Subsaturation Densities Research Articles

Constraining Symmetry Energy from Pygmy Dipole Resonances in 68Ni and 132Sn

Abstract We make a new investigation on the correlation at saturation (subsaturation) density between the density dependence of symmetry energy and the percentage of energy-weighted sum rule (EWSR) exhausted by the pygmy dipole resonances (PDR) in $^{68}$Ni and $^{132}$Sn. The calculations are performed within Skyrme HF (or HF+BCS) plus random phase approximation (RPA) (or quasiparticle RPA) by using SAMi-J effective interactions. The effect of pairing on the dipole strength distribution of $^{68}$Ni and the density dependence of symmetry energy is discussed. The slope parameter L and symmetry energy J at saturation (subsaturation) density are 41.8-90.2 MeV (39.3-64.1 MeV) and 28.0-32.5 MeV (23.0-23.8 MeV). They are consistent with the currently accepted values except for the symmetry energy J at subsaturation density, it is slightly smaller than the data from nuclear mass differences and electric dipole polarizability.

Finite-temperature equations of state of compact stars with hyperons: three-dimensional tables

We construct tables of finite temperature equation of state (EoS) of hypernuclear matter in the range of densities, temperatures, and electron fractions that are needed for numerical simulations of supernovas, proto-neutron stars, and binary neutron star mergers and cast them in the format of CompOSE database. The tables are extracted from a model that is based on covariant density functional (CDF) theory that includes the full JP=1/2+\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$J^P=1/2^+$$\\end{document} baryon octet in a manner that is consistent with the current astrophysical and nuclear constraints. We employ a parameterization with three different values of the slope of the symmetry energy Lsym=30\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L_\ extrm{sym}=30$$\\end{document}, 50 and 70 MeV and fixed skewness Qsat=400\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Q_\ extrm{sat}= 400$$\\end{document} MeV for above saturation matter. A model for the EoS of inhomogeneous matter is matched at sub-saturation density to the high-density hypernuclear EoS. We discuss the generic features of the resulting EoS and the composition of matter as a function of density, temperature, and electron fraction. The nuclear characteristics and strangeness fraction of these models are compared to the alternatives from the literature. The integral properties of static and rapidly rotating compact stars in the limit of zero temperature are discussed and confronted with the multimessenger astrophysical constraints.

Studying sub-saturation density symmetry energy with different nuclear thermometers

Studying sub-saturation density symmetry energy with different nuclear thermometers

Probing the Neutron Skin of Unstable Nuclei with Heavy-Ion Collisions

To improve the constraints of symmetry energy at subsaturation density, measuring and accumulating more neutron skin data for neutron-rich unstable nuclei is naturally required. Aiming to probe the neutron skin of unstable nuclei by using low-intermediate-energy heavy-ion collisions, we develop a new version of an improved quantum molecular dynamics model, in which the neutron skin of the initial nucleus and the mean-field potential in nucleon propagation are consistently treated. Our calculations show that the three observables, such as the cross-sections of the primary projectile-like residues with A>100 (σA>100), the difference of σA>100 between 132Sn + 124Sn and 124Sn + 124Sn systems (δσA>100), and the neutron-to-proton yield ratio (R(n/p)) in the transverse direction, could be used to measure the neutron skin of the unstable nuclei and to constrain the slope of the symmetry energy in the future.

Pasta properties of the neutron star within effective relativistic mean-field model

We study the properties of pasta structures and their influence on the neutron star observables employing the effective relativistic mean-field (E-RMF) model. The compressible liquid drop model is used to incorporate the finite size effects, considering the possibility of nonspherical structures in the inner crust. The unified equation of states are constructed for several E-RMF parameters to study various properties such as pasta mass and thickness in the neutron star's crust. The majority of the pasta properties are sensitive to the symmetry energy in the subsaturation density region. Using the results from Monte Carlo simulations, we estimate the shear modulus of the crust in the context of quasiperiodic oscillations from soft gamma-ray repeaters and calculate the frequency of fundamental torsional oscillation mode in the inner crust. Global properties of the neutron star such as mass-radius profile, the moment of inertia, crustal mass, crustal thickness, and fractional crustal moment of inertia are worked out. The results are consistent with various observational and theoretical constraints.

