Determination of the stiffness of the nuclear symmetry energy from isospin diffusion

A Modern View of the Equation of State in Nuclear and Neutron Star Matter

Background: We analyze several constraints on the nuclear equation of state (EOS) currently available from neutron star (NS) observations and laboratory experiments and study the existence of possible correlations among properties of nuclear matter at saturation density with NS observables. Methods: We use a set of different models that include several phenomenological EOSs based on Skyrme and relativistic mean field models as well as microscopic calculations based on different many-body approaches, i.e., the (Dirac–)Brueckner–Hartree–Fock theories, Quantum Monte Carlo techniques, and the variational method. Results: We find that almost all the models considered are compatible with the laboratory constraints of the nuclear matter properties as well as with the largest NS mass observed up to now, 2.14−0.09+0.10M⊙ for the object PSR J0740+6620, and with the upper limit of the maximum mass of about 2.3–2.5M⊙ deduced from the analysis of the GW170817 NS merger event. Conclusion: Our study shows that whereas no correlation exists between the tidal deformability and the value of the nuclear symmetry energy at saturation for any value of the NS mass, very weak correlations seem to exist with the derivative of the nuclear symmetry energy and with the nuclear incompressibility.

Probing the Neutron Skin with Ultrarelativistic Isobaric Collisions

Particle production in ultrarelativistic heavy ion collisions depends on the details of the nucleon density distributions in the colliding nuclei. We demonstrate that the charged hadron multiplicity distributions in isobaric collisions at ultrarelativistic energies provide a novel approach to determine the poorly known neutron density distributions and thus the neutron skin thickness in finite nuclei, which can in turn put stringent constraints on the nuclear symmetry energy.

The Equation of State of Nuclear Matter: From Finite Nuclei to Neutron Stars

Background. We investigate possible correlations between neutron star observables and properties of atomic nuclei. In particular, we explore how the tidal deformability of a 1.4 solar mass neutron star, M1.4, and the neutron-skin thickness of 48Ca and 208Pb are related to the stellar radius and the stiffness of the symmetry energy. Methods. We examine a large set of nuclear equations of state based on phenomenological models (Skyrme, NLWM, DDM) and ab initio theoretical methods (BBG, Dirac–Brueckner, Variational, Quantum Monte Carlo). Results: We find strong correlations between tidal deformability and NS radius, whereas a weaker correlation does exist with the stiffness of the symmetry energy. Regarding the neutron-skin thickness, weak correlations appear both with the stiffness of the symmetry energy, and the radius of a M1.4. Our results show that whereas the considered EoS are compatible with the largest masses observed up to now, only five microscopic models and four Skyrme forces are simultaneously compatible with the present constraints on L and the PREX experimental data on the 208Pb neutron-skin thickness. We find that all the NLWM and DDM models and the majority of the Skyrme forces are excluded by these two experimental constraints, and that the analysis of the data collected by the NICER mission excludes most of the NLWM considered. Conclusion. The tidal deformability of a M1.4 and the neutron-skin thickness of atomic nuclei show some degree of correlation with nuclear and astrophysical observables, which however depends on the ensemble of adopted EoS.

Evidence for the Role of Proton Shell Closure in Quasifission Reactions from X-Ray Fluorescence of Mass-Identified Fragments

The atomic numbers and the masses of fragments formed in quasifission reactions are simultaneously measured at scission in ^{48}Ti+^{238}U reactions at a laboratory energy of 286 MeV. The atomic numbers are determined from measured characteristic fluorescence x rays, whereas the masses are obtained from the emission angles and times of flight of the two emerging fragments. For the first time, thanks to this full identification of the quasifission fragments on a broad angular range, the important role of the proton shell closure at Z=82 is evidenced by the associated maximum production yield, a maximum predicted by time-dependent Hartree-Fock calculations. This new experimental approach gives now access to precise studies of the time dependence of the N/Z (neutron over proton ratios of the fragments) evolution in quasifission reactions.

Has a thick neutron skin in 208Pb been ruled out?

The Lead Radius Experiment has provided the first model-independent evidence in favor of a neutron-rich skin in 208Pb. Although the error bars are large, the reported large central value of 0.33 fm is particularly intriguing. To test whether such a thick neutron skin in 208Pb is already incompatible with laboratory experiments or astrophysical observations, we employ relativistic models with neutron-skin thickness in 208Pb ranging from 0.16 to 0.33 fm to compute ground-state properties of finite nuclei, their collective monopole and dipole response, and mass-versus-radius relations for neutron stars. No compelling reason was found to rule out models with large neutron skins in 208Pb from the set of observables considered in this Letter.

