Although light nuclear clusters are known to form abundantly in warm and dilute nuclear matter, their role in hot and dense nuclear matter remains unclear due to the lack of experimental indication for their modifications by the Mott effect under such conditions. To address this issue, we resort to intermediate-energy heavy-ion collisions, where light clusters are mainly produced in the transiently formed hot and dense matter. A kinetic approach, which includes dynamically the formation and dissociation of light clusters, is employed to deduce the strength of the Mott effect and the α -particle fraction in hot and dense nuclear matter from the light-nuclei yields measured by the FOPI Collaboration in central Au + Au collisions at energies of 0.25 A to 0.6 A GeV . We find an unexpectedly abundant α clustering in this environment, which will have profound implications for modeling the nuclear equation of state and describing supernovae and neutron star mergers.

Anisotropic flows in heavy-ion collisions provide a basic experimental observable to understand nuclear collision dynamics and to constrain the dense nuclear matter equation of state (EOS). Within the framework of the lattice Boltzmann-Uehling-Uhlenbeck transport model, we present a systematic study of proton anisotropic flow observables measured by the HADES Collaboration, by utilizing the recently developed nuclear effective interaction based on the density-, momentum-, and isospin-dependent N5LO Skyrme pseudopotential. In particular, we investigate the impacts of the momentum dependence of nucleon mean-field potentials, the stiffness of the symmetric nuclear matter (SNM) EOS, the high-density behaviors of the symmetry energy, and the in-medium modification of nucleon-nucleon elastic cross sections on proton directed (v1), elliptic (v2), triangular (v3), and quadrangular (v4) flows in Au+Au collisions at root sNN = 2.4 GeV. Our results show that the proton anisotropic flows are strongly sensitive to the momentum dependence of the nucleon mean-field potential as well as the incompressibility coefficient K0 of SNM. In addition, the transverse momentum dependence of the proton v2 exhibits a modest sensitivity to the higher-order skewness coefficient J0 and kurtosis coefficient I0 of SNM as well as the momentum dependence of the symmetry potential, while the transverse momentum dependence of the proton v1 is shown to modestly depend on the in-medium modification of nucleon-nucleon elastic cross sections. Moreover, the high-density symmetry energy seems to have limited effects on the proton anisotropic flows. These findings highlight the necessity of considering the momentum dependence of nucleon mean-field potentials including the symmetry potential, the higher-order characteristic parameters of the SNM EOS beyond K0, and the in-medium modification of nucleon-nucleon elastic cross sections, in future Bayesian transport model analyses on proton anisotropic flows in heavy-ion collisions at HADES energies, for the purpose of extracting information on the nuclear matter EOS as well as the associated underlying nuclear effective interactions.

We present a phase-space excluded-volume approach applicable to both nuclear matter and nonequilibrium processes, such as heavy-ion collisions, to account for in-medium effects on light clusters. In this approach, light clusters can exist only if the nucleon one-body phase-space occupation of the surrounding nuclear medium-including explicit contributions from light clusters-is sufficiently low. The nucleon occupation is determined self-consistently by accounting for the interplay between in-medium effects and thermodynamic properties, thereby improving upon the conventional treatment based on an uncorrelated medium (i.e., an overall nucleonic Fermi-Dirac distribution) typically employed in studies of light clusters in nuclear matter. We apply the approach to evaluate the Mott momenta and the fractions of light clusters in nuclear matter. Their differences from results obtained under the uncorrelated-medium assumption are found to be moderate. The main advantage of the present approach lies in its ability to be integrated into dynamical models, enabling more accurate studies of in-medium effects on light clusters, based on their measured yields in heavy-ion collisions.