Embedding short-range correlations in relativistic density functionals through quasi-deuterons

The formation of clusters at sub-saturation densities, as a result of many-body correlations, constitutes an essential feature for a reliable modelization of the nuclear matter equation of state (EoS). Phenomenological models that make use of energy density functionals (EDFs) offer a convenient approach to account for the presence of these bound states of nucleons when introduced as additional degrees of freedom. However, in these models clusters dissolve, by construction, when the nuclear saturation density is approached from below, revealing inconsistencies with recent findings that evidence the existence of short-range correlations (SRCs) even at larger densities. The idea of this work is to incorporate SRCs in established models for the EoS, in light of the importance of these features for the description of heavy-ion collisions, nuclear structure and in the astrophysical context. Our aim is to describe SRCs at supra-saturation densities by using effective quasi-clusters immersed in dense matter as a surrogate for correlations, in a regime where cluster dissolution is usually predicted in phenomenological models. Within the EDF framework, we explore a novel approach to embed SRCs within a relativistic mean-field model with density dependent couplings through the introduction of suitable in-medium modifications of the cluster properties, in particular their binding energy shifts, which are responsible for describing the cluster dissolution. As a first exploratory step, the example of a quasi-deuteron within the generalized relativistic density functional approach is investigated. The zero temperature case is examined, where the deuteron fraction is given by the density of a boson condensate. For the first time, suitable parameterizations of the cluster mass shift at zero temperature are derived for all baryon densities. They are constrained by experimental results for the effective deuteron fraction in nuclear matter near saturation and by microscopic many-body calculations in the low-density limit. A proper description of well-constrained nuclear matter quantities at saturation is kept through a refit of the nucleon meson coupling strengths. The proposed parameterizations allow to also determine the density dependence of the quasi-deuteron mass fraction at arbitrary isospin asymmetries. The strength of the deuteron-meson couplings is assessed to be of crucial importance. Novel effects on some thermodynamic quantities, such as the matter incompressibility, the symmetry energy and its slope, are finally discerned and discussed. The findings of the present study represent a first step to improve the description of nuclear matter and its EoS at supra-saturation densities in EDFs by considering correlations in an effective way. In a next step, the single-particle momentum distributions in nuclear matter can be explored using proper wave functions of the quasi-deuteron in the medium. The momentum distributions are expected to exhibit a high-momentum tail, as observed in the experimental study of SRCs by nucleon knockout with high-energy electrons. This will be studied in a forthcoming publication with an extensive presentation of the theoretical method and the results.

Further insights of free and bound particles in the fragmentation of symmetric and asymmetric collisions

We have checked the sensitivity of different observables such as fragment multiplicities, anisotropy ratios and N/Z ratios of free and bound nucleons towards the density dependence of nuclear symmetry energy for different mass asymmetric reactions at beam energy of 20 MeV/nucleon. These investigations revealed that neutron-to-proton ratios of free particles and the power-law exponent obtained from the mass dependence of these ratios in mass asymmetric reactions are highly sensitive to density dependence of symmetry energy and could be utilized to constrain nuclear symmetry energy. Comparison of our calculations with available measurements at low energies favors softer symmetry energy at sub-saturation densities.

Density dependence of symmetry energy and neutron skin thickness revisited using relativistic mean field models with nonlinear couplings

The correlation between neutron skin-thickness of a nucleus with neutron excess and density slope parameter of symmetry energy is assessed as a function of density using relativistic mean-field models containing nonlinear couplings among different mesons. Models with larger skin were found to probe the density slope parameter even at suprasaturation densities, whereas models with smaller skin were observed to be sensitive only at specific subsaturation density, connected to the average density of nuclei. Possible reasons behind this density dependence are explored systematically. These results might be model specific, which need to be reassessed in other types of interactions existing in the literature. Nevertheless, extrapolating the predictions at high densities from models, which are optimized by data at saturation or subsaturation densities, needs to be handled with care.

