Nuclear equation of state from ground and collective excited state properties of nuclei

Abstract

This contribution reviews the present status on the available constraints to the nuclear equation of state (EoS) around saturation density from nuclear structure calculations on ground and collective excited state properties of atomic nuclei. It concentrates on predictions based on self-consistent mean-field calculations, which can be considered as an approximate realization of an exact energy density functional (EDF). EDFs are derived from effective interactions commonly fitted to nuclear masses, charge radii and, in many cases, also to pseudo-data such as nuclear matter properties. Although in a model dependent way, EDFs constitute nowadays a unique tool to reliably and consistently access bulk ground state and collective excited state properties of atomic nuclei along the nuclear chart as well as the EoS. For comparison, some emphasis is also given to the results obtained with the so called ab initio approaches that aim at describing the nuclear EoS based on interactions fitted to few-body data only. Bridging the existent gap between these two frameworks will be essential since it may allow to improve our understanding on the diverse phenomenology observed in nuclei. Examples on observations from astrophysical objects and processes sensitive to the nuclear EoS are also briefly discussed. As the main conclusion, the isospin dependence of the nuclear EoS around saturation density and, to a lesser extent, the nuclear matter incompressibility remain to be accurately determined. Experimental and theoretical efforts in finding and measuring observables specially sensitive to the EoS properties are of paramount importance, not only for low-energy nuclear physics but also for nuclear astrophysics applications. 7 The expression introduced by Migdal in Ref. [43] neglected the term in a AS . 8 From a macroscopic picture it would correspond to an isotropic compression. 9 From a macroscopic picture it would correspond to a non-isotropic compression. 15

Particle-vibration coupling for giant resonances beyond the diagonal approximation

“…The HF equation is solved in a spherical box with size R = 20 fm and a radial step dr = 0.1 fm. In the RPA calculation, the single-particle energy cut-off is e cut = 80 MeV, so that it ensures the convergence of our results as it can be seen from the EWSR for IS-GMR, ISGDR, and ISGQR in 16 O that are all 100% fulfilled, see the column "RPA" in Table I. For the PVC calculation, the phonons selected in the doorway states, i.e., the summation index n in Eq.…”

“…The correlation between the excitation energy calculated at RPA level and nuclear matter properties has been extensively studied (cf. [16] and references therein). For instance, the compression mode ISGMR and ISGDR are correlated with the incompressibility coefficient K ∞ ; the ISGQR is correlated with the effective mass m * /m.…”

“…For example, among the four functionals, SAMi gives the smallest incompressibility coefficient with K In this work we have developed the fully self-consistent particle-vibration model without the diagonal approximation, that is, the interaction among the doorway states has been taken into account. The full PVC has been used to study the isoscalar giant monopole, dipole, and quadrupole resonances of 16 O using Skyrme functionals. The results are compared with the second RPA [23,62] and time-blocking approximation [61].…”

“…III. Results for the isoscalar giant monopole, dipole, and quadrupole resonances of 16 O by full PVC are presented in Sec. IV.…”

Collision dynamics at medium and relativistic energies

“…The low-density regime has an impact on reaction dynamics at Fermi energy (isotopic features in fragmentation [2], charge equilibration [3,4]), as well as on nuclear structure (neutron skins, pygmy resonances [5]) and in the astrophysical context (neutron star formation and crust [6,7,8]). On the other hand, relativistic heavy ion reactions (isospin flows, meson production [9,10]) and compact star features (neutron star mass-radius relation, cooling, hybrid structure, formation of black holes [6,11]) are strongly influenced by the high density behavior of the symmetry energy.…”