Experimental measurements of nuclear systems with different neutron and proton numbers have enabled significant progress in constraining the EoS of nuclear matter. Careful experimental and theoretical analyses can now provide experimentally grounded constraints on the nuclear symmetry energy over a range of densities and isospin asymmetries. Over such densities, existing constraints on the...

We review the current status of studies related to the equation of state as extracted from HADES data and will discuss future perspectives in heavy-ion runs at lower energies.

The study of strongly interacting matter under extreme conditions is one of the most important topics in the exploration of Quantum Chromodynamics (QCD).

In this talk, we present new measurements by the High Acceptance DiElectron Spectrometer (HADES) at GSI Helmholtzzentrum für Schwerionenforschung, relating to flow phenomena at high nuclear densities. HADES provides a large acceptance,...

Constraining the equation of state (EOS) of dense symmetric nuclear matter has been the goal of numerous experimental heavy-ion efforts worldwide, including the early experiments at the AGS and SPS, the currently ongoing efforts such as the Beam Energy Scan program at RHIC and the HADES experiment at GSI, and future experiments such as the Compressed Baryonic Matter experiment at FAIR. Beyond...

Within the framework of the quantum molecular dynamics transport model, the pion production and constraint of the high-density symmetry energy in heavy-ion collisions near threshold energy have been thoroughly investigated. The energy conservation in the decay of resonances and reabsorption of pions in nuclear medium are taken into account. The isospin and momentum dependent hyperon-nucleon...

Rapidity dependence of directed flow ($v_1$) and elliptic flow ($v_2$) were analyzed for various particles, including proton, deuteron, triton, $\mathrm{^{3}He}$, and $\mathrm{^{4}He}$ observed in collisions involving $\mathrm{^{132}Sn+{}^{124}Sn}$ and $\mathrm{^{108}Sn+{}^{112}Sn}$ collisions at 270 $\mathrm{MeV/u}$.

The flow was larger for heavier charged particles, i.e.,

the slope of...

This work presents an investigation of isospin equilibration in cross-bombarding $^{48,40}$Ca$+^{48,40}$Ca reactions at 35 MeV/nucleon, by comparing experimental data with filtered transport model calculations. In particular, isospin diffusion is studied from the evolution of the isospin transport ratio with centrality. The asymmetry $\delta = (N − Z)/A$ of the quasiprojectile residue is used...

In the framework of heavy ion collisions, isospin transport phenomena can be used as a tool to gather information on the properties of nuclear matter far from equilibrium conditions. The INDRA-FAZIA apparatus, operating in GANIL, is particularly well suited to investigate such kind of phenomena; it exploits the best characteristics of FAZIA (covering the forward polar angles and providing...

The isospin-dependent equation of state of nuclear matter, i.e. symmetry energy $E_{sym}(\rho)$ plays an important role in the study of nuclear physics and Astrophysics. In terrestrial lab, heavy ion collision provides a unique way to constrain $E_{sym}(\rho)$. So a compact spectrometer for heavy ion experiment（CSHINE）is built and coincident events are measured.

Via HBT intensity...

Since 2020 the FAZIA detector performs experiment at GANIL coupled with the large acceptance INDRA array. This combined detector for charged reaction products represents one of the most advanced tools to study the details of the reaction mechanisms at the Fermi energies, with special attention to the role of the symmetry energy term of the EOS. The ...

A new radioactive-ion-beam (RIB) accelerator complex RAON is under construction in Korea. RAON will be equipped with both ISOL (Isotope Separation On-Line) and IF (In-flight Fragmentation) systems and explore the possibility to combine them to provide more neutron-rich ion beams than any single mode. The ISOL and low-energy systems were completed in 2022 and the high-energy section will be...

The HIRFL-CSR external-target experiment (CEE) will be the first large-scale nuclear physics experiment working at GeV/u energy regime in China, providing new opportunities to the studies of nuclear equation of state. The construction of the whole spectrometers is in good progress, most of the design parameters of the detector are fixed. Based on these parameters, we have conducted the fast...