Properties of hot finite nuclei and associated correlations with infinite nuclear matter

This work aims to study the various thermal characteristics of nuclei in view of the saturation and critical behavior of infinite nuclear matter. The free energy of a nucleus is parametrized using the density and temperature-dependent liquid-drop model, and interaction among nucleons is worked out within the effective relativistic mean-field theory (E-RMF). The effective mass (${m}^{*}$) and critical temperature of infinite symmetric nuclear matter (${T}_{c}$) of a given E-RMF parameter force play a seminal role in the estimation of thermal properties. Larger ${m}^{*}$ and ${T}_{c}$ of the E-RMF set estimate larger excitation energy, level density, and limiting temperature $({T}_{l})$ for a given nucleus. The limiting temperature of a nucleus also depends on the behavior of the nuclear gas surrounding the nucleus, making the equation of state (EoS) at subsaturation densities an important input. A stiff EoS in the subsaturation region estimates a higher pressure of the nuclear gas, making it less stable. Since ${T}_{c}$ plays an important part in these calculations, we perform a Pearson correlation statistical study of twenty E-RMF parameter sets, satisfying the relevant constraint on the EoS. Effective mass seems to govern the thermal characteristics of infinite as well as finite nuclear matter in the framework of E-RMF theory.

Pairing effects in nuclear pasta phase within the relativistic Thomas–Fermi formalism

Pairing effects in non-uniform nuclear matter, surrounded by electrons, are studied in the protoneutron star early stage and in other conditions. The so-called nuclear pasta phases at subsaturation densities are solved in a Wigner–Seitz cell, within the Thomas–Fermi approximation. The solution of this problem is important for the understanding of the physics of a newly born neutron star after a supernova explosion. It is shown that the pasta phase is more stable than uniform nuclear matter on some conditions and the pairing force relevance is studied in the determination of these stable phases.

Prior Probability Distributions of Neutron Star Crust Models

Abstract To make best use of multifaceted astronomical and nuclear data sets, probability distributions of neutron star models that can be used to propagate errors consistently from one domain to another are required. We take steps toward a consistent model for this purpose, highlight where model inconsistencies occur, and assess the resulting model uncertainty. Using two distributions of nuclear symmetry energy parameters—one uniform, the other based on pure neutron matter theory—we prepare two ensembles of neutron star inner crust models. We use an extended Skyrme energy density functional within a compressible liquid drop model (CLDM). We fit the surface parameters of the CLDM to quantum 3D Hartree–Fock calculations of crustal nuclei. All models predict that more than 50% of the crust by mass and 15% of the crust by thickness comprises pasta with medians of around 62% and 30%, respectively. We also present 68% and 95% ranges for the crust composition as a function of density. We examine the relationships between crust–core boundary and pasta transition properties, the thickness of the pasta layers, the symmetry energy at saturation and subsaturation densities, and the neutron skins of 208Pb and 48Ca. We quantify the correlations using the maximal information coefficient, which can effectively characterize nonlinear relationships. Future measurements of neutron skins, information from nuclear masses and giant resonances, and theoretical constraints on PNM will be able to place constraints on the location of the pasta and crust–core boundaries and the amount of pasta in the crust.

Nuclear symmetry energy from neutron skins and pure neutron matter in a Bayesian framework

