy/potential plays the role of the restoring force [37,95,96]. Since the isovector potential is normally small compared to the isoscalar potential, isospin-sensitive observables often involve relative or differential quantities/motions of neutrons and protons to enhance (reduce) effects of the isovector (isoscalar) potential [91][92][93][94].…”

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].…”