The equation of state (EOS) is a fundamental property of nuclear matter, important for studying the structure of systems as diverse as the atomic nucleus and neutron stars. Understanding the physics of neutron stars is becoming even more important recently because of the observation of gravitational waves from the neutron star merger. Nuclear reactions involving heavy-ion collisions in the...

Elliptic flow as measured in heavy-ion collisions has proven to be very effective in constraining nuclear matter equation of state at supra-saturation densities. In particular neutron-to-proton and neutron-to-charged particles elliptic flow ratio in Au+Au at 400 MeV/nucleon collisions, measured at GSI in FOPI-LAND and ASY-EOS experiments, have allowed to investigate the symmetry energy...

The investigation of the nuclear equation of state (EoS) has been fundamental to the exploration of the QCD phase diagram at non-zero baryonic densities. This has garnered multi-messenger interest from nuclear theory, astrophysics, and heavy-ion collisions, especially due to its potential synergy with astrophysical objects and events, such as binary neutron mergers. At densities greater than...

Transport models are indispensable in order to obtain information on the nuclear equation-of-state and in-medium properties of nucleons from heavy-ion collisions generally, and, in particular, in the hadronic intermediate-energy regime to constrain such quantities as the density dependence of the symmetry energy, since they are able to take into account the non-equilibrium features of such...

Recent results connected to nuclear collision dynamics, from Fermi up to intermediate energies, will be reviewed.

Dissipative heavy ion reactions offer the unique opportunity to probe the complex nuclear many-body dynamics and to explore, in laboratory experiments, transient states of nuclear matter under several conditions of density, temperature and charge asymmetry.

Transport models are...

The heavy-ion experimental program at SIS and the future FAIR facility explore nuclear matter at extreme conditions of large densities and temperatures where according to many-body theory a strong modification of hadron properties occurs. An understanding of the properties of strongly-interacting hadronic and partonic matter - created in heavy-ion collisions - from a microscopic point of...

We develop a kinetic approach to the production of light nuclei up to mass number A = 4 in intermediate-energy heavy-ion collisions by including them as dynamic degrees of freedom. The conversions between nucleons and light nuclei during the collisions are incorporated dynamically via the breakup of light nuclei by a nucleon and their inverse reactions. We also include the Mott effect on light...

The equation of state of nuclear matter, momentum dependence of the effective interaction and in-medium modification of elastic nucleon-nucleon cross-sections are studied by comparing theoretical predictions for collective flows in intermediate energy heavy-ion collisions to experimental data. To that end, the dcQMD transport model [1] is upgraded by implementing medium modifications of...

Four different reactions, $^{32}$S+$^{12}$C and $^{20}$Ne+$^{12}$C at 25 and 50 MeV/nucleon, have been measured with the FAZIA detector, isotopically resolving the systems. Events have been well classified and fragment properties have been compared with AMD simulation coupled with the HFl afterburner, dedicated to light nuclei de-excitation. Here we report on a first comparison, shown in C....

In this contribution we consider hybrid compact stars located in the third branch of the corresponding mass-radius diagram. We introduce a set of equations of state whose symmetry energy parameters vary. These are described by multi-polytropes and by a RMF model with several isovector mesons, fulfilling laboratory constraints. We find correlations between tidal deformabilities, stellar radii...

The statistical approaches were previously successfully applied

for the description of the disintegration of excited nuclear sources.

Such single sources in equilibrium with the temperature around

6-8 MeV (also with smaller temperatures) can be produced both

from spectator residues in peripheral collisions of nuclei and

after the fusion of nuclei in central collisions at Fermi...

Neutrinos play a crucial role in neutron star physics, from their birth in a core-collapse supernovae where neutrinos dictate the dynamics of the explosion, to the merger by determining the matter composition in the ejecta for heavy element nucleosynthesis. They are also key actors of cooling in (proto-)neutron stars and of the thermal relaxation of accreting neutron stars. Identifying...

Collisions of heavy ions are the best tools at our disposal to probe nuclear matter. It allows us to reach extreme densities, giving us the possibility to constraint transport models. In particular, at incident energies around 100 MeV/nucleon, a participant zone is formed by a part of projectile and target nuclei.