We present an inference of the nuclear symmetry energy magnitude $J$, the slope $L$, and the curvature ${K}_{\mathrm{sym}}$ from combining neutron skin data on calcium, lead and tin isotopes, and our best theoretical information about pure neutron matter. A Bayesian framework is used to consistently incorporate prior knowledge of the pure neutron matter equation of state from chiral effective field theory calculations. Neutron skins are modeled in a fully quantum Skyrme-Hartree-Fock approach using an extended Skyrme energy-density functional which allows for independent variation of $J$, $L$, and ${K}_{\mathrm{sym}}$ without affecting the symmetric nuclear matter equation of state. The effect of using neutron skin data obtained with different physical probes is quantified. We argue that, given the existing data, combining the errors in quadrature is the more appropriate way to obtain unified errors for each nuclide, and in doing so we obtain 95% credible values of $J=31.3\begin{array}{c}+4.2\\ \ensuremath{-}5.9\end{array}\phantom{\rule{0.28em}{0ex}}\mathrm{MeV}$, $L=40\begin{array}{c}+34\\ \ensuremath{-}26\end{array}\phantom{\rule{0.28em}{0ex}}\mathrm{MeV}$, and ${K}_{\ensuremath{\tau}}=L\ensuremath{-}6{K}_{\mathrm{sym}}=\ensuremath{-}444\begin{array}{c}+100\\ \ensuremath{-}84\end{array}\phantom{\rule{0.28em}{0ex}}\mathrm{MeV}$ using uninformative priors in $J$, $L$, and ${K}_{\mathrm{sym}}$, and $J=31.9\begin{array}{c}+1.3\\ \ensuremath{-}1.3\end{array}\phantom{\rule{0.28em}{0ex}}\mathrm{MeV}$, $L=37\begin{array}{c}+9\\ \ensuremath{-}8\end{array}\phantom{\rule{0.28em}{0ex}}\mathrm{MeV}$, and ${K}_{\ensuremath{\tau}}=\ensuremath{-}480\begin{array}{c}+25\\ \ensuremath{-}26\end{array}\phantom{\rule{0.28em}{0ex}}\mathrm{MeV}$ using pure neutron matter (PNM) priors. We also show that the nonpositive correlation between $J$ and $L$ induced by neutron skin data is consistent with the nuclear droplet model. Neutron skin data alone are shown to place limits on the symmetry energy parameters as stringent as those obtained from chiral effective field theory alone, and when combined the 95% credible intervals are reduced by a factor of 4--5. It is also shown that the majority of nuclear interactions used in the literature have subsaturation density dependencies that are inconsistent with the combination of PNM priors and neutron skin data. We show measurements of lead and calcium neutron skins from upcoming parity-violating electron scattering experiments at Jefferson Lab and Mainz Superconducting Accelerator should obtain total error ranges $\mathrm{\ensuremath{\Delta}}L\ensuremath{\approx}50\phantom{\rule{0.28em}{0ex}}\mathrm{MeV}$ and $\mathrm{\ensuremath{\Delta}}{K}_{\ensuremath{\tau}}\ensuremath{\approx}240\phantom{\rule{0.28em}{0ex}}\mathrm{MeV}$ for uninformative priors and $\mathrm{\ensuremath{\Delta}}L\ensuremath{\approx}30\phantom{\rule{0.28em}{0ex}}\mathrm{MeV}$ and $\mathrm{\ensuremath{\Delta}}{K}_{\ensuremath{\tau}}\ensuremath{\approx}100\phantom{\rule{0.28em}{0ex}}\mathrm{MeV}$ for PNM priors at 67% credible bounds. Ahead of those experiments, we make predictions based on existing data on neutron skins of tin alone for the neutron skins of calcium and lead of $0.166\ifmmode\pm\else\textpm\fi{}0.008$ fm and $0.169\ifmmode\pm\else\textpm\fi{}0.014$ fm, respectively, using uninformative priors and $0.167\ifmmode\pm\else\textpm\fi{}0.008$ fm and $0.172\ifmmode\pm\else\textpm\fi{}0.015$ fm, respectively, using PNM priors.

Bayesian inference on isospin splitting of nucleon effective mass from giant resonances in 208Pb * *Supported in part by the National Natural Science Foundation of China (11905302, 11625521) and National SKA Program of China (2020SKA0120300)

From a Bayesian analysis of the electric dipole polarizability, the constrained energy of isovector giant dipole resonance, the peak energy of isocalar giant quadrupole resonance, and the constrained energy of isocalar giant monopole resonance in 208Pb, we extract the isoscalar and isovector effective masses in nuclear matter at saturation density as and , respectively, at 90% confidence level. The constraints obtained on and lead to a positive isospin splitting of nucleon effective mass in asymmetric nuclear matter of isospin asymmetry at as . In addition, the symmetry energy at the subsaturation density is determined to be MeV at 90% confidence level.