Determining the density content of symmetry energy and neutron skin: an empirical approach

The density dependence of nuclear symmetry energy remains poorly constrained. Starting from precise empirical values of the nuclear volume and surface symmetry energy coefficients and the nuclear saturation density, we show how in the ambit of microscopic calculations with different energy density functionals, the value of the symmetry energy slope parameter L along with that for neutron skin can be put in tighter bounds. The value of L is found to be L=64±5  MeV. For 208Pb, the neutron skin thickness comes out to be 0.188±0.014  fm. Knowing L, the method can be applied to predict neutron skin thicknesses of other nuclei.

Properties of the nuclear medium

We review our knowledge on the properties of the nuclear medium that have been studied, over many years, on the basis of many-body theory, laboratory experiments and astrophysical observations. Throughout the presentation particular emphasis is placed on the possible relationship and links between the nuclear medium and the structure of nuclei, including the limitations of such an approach. First we consider the realm of phenomenological laboratory data and astrophysical observations and the hints they can give on the characteristics that the nuclear medium should possess. The analysis is based on phenomenological models, that however have a strong basis on physical intuition and an impressive success. More microscopic models are also considered, and it is shown that they are able to give invaluable information on the nuclear medium, in particular on its equation of state. The interplay between laboratory experiments and astrophysical observations is particularly stressed, and it is shown how their complementarity enormously enriches our insights into the structure of the nuclear medium. We then introduce the nucleon-nucleon interaction and the microscopic many-body theory of nuclear matter, with a critical discussion about the different approaches and their results. The Landau-Fermi liquid theory is introduced and briefly discussed, and it is shown how fruitful it can be in discussing the macroscopic and low-energy properties of the nuclear medium. As an illustrative example, we discuss neutron matter at very low density, and it is shown how it can be treated within the many-body theory. The general bulk properties of the nuclear medium are reviewed to indicate at which stage of our knowledge we stand, taking into account the most recent developments both in theory and experiments. A section is dedicated to the pairing problem. The connection with nuclear structure is then discussed, on the basis of the energy density functional method. The possibility of linking the physics of exotic nuclei and the astrophysics of neutron stars is particularly stressed. Finally, we discuss the thermal properties of the nuclear medium, in particular the liquid-gas phase transition and its connection with the phenomenology on heavy ion reactions and the cooling evolution of neutron stars. The presentation has been taken for non-specialists and possibly for non-nuclear physicists.

Symmetry energy of dilute warm nuclear matter

The symmetry energy of nuclear matter is a fundamental ingredient in the investigation of exotic nuclei, heavy-ion collisions, and astrophysical phenomena. New data from heavy-ion collisions can be used to extract the free symmetry energy and the internal symmetry energy at subsaturation densities and temperatures below 10 MeV. Conventional theoretical calculations of the symmetry energy based on mean-field approaches fail to give the correct low-temperature, low-density limit that is governed by correlations, in particular, by the appearance of bound states. A recently developed quantum-statistical approach that takes the formation of clusters into account predicts symmetry energies that are in very good agreement with the experimental data. A consistent description of the symmetry energy is given that joins the correct low-density limit with quasiparticle approaches valid near the saturation density.

Isoscaling as a measure of symmetry energy in the lattice gas model

The energetic properties of nuclear clusters inside a low-density, finite-temperature medium are studied with a lattice gas model including isospin dependence and Coulomb forces. Important deviations are observed with respect to the Fisher approximation of an ideal gas of noninteracting clusters, but a simple modified energy-density functional can still describe the global energetics. The multifragmentation regime is dominated by combinatorial effects, but the isoscaling of the largest fragment appears to be a promising observable for the experimental measurement of the symmetry energy.

Nuclear symmetry energy probed by neutron skin thickness of nuclei

We describe a relation between the symmetry energy coefficients c(sym)(rho) of nuclear matter and a(sym)(A) of finite nuclei that accommodates other correlations of nuclear properties with the low-density behavior of c(sym)(rho). Here, we take advantage of this relation to explore the prospects for constraining c(sym)(rho) of systematic measurements of neutron skin sizes across the mass table, using as example present data from antiprotonic atoms. The found constraints from neutron skins are in harmony with the recent determinations from reactions and giant resonances.

Circumstantial evidence for a soft nuclear symmetry energy at suprasaturation densities

Within an isospin- and momentum-dependent hadronic transport model, it is shown that the recent FOPI data on the pi;{-}/pi;{+} ratio in central heavy-ion collisions at SIS/GSI energies [Willy Reisdorf, Nucl. Phys. A 781, 459 (2007)10.1016/j.nuclphysa.2006.10.085] provide circumstantial evidence suggesting a rather soft nuclear symmetry energy E_{sym}(rho) at rho> or =2rho_{0} compared to the Akmal-Pandharipande-Ravenhall prediction. Some astrophysical implications and the need for further experimental confirmations are discussed.