The aim of this work is to characterize the participant zone. We will focus...

Heavy nuclear systems formed in dissipative collisions at Fermi energy develop a variety of possible sites where density gradients and instabilities combine in different possible ways.

Depending on physical conditions, these sites may host different distinct isospin processes, either related to isospin transport or to phase transitions.

As we will show on the basis of a suited set of...

Neutron stars are the universe’s best natural laboratories to study dense nuclear, matter. At high densities, low temperatures, and high isospin asymmtery inaccessible in terrestrial collider experiments, neutron stars host the most extreme matter in the universe. Different regions of neutron stars will probe different physics, with some observables dominated by the poorly understood physics...

Asteroseismic modes within neutron stars (NSs) provide can provide novel insight into NS structure and the physics of dense matter, as they are sensitive to a variety of different stellar properties. The multimessenger detection of a resonant shattering flare and gravitational waves from a binary NS merger could allow us to measure the frequency of the crust-core interface mode. This mode is...

In this work, we aim to put constraints on the equation of state of nuclear matter by comparing transport calculations with SMASH to the recent high-precision data from the HADES experiment.

In order to achieve reliable constraints, we first investigate different methods of taking light nuclei formation into account, as a large fraction of nucleons is bound to nuclei. We find that flow...

The understanding of neutron star properties from fundamental physics is still far from being completed. One of the reasons is that the theory for strong force, QCD, does not apply simply to neutron star matter at a few times the nuclear saturation density. At low density, chiral effective field theory is fixing a limit which can be incorporated in the description of the crust of neutron...

Core-collapse supernovae are one of the most fascinating phenomena in astrophysics but the explosion mechanism is not clearly understood yet because of their intricacies. I will give an overview about the role of nuclear equation-of-state (EOS) and nuclei in supernovae. I will also discuss key nuclei and their key information to be investigated for further supernova study, and introduce recent...

Using a meta model for nuclear Equation of State (EOS) with its parameters constrained by astrophysical observations and terrestrial nuclear experiments, we examine effects of nuclear EOS especially its symmetry energy \esym term on the speed of sound squared $C^2_s(\rho)$ and the critical density $\rho_t$ where $C^2_s(\rho_t)$ vanishes (indicating the onset of spinodal decomposition) in both...

I will argue that if black holes represent one the most fascinating implications of Einstein's theory of gravity, neutron stars in binary system are its richest laboratory, where gravity blends with astrophysics and particle physics. I will discuss the rapid recent progress made in modelling these systems and show how the gravitational signal can provide tight constraints on the equation of...

Microscopic nuclear theory is based on the tenet that atomic nuclei and nucleonic matter can be accurately described as collections of point-like nucleons interacting via two- and many-body forces obeying nonrelativistic quantum mechanics---and the concept of the ab initio approach is to calculate nuclear systems accordingly. The forces are fixed in free-space scattering and must be accurate....

Modern formulations of nuclear forces, such as pionless or chiral effective field theory, are typically based on a perturbative approach. Such interactions are then often employed by state-of-the-art nuclear many-body techniques (such as quantum Monte Carlo) which are non-perturbative in nature. The equation of state of a compact star is thus the result of this interplay of perturbative...

Recently, quite significant progress has been made in the description of nuclear matter and, in particular, its symmetry energy, at sufficiently high densities using skyrmion crystals and their semiclassical quantization. We briefly review these recent results and describe the challenges which still must be mastered in order to establish the Skyrme model framework as a reliable tool for the...

The iso-scalar and iso-vector nuclear matter parameters (NMPs) are frequently used to characterise the equations of state (EoSs) that govern the properties of neutron stars (NSs). Recent attempts to relate the radius and tidal deformability of a NS to the individual NMPs have been inconclusive. These properties display strong correlations with the pressure of NS matter which depends on several...

