Background: The microscopic composition and properties of infinite hadronic matter at a wide range of densities and temperatures have been subjects of intense investigation for decades. The equation of state (EoS) relating pressure, energy density, and temperature at a given particle number density is essential for modeling compact astrophysical objects such as neutron stars, core-collapse supernovae, and related phenomena, including the creation of chemical elements in the universe. The EoS depends not only on the particles present in the matter, but, more importantly, also on the forces acting among them. Because a realistic and quantitative description of infinite hadronic matter and nuclei from first principles in not available at present, a large variety of phenomenological models has been developed in the past several decades, but the scarcity of experimental and observational data does not allow a unique determination of the adjustable parameters.Purpose: It is essential for further development of the field to determine the most realistic parameter sets and to use them consistently. Recently, a set of constraints on properties of nuclear matter was formed and the performance of 240 nonrelativistic Skyrme parametrizations was assessed [M. Dutra et al., Phys. Rev. C 85, 035201 (2012)] in describing nuclear matter up to about three times nuclear saturation density. In the present work we examine 263 relativistic-mean-field (RMF) models in a comparable approach. These models have been widely used because of several important aspects not always present in nonrelativistic models, such as intrinsic Lorentz covariance, automatic inclusion of spin, appropriate saturation mechanism for nuclear matter, causality, and, therefore, no problems related to superluminal speed of sound in medium.Method: Three different sets of constraints related to symmetric nuclear matter, pure neutron matter, symmetry energy, and its derivatives were used. The first set (SET1) was the same as used in assessing the Skyrme parametrizations. The second and third sets (SET2a and SET2b) were more suitable for analysis of RMF and included, up-to-date theoretical, experimental and empirical information.Results: The sets of updated constraints (SET2a and SET2b) differed somewhat in the level of restriction but still yielded only 4 and 3 approved RMF models, respectively. A similarly small number of approved Skyrme parametrizations were found in the previous study with Skyrme models. An interesting feature of our analysis has been that the results change dramatically if the constraint on the volume part of the isospin incompressibility $({K}_{\ensuremath{\tau},\mathrm{v}})$ is eliminated. In this case, we have 35 approved models in SET2a and 30 in SET2b.Conclusions: Our work provides a new insight into application of RMF models to properties of nuclear matter and brings into focus their problematic proliferation. The assessment performed in this work should be used in future applications of RMF models. Moreover, the most extensive set of refined constraints (including nuclear matter and finite-nuclei-related properties) should be used in future determinations of new parameter sets to provide models that can be used with more confidence in a wide range of applications. Pointing to reasons for the many failures, even of the frequently used models, should lead to their improvement and to the identification of possible missing physics not included in present energy density functionals.

/pdf/relativistic-mean-field-hadronic-models-under-nuclear-matter-576xalqdcq.pdf

Relativistic mean-field hadronic models under nuclear matter constraints

We review recent studies of the evolution of collective excitations in atomic nuclei far from the valley of β-stability. Collective degrees of freedom govern essential aspects of nuclear structure, and for several decades the study of collective modes such as rotations and vibrations has played a vital role in our understanding of complex properties of nuclei. The multipole response of unstable nuclei and the possible occurrence of new exotic modes of excitation in weakly bound nuclear systems, present a rapidly growing field of research, but only few experimental studies of these phenomena have been reported so far. Valuable data on the evolution of the low-energy dipole response in unstable neutron-rich nuclei have been gathered in recent experiments, but the available information is not sufficient to determine the nature of observed excitations. Even in stable nuclei various modes of giant collective oscillations had been predicted by theory years before they were observed, and for that reason it is very important to perform detailed theoretical studies of the evolution of collective modes of excitation in nuclei far from stability. We therefore discuss the modern theoretical tools that have been developed in recent years for the description of collective excitations in weakly bound nuclei. The review focuses on the applications of these models to studies of the evolution of low-energy dipole modes from stable nuclei to systems near the particle emission threshold, to analyses of various isoscalar modes, those for which data are already available, as well as those that could be observed in future experiments, to a description of charge-exchange modes and their evolution in neutron-rich nuclei, and to studies of the role of exotic low-energy modes in astrophysical processes.

https://iopscience.iop.org/article/10.1088/0034-4885/70/5/R02/pdf

Exotic modes of excitation in atomic nuclei far from stability

The strength distributions of the giant monopole resonance (GMR) have been measured in the even-A Sn isotopes (A = 112-124) with inelastic scattering of 400-MeV alpha particles in the angular range 0 degrees-8.5 degrees. We find that the experimentally observed GMR energies of the Sn isotopes are lower than the values predicted by theoretical calculations that reproduce the GMR energies in Pb-208 and Zr-90 very well. From the GMR data, a value of K-tau = -550 +/- 100 MeV is obtained for the asymmetry term in the nuclear incompressibility.

Isotopic dependence of the giant monopole resonance in the even-A Sn112-124 isotopes and the asymmetry term in nuclear incompressibility

Cross sections and analyzing powers for polarized proton elastic scattering from $^{58}\mathrm{Ni}$, and $^{204,206,208}\mathrm{Pb}$ were measured at intermediate energy ${E}_{p}=295$ MeV. An effective relativistic Love-Franey interaction is tuned to reproduce $^{58}\mathrm{Ni}$ scattering data within the framework of the relativistic impulse approximation. The neutron densities of the lead isotopes are deduced using model-independent sum-of-Gaussians distributions. Their error envelopes are estimated by a new ${\ensuremath{\chi}}^{2}$ criterion including uncertainties associated with the reaction model. The systematic behaviors of extracted error envelopes of the neutron density distributions in $^{204,206,208}\mathrm{Pb}$ are presented. The extracted neutron and proton density distribution of $^{208}\mathrm{Pb}$ gives a neutron skin thickness of $\ensuremath{\Delta}{r}_{\mathit{np}}={0.211}_{\ensuremath{-}0.063}^{+0.054}$ fm.

/pdf/neutron-density-distributions-of-pb-204-206-208-deduced-via-4k6trjvgnz.pdf

Neutron density distributions of Pb 204 , 206 , 208 deduced via proton elastic scattering at E p = 295 MeV

The compression-mode giant resonances and nuclear incompressibility

The systematic behavior of the isoscalar giant dipole resonance (ISGDR) in Zr-90, Sn-116, S-144 m, and Pb-208 is studied with inelastic a scattering at E-alpha=386 MeV. Multipole-decomposition analysis is applied to extract the excitation strengths of giant resonances from the (alpha, alpha') differential cross sections at theta(lab)= 0.64degrees-13.5degrees. The bimodal structure of the ISGDR is discussed and compared with recent theoretical results from Hartree-Fock + random-phase-approximation calculations.

Systematics of the bimodal isoscalar giant dipole resonance

Giant monopole resonances in deformed nuclei

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Systematics of the bimodal isoscalar giant dipole resonance

Giant monopole resonances in deformed nuclei