Neutron–proton interaction, bubble structure and neutron skin properties of Co in a Supernova

In the present paper, we investigated the neutron skin properties, central depletion effects, residual and average neutron–proton interactions for Co in a Type II Supernova 1987A. The neutron skin thicknesses performed by Skyrme–Hartree–Fock model for the isotopic chain of Co $$(17\le N\le 82)$$ are obtained with different methods to investigate the bulk and surface contributions to neutron skin thicknesses as a function of neutron number N and relative neutron excess I = (N-Z)/A. For this purpose, two-parameter Fermi (2pF) distributions for each nucleus are obtained by the proton and neutron density distributions. Since the neutron skin thickness demonstrates the dependency on the symmetry pressure of neutron matter and sensitive to the symmetry energy at the sub-saturation density, the neutron skin properties lead to the investigation on the formation and composition of the crusts in Supernova and neutron stars. For a proper understanding of surface effects of nuclei, the central depletion (or bubble structure) effects on neutron skin of nuclei in the Supernova are explained by calculating the bubble parameters b and b′. Furthermore, in order to illustrate accuracy of theoretical model used in the current work, the mass model approach is also analyzed by the calculating residual and average neutron–proton interactions, where the fluctuations in the mass model approaches have also been compared with the experimental and theoretical results in the literature. In order to evaluate more nuclear properties, we also analyzed the charge form factors and the single- particle energy levels for Co isotopes in the Supernova for providing nuclear data for electron-nucleus scattering experimental processes.

Nuclear symmetry energy parameters from neutron skin thickness in 208Pb and electric dipole polarizability in 68Ni , 120Sn and 208Pb

Observables like neutron skin thickness and electric dipole polarizability in heavy nuclei are considered as most effective probes for the density dependence of nuclear symmetry energy at subsaturation density region. In the present work, within the framework of droplet model, we use finite range effective interactions to calculate the neutron skin thickness in 208Pb and the electric dipole polarizability in 68Ni, 120Sn and 208Pb. We correlate these quantities with the parameters of nuclear symmetry energy. Available experimental data on the neutron skin thickness in 208Pb and electric dipole polarizability in 68Ni, 120Sn and 208Pb are used to deduce information on the density slope parameter of nuclear symmetry energy at saturation and at subsaturation densities. Constraints such as 35.2 ≤ L(ρ 0) ≤ 64.4 MeV and 43 ≤ L(ρ c ) ≤ 55 MeV are obtained using experimental values for neutron skin thickness.

Clusters as surrogate for explicit short-range correlations in relativistic mean-field models

The formation of clusters at sub-saturation densities in nuclear matter can be seen as a result of many-body correlations. Various theoretical models have been developed to take this effect into account, mostly on a phenomenological level using energy density functionals. These models are constructed in such a way that clusters appear solely in dilute matter and dissolve when the density approaches the nuclear saturation density. At higher densities only nucleons survive as quasi-particles and no explicit correlations between the constituents of nuclear matter are considered. The possible description of correlations with cluster degrees of freedom at supra-saturation densities is explored using the example of a quasi-deuteron in a generalized relativistic density functional. The required change in the density dependence of the cluster mass shift, responsible for describing the cluster dissolution in the present model, is derived for nuclear matter at zero temperature.