A simplified version of the density dependent covariant density functional model is employed in a Bayesian analysis to determine the equation of state (EOS) of dense matter. Various constraints from nuclear physics; ab initio calculations of pure neutron matter (PNM); a lower bound on the maximum mass of neutron stars (NSs) are imposed in the order to investigate the effectiveness of their...

The non-radial oscillations of the neutron stars (NSs) have been suggested as an useful tool to probe the composition of neutron star matter (NSM). With this scope in mind, we consider a large number of equations of states (EOSs) that are consistent with nuclear matter properties and pure neutron matter EOS based on a chiral effective field theory (chEFT) calculation for the low densities and...

In this talk, I will address the question of the understanding of dense matter from a model incorporating properties from quantum chromodynamics (QCD). QCD is a fundamental theory that poses challenges when applied to low-energy nuclear physics, such as finite nuclei and neutron star matter, due to its non-perturbative nature. While solving QCD numerically on a lattice is possible, it...

The R3B (Reactions with Relativistic Radioactive ion Beams) experiment

as a major instrument of the NUSTAR collaboration for the research facility

FAIR in Darmstadt, enables kinematically complete measurements of reactions

with high-energy radioactive beams. Part of the broad physics program of R3B

is to gain a deep insight into the nuclear structure and dynamics of exotic nuclei

far off...

Recently, we constructed a new equation of state (EoS) table including the Bose-Einstein

condensate of negatively charged kaons for core collapse supernova and binary neutron star merger simulations. The nuclear statistical equilibrium model

including excluded volume effects was used to describe the matter below the saturation density whereas the uniform matter composed of

neutrons,...

The deepest region of the neutron star (NS) crust may consist of a layer of so-called nuclear pastas. If they exist, these exotic nuclear structures could significantly affect the transport and mechanical properties of dense matter, leaving their imprints on such NS observables as continuous gravitational-wave emission, NS oscillations and their damping, the spin period of x-ray pulsars, and...

First results of the tests of the newly constructed KRAB detector will be

presented. The tests have been performed with the Bi source, cosmic rays and

with the proton beams from the CCB cyclotron in Krakow. The detector was

designed to provide fast, multiplicity based trigger for the future ASY-EOS II

experiment as well as the information on the azimuthal distributions of the

reaction...

TThe ratio $Y(\pi^-)/Y(\pi^+)$ ($\pi^-/\pi^+$) of the yields of the different charge states of $\pi$ is considered an important observable for determining the symmetry energy density in the high-density region. However, there remains much controversy in using it to constrain the resulting symmetry energy. This requires us to further explore the physical mechanisms associated with the...

New insights into the nuclear symmetry energy and related formation of neutron skin in nuclei have been gained through recent precise parity-violating electron scattering experiments on $^{48}$Ca (CREX) and $^{208}$Pb (PREX-II). To understand the implications of these experiments for the nuclear energy density functionals (EDF), consistent investigation is required to address the nuclear...

Infinite nuclear matter is a suitable laboratory to learn about nuclear forces in many-body systems. Modern theoretical predictions of neutron-rich matter are particularly timely in view of recent and planned measurements of observables which are sensitive to the equation of state of isospin-asymmetric matter. For these reasons, over the past several years we have taken a broad look at the...

The last decade observational data show that massive neutron star have masses

above 2.1 Msun what indicate rather stiff EOS, whereas the lightweight

star observed by NICER and HESS appears to be very compact what suggest rather

soft EOS. Such opposite properties (stiff at higher densities and soft at lower)

are available in RMF nuclear model equipped with new kind of crossing...

The electric dipole polarizability is a key observable for the understanding of nuclear matter. Strong correlations between the neutron skin thickness, the dipole polarizability and the parameters of the symmetry energy term in the equation of state of neutron rich matter have been found within the framework of energy density functional theory [1].

The polarizability is experimentally...

Large-scale models of nuclear structure play an essential role in many astrophysics applications. Nucleosynthesis simulations of heavy elements, through the rapid neutron-capture process (or r-process), for example, require nuclear information inputs across the whole nuclear chart, far beyond the region where experimental data is available. Likewise, describing the extremely dense neutron-rich...