Within a lattice Boltzmann-Uehling-Uhlenbeck transport model coupled to a kinetic approach for light-cluster formation, we investigate the impact of explicit light-cluster degrees of freedom on collective flows in Au+Au collisions at FOPI energies with beam energies E_ beam= 120–1500 A MeV by using a density-, momentum-, and isospin-dependent N5LO Skyrme pseudopotential. We first benchmark the kinetic approach by comparing the calculated light-cluster yields with FOPI data in central Au+Au collisions. We then analyze the collective flows of protons and light nuclei (deuterons, tritons, ^3He, and ^4He) in mid-central collisions. For protons, calculations with and without dynamical light-cluster degrees of freedom are compared to quantify the influence of dynamical cluster formation on proton directed (v_1), elliptic (v_2), triangular (v_3), and quadrangular (v_4) flows. We find that the dynamical light-cluster effect appreciably modifies proton v_1–v_4 flows at E_ beam=120–150 A MeV, remains visible at E_ beam=250–400 A MeV, and gradually weakens at E_ beam≳ 600 A MeV. For light nuclei, the kinetic approach captures the overall beam-energy dependence of the FOPI flow data, with better agreement for E_ beam≥ 400 A MeV. We further examine the nucleon-number scaling of v_2/A in both model calculations and experimental data, finding that the kinetic light-cluster formation approach qualitatively reproduces the observed scaling behavior. These results highlight the importance of a dynamical treatment of light-cluster formation for interpreting collective flows in heavy-ion collisions below about 600 A MeV, although the clustering effects on proton flows are minor at higher collision energies.

We propose an extension of the quarkyonic matter framework that includes u, d, and s quarks and the full baryon octet. Within this extended framework, we impose beta-equilibrium between baryons and leptons, while determining the quark fractions from the constituent quark contents of baryons. The hadronic sector of octet baryons is described by a recently developed density, momentum and isospin dependent effective interaction based on the N3LO Skyrme pseudopotential, whereas quarks and leptons are treated as free particles. We find that the quarkyonic mechanism can obviously reduce the critical density for hyperon appearance in neutron stars due to the fact that the nucleons are displaced to higher momentum states in quarkyonic matter and their chemical potentials rise accordingly. Furthermore, the quarkyonic mechanism can significantly stiffen the equation of state of hyperon star matter and thereby enhance the hyperon star maximum mass, thus helping to mitigate the hyperon puzzle.

Pion production in heavy-ion collisions at intermediate energies provides an important probe of the collision dynamics and nuclear matter equation of state, especially the high-density behavior of the symmetry energy. Using the lattice Boltzmann-Uehling-Uhlenbeck transport model with a recently developed nuclear effective interaction based on the so-called N5LO Skyrme pseudopotential, we investigate the effects of the momentum dependence of nucleon mean-field potentials on the pion production in Au+Au collisions at a beam energy of 1.23 GeV/nucleon. We find that a stronger momentum dependence, for which the nucleon mean-field potentials increase faster with momentum, generally suppresses pion production. This feature can be understood in terms of the mean-field-induced modification of nucleon high-momentum phase space during the compression stage: a stronger momentum dependence can reduce the relative fraction of high-momentum nucleons in heavy-ion collisions, thereby suppressing the production of Δ resonances and pions.

The recently developed nuclear effective interaction based on the so-called N3LO Skyrme pseudopotential is extended to include hyperon–nucleon and hyperon–hyperon interactions by assuming similar density, momentum, and isospin dependence as for the nucleon–nucleon interaction. The parameters in these interactions are determined from either experimental information, if any, or chiral effective field theory or lattice quantum chromodynamics calculations of the hyperon potentials in nuclear matter around nuclear saturation density ρ _0 . We find that varying the high-density behavior of the symmetry energy E _sym ( ρ ) can significantly change the critical density for hyperon appearance in neutron stars and thus the maximum mass M _TOV of static hyperon stars. In particular, a symmetry energy that is soft around 2 ρ _0 –3 ρ _0 but stiff above about 4 ρ _0 can lead to M _TOV ≳ 2 M _⊙ for hyperon stars and simultaneously be compatible with (1) the constraints on the equation of state of symmetric nuclear matter at suprasaturation densities obtained from flow data in heavy-ion collisions; (2) the microscopic calculations of the equation of state for pure neutron matter; (3) the tidal deformability of stars extracted from gravitational wave signal GW 170817; (4) the mass–radius relations of PSR J0030+0451, PSR J0740+6620, and PSR J0437-4715 measured from NICER; and (5) the observation of an unusually low mass and small radius in the central compact object of HESS J1731-347. Furthermore, the squared sound speed of the hyperon star matter naturally displays a strong peak structure around a baryon density of 3 ρ _0 –4 ρ _0 , consistent with a model-independent analysis of the multimessenger data. Our results suggest that the high-density symmetry energy could be a key to the solution of the hyperon puzzle in neutron star physics.