Properties of nuclear pastas

In this review we study the nuclear pastas as they are expected to be formed in neutron star crusts. We start with a study of the pastas formed in nuclear matter (composed of protons and neutrons), we follow with the role of the electron gas on the formation of pastas, and we then investigate the pastas in neutron star matter (nuclear matter embedded in an electron gas).Nuclear matter (NM) at intermediate temperatures (1 MeV ≲ T ≲ 15 MeV), at saturation and sub-saturation densities, and with proton content ranging from 30% to 50% was found to have liquid, gaseous and liquid-gas mixed phases. The isospin-dependent phase diagram was obtained along with the critical points, and the symmetry energy was calculated and compared to experimental data and other theories. At low temperatures (T ≲ 1 MeV) NM produces crystal-like structures around saturation densities, and pasta-like structures at sub-saturation densities. Properties of the pasta structures were studied with cluster-recognition algorithms, caloric curve, the radial distribution function, the Lindemann coefficient, Kolmogorov statistics, Minkowski functionals; the symmetry energy of the pasta showed a connection with its morphology.Neutron star matter (NSM) is nuclear matter embedded in an electron gas. The electron gas is included in the calculation by the inclusion of an screened Coulomb potential. To connect the NM pastas with those in neutron star matter (NSM), the role the strength and screening length of the Coulomb interaction have on the formation of the pastas in NM was investigated. Pasta was found to exist even without the presence of the electron gas, but the effect of the Coulomb interaction is to form more defined pasta structures, among other effects. Likewise, it was determined that there is a minimal screening length for the developed structures to be independent of the cell size.Neutron star matter was found to have similar phases as NM, phase transitions, symmetry energy, structure function and thermal conductivity. Like in NM, pasta forms at around T ≈ 1.5 MeV, and liquid-to-solid phase changes were detected at T ≈ 0.5 MeV. The structure function and the symmetry energy were also found to depend on the pasta structures.

Symmetry energy effect on emissions of light particles in coincidence with fast fission

The emission of light particles in coincidence with fast fission in near peripheral reactions of 40Ar+197Au at 30 MeV/u beam energy has been studied by using the Improved Quantum Molecular Dynamics Model (ImQMD). It is demonstrated that in the symmetrical fast fission of the heavy target-like fragment (TLF), the emission of the coalescence-invariant neutrons (CIN) is enhanced particularly at large angles in comparison to that in the events without fission. Due to the enhanced CIN emission and the accumulation of the isospin effect in the long-time process, the yield ratio of the CIN to the coalescence-invariant protons (CIP) in the fission events exhibits significant dependence on the symmetry energy Esym(ρ) varying with density. Considering that the large angle neutrons are experimentally advantageous to measure for the lower flying velocity and lower multiplicity, we emphasize that the yield ratio RCINP at large angles in the fast fission events can be used as a novel probe of the nuclear symmetry energy at sub-saturation densities.

Light clusters in dilute heavy-baryon admixed nuclear matter

We study the composition of nuclear matter at sub-saturation densities, non-zero temperatures, and isospin asymmetry, under the conditions characteristic of binary neutron star mergers, stellar collapse, and low-energy heavy-ion collisions. The composition includes light clusters with mass number Ale 4, a heavy nucleus (^{56}{Fe}), the varDelta -resonances, the isotriplet of pions, as well as the Lambda hyperon. The nucleonic mean-fields are computed from a zero-range density functional, whereas the pion-nucleon interactions are treated to leading order in chiral perturbation theory. We show that with increasing temperature and/or density the composition of matter shifts from light-cluster to heavy baryon dominated one, the transition taking place nearly independent of the magnitude of the isospin. Our findings highlight the importance of simultaneous treatment of light clusters and heavy baryons in the astrophysical and heavy-ion physics contexts.

Nuclear symmetry energy and neutron skin thickness of 208Pb using a finite range effective interaction

We use a finite range simple effective interaction to construct nuclear equations of state for the study of the density dependence of the nuclear symmetry energy. The EoSs provide good descriptions of the nuclear symmetry energy at a subsaturation density ρc = 0.11 fm−3 and at a density around two times the saturation density ρ0. We obtain a correlation between the neutron skin thickness in 208Pb and the density slope parameter at the subsaturation density. A linear relation is obtained between the neutron skin thickness and the parameter , where Es(ρ0) and L(ρc) are respectively the nuclear symmetry energy at saturation density and the density slope parameter at the subsaturation density.