The neutron-skin thickness is one of the most robust probes of the slope parameter of the nuclear symmetry energy, which is responsible for the main uncertainty of the nuclear matter equation of state. Relativistic heavy-ion collisions may serve as a complementary measurement of the neutron-skin thickness, in addition to various methods in nuclear structure studies. In these collisions, we...

An experiment measuring the Coulomb-excitation cross section, σC [1] in neutron-rich tin nuclei

( 124 Sn– 134 Sn) at relativistic energies was performed at GSI, Darmstadt with the aim to constrain

the slope of the symmetry energy, L. This particular cross section correlates with dipole polariz-

ability, α D , a well-established observable for constraining L [2], which enables achieving the...

We study the pionic self-energy and its impact on the energy-momentum dispersion relation of

pion in neutron-rich conditions such as interior of a neutron star. In such neutron-rich state, the

negatively charged pions can be produced copiously. Furthermore, these negatively charged pions

can form a Bose-Einstein condensate with zero momentum above nuclear saturation densities. In

this...

It is still a challenging task to derive the symmetry energy and equation of state for neutron stars from the underlying realistic nucleon-nucleon interaction. The relativistic Brueckner-Hartree-Fock (RBHF) theory provides a relativistic ab-initio approach, which is able to reproduce saturation properties of symmetric nuclear matter without three-body forces. However, most of the past work...

Here we provide experimental evidence for an increasing nuclear symmetry energy for nuclei at temperatures typically found in neutron mergers and collapsars, which may lead to the close in of the nuclear chart (or neutron dripline) at the limits of stability, and constrain the paths of various r-process nucleosynthesis mechanisms; hence, supporting the universal pattern of abundances for...

This contribution reviews a selection of available constraints to the nuclear symmetry energy around saturation density from nuclear structure calculations on ground and collective excited state properties of atomic nuclei. Special focus will be given to the parity violating asymmetry and dipole polarizability in 48Ca and 208Pb. Phenomenologic as well as microscopic results --whenever...

Nuclear many-body system is a self-organizing active matter, which has seemingly contradictory aspects of uniform single-particle matter and non-uniform cluster-forming matter. Recently, we have launched two complementary experimental programs "ESPRI/ONOKORO" to study uniform/non-uniform properties in nuclei and nuclear matter. In the projects, direct reaction methods with hadronic probes at...

Isobar $^{96}_{44}$Ru+$^{96}_{44}$Ru and $^{96}_{40}$Zr+$^{96}_{40}$Zr collisions at nucleon-nucleon center-of-mass energy of 200 GeV at the Relativistic Heavy Ion Collider (RHIC) were initially proposed as a decisive experiment on the chiral magnetic effect, presuming identical QCD background [1]. They turned out to be rather different, by, for instance, as large as 5% in multiplicity [2]....

We present results for the equation of state of asymmetric nuclear matter at finite temperature based on

chiral effective field theory interactions to next-to-next-to-next-to-leading order. Our results assess

the theoretical uncertainties from the many-body calculation and the chiral expansion. Using a

Gaussian process emulator for the free energy, we derive the thermodynamic properties of...

Our knowledge about dense matter explored in the cores of neutron stars remains limited. Fortunately, the detections of gravitational waves emitted from the merger of neutron stars and the corresponding electromagnetic signals provide a new way of studying supranuclear-dense material. Making use of the strength of multi-messenger astronomy, one can combine the information obtained from...

Interpreting high-energy, astrophysical phenomena, such as supernova explosions or neutron-star collisions, requires a robust understanding of matter at supranuclear densities. However, our knowledge about dense matter explored in the cores of neutron stars remains limited. Fortunately, dense matter is not only probed in astrophysical observations, but also in terrestrial heavy-ion collision...

With recent advances in astronomical observations, major progress has been made in determining the pressure of neutron star matter at high density. This pressure is constrained by the neutron star deformability, determined from gravitational waves emitted in a neutron-star merger, and measurements of radii for two neutron stars with measured masses, using a new X-ray observatory on the...