Large density fluctuations of conserved charges have been proposed as a promising signature for exploring the QCD critical point in heavy-ion collisions. These fluctuations are expected to exhibit a fractal or scale-invariant behavior, which can be probed by intermittency analysis. Recent high-energy experimental studies reveal that the signal of critical fluctuations related to intermittency is very weak and thus could be easily obscured by the overwhelming background particles in the data sample. Employing a point cloud neural network with topological machine learning, we can successfully classify weak signal events from background noise by the extracted distinct topological features, and accurately determine the intermittency index for weak signal event samples.

High-energy nuclear collisions provide a unique environment for synthesizing both nuclei and antinuclei (such as d̅ and ^4He) at temperatures (k_BT∼100 MeV) much higher than their binding energies per nucleon of a few MeV. The underlying production mechanism, whether through statistical hadronization, nucleon coalescence, or dynamical regeneration and disintegration, remains unsettled. Here we address this question using pion-nucleus femtoscopy. By solving relativistic kinetic equations for pion-catalyzed reactions (πNN ↔ πd) for deuteron production and including final-state p-wave scatterings derived from an established effective interaction, we successfully reproduce the resonance peaks of both π^+-p and π^+-d femtoscopic correlations observed in pp collisions at √(s) = 13 TeV. The interplay between Δ resonance and p-wave scatterings shifts both correlation peaks downward by about 70 MeV relative to vacuum Δ decay. Conversely, both the nucleon coalescence model and the statistical hadronization model significantly underestimate the data and produce additional dips that are absent from the data. These results provide compelling evidence that pion-catalyzed reactions play a dominant role in the production of light (anti-)nuclei in high-energy nuclear collisions and cosmic rays.

A phase-space excluded-volume approach is developed to investigate the in-medium properties of light clusters in nuclear matter. In this approach, light clusters can exist only if the total nucleon phase-space occupation of the surrounding nuclear medium – including explicit contributions from light clusters – is sufficiently low. The distribution functions of nucleons and light clusters are determined self-consistently by accounting for the interplay between in-medium effects and thermodynamic properties. By employing standard Skyrme energy-density functionals to model the nuclear mean-field potential, the approach enables the evaluation of the Mott momentum and the fraction of light clusters in nuclear matter. Furthermore, it can be readily integrated into dynamical models, to study in-medium effects on light clusters, based on measured yields in heavy-ion collisions.

Although light nuclear clusters are known to affect the properties of warm and dilute nuclear matter, their role in warm and dense nuclear matter remains unclear due to the lack of experimental evidence for their modifications by the Mott effect in such an environment. To address this issue, we resort to intermediate-energy heavy-ion collisions, where light clusters are mainly produced in the transiently formed warm and dense matter. A kinetic approach, which includes dynamically the formation and dissociation of light clusters, is employed to deduce the strength of the Mott effects and the α-particle fraction in warm and dense nuclear matter from the light-nuclei yields measured by the FOPI Collaboration in central Au+Au collisions at energies of 0.25A to 0.6A GeV. We find an unexpectedly abundant α clustering in this environment, which will have profound implications for modeling the nuclear equation of state and describing supernovae and neutron star mergers.