The impacts of various symmetry energy parameters on the properties of neutron stars have been recently investigated, and the outcomes are at variance. Results obtained from systematic analysis of the correlations of slope and curvature parameters of symmetry energy at the saturation density with the tidal deformability and stellar radius of non-spinning neutron stars in the mass range of...

The last few years have seen tremendous progress in multi-messenger observations of neutron stars (NS) that have constrained their global properties such as their masses, radii and tidal deformabilities. These constraints could be used to obtain valuable information on the nuclear symmetry energy. However, in order to do so, we require rigorous theoretical nuclear physics inputs to interpret...

This contribution concerns the characterization of the nuclear equation of state (EOS) evaluated from ground state properties of nuclei, i.e. from nuclear masses, charge radii and neutron thickness. By using a Thomas-Fermi framework combined with a specific Seyler-Blanchard nucleon-nucleon interaction containing both non-local and density terms, I will show that quantitative information about...

The Neutron Star Interior Composition Explorer (NICER) has been in operation from the International Space Station for over 6 years now. By accurately modelling the phase-energy resolved light curves of millisecond pulsars (caused by their hot polar caps) and the effects of general relativity on these light curves, we can obtain measurements of the pulsars’ masses and radii. NICER has...

Gravitational-wave observatories have established a new field of transient astronomy. The most recent LIGO-Virgo-Kagra catalog, GWTC-3, identifies 90 merging binaries, which range from a double neutron star with a total mass of 2.7 at 40 Mpc (GW170817) to a double black hole with a total mass of 150 at 5.3 Gpc (GW190521). These observations have many potential implications for dense matter...

Binary neutron star (BNS) mergers provide a unique probe of the dense-matter equation of state (EOS) across a wide range of parameter space, from the cold, equilibrium conditions of the inspiral to the shock-heated and dynamical environment of the post-merger remnant. In this talk, I will discuss what we can (and cannot) learn about the EOS from current and upcoming observations of binary...

I will discuss the equation of state and composition of dense matter with heavy baryons within covariant density functional (CDF) theory. The sensitivity of the results on the structure of compact stars to variation of the slope of symmetry energy and the skewness is demonstrated. The finite temperature equation of state and its implications for multimessenger astrophysics is also discussed

Observed for the first time in 1967 as pulsars, neutron

stars represent the most extreme bodies known in our universe. Relict

of the gravitational collapse and subsequent supernova explosion of a

massive star at the end of his life, they gather a mass of up to twice

that of our sun in a sphere with a radius of about 10 km. Their

phenomenology is very rich and complex. Modelling requires...

In central heavy-ion collisions at several hundred MeV/nucleon, a compressed nuclear system is formed up to about twice the saturation density and then rapidly expands, to produce a lot of light clusters. Recently, cluster observables from the SpiRIT experiment have been compared with the AMD calculation in some published papers and a paper in preparation. Some cluster observables showed...

In the last years Bayesian techniques are employed more and more frequently to build equations of state of dense neutron rich matter by imposing various sets of constraints on functional relations derived within models with different degrees of sophistication and physical underpinning. In this talk I shall confront the results obtained when the same constraints are imposed to models of...

In my talk, I will present the efforts on the refinement of the transport models after the TMEP projection. The improvements include the refined nonlinear term in the nucleonic mean field, momentum-dependent interactions, and NN$\to$N$\Delta$ cross sections. Based on the updated models, the influence of symmetry energy and effective mass splitting on the neutron to proton yield ratios, triton...

We have entered the era of multi-messenger nuclear astrophysics; bringing a host of astrophysical observations and nuclear experimental data to collectively measure the properties of neutron star matter and the nuclear force in neutron-rich systems. In order to combine disparate data sets with meaningful uncertainty quantification, over the past decade the statistical inference techniques...

The momentum dependence of the nucleon mean-field potential in a wide momentum range can be an important factor to determine the $\Delta$ resonance and pion production in intermediate-energy heavy-ion collisions. In particular, in neutron-rich systems such as 132Sn+124Sn collisions, we need to carefully treat the momentum dependence because the neutron and proton potentials can have different...