Based on the Boltzmann-Uehling-Uhlenbeck equation, we investigate the effects of the isovector nucleon effective mass m(v,0)* and the in-medium nucleon-nucleon cross section sigma* on the isovector giant dipole resonance (IVGDR) in Pb-208, employing a set of representative Skyrme energy density functionals. We find that the energy-weighted sum rule m(1) of the IVGDR is highly sensitive to m*(v,0) and only mildly dependent on sigma*, while the width Gamma of the IVGDR is primarily governed by sigma* with a moderate sensitivity to m(v,0)*. From a Bayesian analysis of both m(1) and Gamma, we infer that the m(v,0)*/m = 0.730+0.036-0.034, where m is the bare nucleon mass. Furthermore, by incorporating the isoscalar nucleon effective mass m(s,0)*/m = 0.820 +/- 0.030, extracted from the isoscalar giant quadrupole resonance in Pb-208, the linear neutron-proton effective mass splitting coefficient at saturation density rho(0) is determined to be Delta m*1(rho(0))/m = 0.202(-0.114)(+0.118).

The recently developed extended Skyrme effective interaction based on the so-called N3LO Skyrme pseudopotential is generalized to the general NnLO case by incorporating the derivative terms up to 2nth order into the central term of the pseudopotential. The corresponding expressions of Hamiltonian density and single-nucleon potential are derived within the Hartree-Fock approximation under general nonequilibrium conditions. The inclusion of the higher-order derivative terms provides additional higher-order momentum dependence for the single-nucleon potential, and in particular, we find that the N5LO single-nucleon potential with momentumdependent terms up to p10 can give a nice description for the empirical nucleon optical potential up to energy of 2 GeV. At the same time, the density-dependent terms in the extended Skyrme effective interaction are extended correspondingly in the spirit of the Fermi momentum expansion, which allows highly flexible variation of density behavior for both the symmetric nuclear matter equation of state and the symmetry energy. Based on the Skyrme pseudopotential up to N3LO, N4LO, and N5LO, we construct a series of interactions with the nucleon optical potential having different high-momentum behaviors and with the symmetry potentials featuring different linear isospin-splitting coefficients for nucleon effective mass, by which we study the properties of nuclear matter and neutron stars. Furthermore, within the lattice Boltzmann-Uehling-Uhlenbeck transport model, some benchmark simulations with selected interactions are performed for the Au+Au collisions at abeam energy of 1.23 GeV per nucleon, and the predicted collective flows for protons are found to nicely agree with the data measured by HADES collaboration.

The application of machine learning methods for predicting potential energy surface and physical properties withinmaterials science has garnered significant attention. Among recent advancements, Kolmogorov-Arnold Networks(KANs) have emerged as a promising alternative to traditional Multi-Layer Perceptrons. This study evaluates theimpact of substituting Multi-Layer Perceptrons with KANs within four established machine learning frameworks:Allegro, Neural Equivariant Interatomic Potentials, Higher Order Equivariant Message Passing Neural Network(MACE), and the Edge-Based Tensor Prediction Graph Neural Network. Our results demonstrate that theintegration of KANs enhances prediction accuracies, especially for complex datasets such as the HfO2 structures.Notably, using KANs exclusively in the output block achieves the most significant improvements, improvingprediction accuracy and computational efficiency. Furthermore, employing KANs exclusively in the output blockfacilitates faster inference and improved computational efficiency relative to utilizing KANs throughout the entiremodel. The selection of optimal basis functions for KANs depends on the specific problem. Our resultsdemonstrate the strong potential of KANs in enhancing machine learning potentials and material propertypredictions. Additionally, the proposed methodology offers a generalizable framework that can be applied to otherML architectures

High-energy nuclear collisions provide a unique site for the synthesis of both nuclei and antinuclei at temperatures of k T ≈ 100 − 150 MeV. In these little bangs of transient collisions, a quark-gluon plasma (QGP) of nearly vanishing viscosity is created, which is believed to have existed in the early universe within the first few microseconds after the Big Bang. Analyses of identified particles produced in these little bangs based on the statistical hadronization model for the QGP have suggested that light (anti)nuclei are produced from the QGP as other hadrons and their abundances are little affected by later hadronic dynamics. Here, we find a strong reduction of the triton yield by about a factor of 1.8 in high-energy heavy-ion collisions based on a kinetic approach that includes the effects of hadronic re-scatterings, particularly that due to pion-catalyzed multi-body reactions. This finding is supported by the latest experimental measurements and thus unveils the important role of hadronic dynamics in the little-bang nucleosynthesis.

It is important to develop a unified theoretical framework to describe the nuclear experiments and astrophysical observations based on the same effective nuclear interactions. Based on the so-called Skyrme pseudopotential up to next-to-next-to-next-to-leading order, we construct a series of extended Skyrme interactions by modifying the density-dependent term and fitting the empirical nucleon optical potential up to above $1$ GeV, the empirical properties of isospin symmetric nuclear matter, the microscopic calculations of pure neutron matter and the properties of neutron stars from astrophysical observations. The modification of the density-dependent term in the extended Skyrme interactions follows the idea of Fermi momentum expansion and this leads to a highly flexible density behavior of the symmetry energy. In particular, the values of the density slope parameter $L$ of the symmetry energy for the new extended Skyrme interactions range from $L = -5$ MeV to $L = 125$ MeV by construction, to cover the large uncertainty of the density dependence of the symmetry energy. Furthermore, in order to consider the effects of isoscalar and isovector nucleon effective masses, we adjust the momentum dependency of the single-nucleon optical potential and the symmetry potential of these new extended Skyrme interactions and construct a parameter set family, by which we systematically study the impacts of the symmetry energy and the nucleon effective masses on the properties of nuclear matter and neutron stars. The new extended Skyrme interactions constructed in the present work will be useful to determine the equation of state of isospin asymmetric nuclear matter, especially the symmetry energy, as well as the nucleon effective masses and their isospin splitting, in transport model simulations for heavy-ion collisions, nuclear structure calculations and neutron star studies.

Understanding the dynamics of dilute nuclear matter is of crucial importance in several contexts, ranging from nuclear fragmentation to supernova collapse and gravitational-wave signal emission. However, within a unified dynamical framework, describing the concurrent appearance of light clusters, emerging from few-nucleon correlations, and heavier fragments formed due to large-scale correlations related to liquid-gas phase instabilities, remains a significant challenge. Within a linearized Vlasov dynamics, we show that light clusters, and in-medium effects in their propagation, have a strong influence on the growth and characteristics of the unstable modes that prelude the fragmentation of the system. These findings might pave the way for novel avenues in the study of dilute composite matter, envisioning intriguing consequences for heavy-ion collisions and in the broader astrophysical context.

We develop a kinetic approach to the production of light nuclei up to mass number $A$ $\leqslant$ $4$ 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 nuclei, i.e., a light nucleus would no longer be bound if the phase-space density of its surrounding nucleons is too large. With this kinetic approach, we obtain a reasonable description of the measured yields of light nuclei in central Au+Au collisions at energies of $0.25$ - $1.0A~\rm GeV$ by the FOPI collaboration. Our study also indicates that the observed enhancement of the $\alpha$-particle yield at low incident energies can be attributed to a weaker Mott effect on the $\alpha$-particle, which makes it more difficult to dissolve in nuclear medium, as a result of its much larger binding energy.

Based on the Boltzmann-Uehling-Uhlenbeck (BUU) transport equation, a medium correction to the elastic nucleon-nucleon (NN) cross sections is given by comparing the width of the isovector giant dipole resonance in 208Pb and the nuclear stopping obtained from the BUU equation with those from experimental measurements. For the nuclear stopping, we choose the scaled rapidity distributions and the nuclear stopping power vartl, denoted as the ratio of the variances of the transverse to that of the longitudinal rapidity distributions, of central 197Au + 197Au collisions at the energy of 150A MeV measured by the INDRA and the FOPI collaborations. This enables us to provide a unified medium correction of elastic NN cross sections for distinct energy regimes. A reliable in-medium NN cross section, as given here, will reduce the uncertainties of the BUU equation when applying it to nuclear collective motion and heavy-ion collisions to extract the information of the nuclear equation of state.

In recent years, machine learning (ML) techniques have emerged as powerful tools for studying many-body complex systems, and encompassing phase transitions in various domains of physics. This mini review provides a concise yet comprehensive examination of the advancements achieved in applying ML to investigate phase transitions, with a primary focus on those involved in nuclear matter studies.