arXiv subjects

Bao-Jun Cai

Publications and source records attributed to Bao-Jun Cai.

At least 19 recordsLinked to original sources

arXiv2026

Neutron Skin Effects on Particle Emission in Heavy-Ion Collisions: A Topic Review with Astrophysical and Nuclear Structure Connections

The neutron skin, defined by the difference between neutron and proton root-mean-square radii, is a characteristic manifestation of isospin asymmetry and an important probe of the isovector nuclear interaction. This focused review examines how neutron skins influence particle emission and collective dynamics in heavy-ion collisions, from the Fermi-energy regime to ultra-relativistic energies. By modifying the initial neutron and proton density profiles, the neutron skin affects the isospin composition and geometry of the participant region, pre-equilibrium emission, particle production, fragment formation, and collective flow. We review neutron-to-proton and $\rm{t}/^3\rm{He}$ yield ratios, light clusters, pion ratios, bremsstrahlung photons, isoscaling and fragment momentum distributions, and neutron-proton differential flow and momentum observables, emphasizing their interplay with the symmetry energy and transport dynamics. At high energies, neutron skins also modify the initial geometry, eccentricities, multiplicities, and anisotropic flows in isobar and heavy-nucleus collisions. We discuss the challenge of disentangling these effects from deformation, surface diffuseness, shell structure, clustering, and model dependence. Broader connections to parity-violating electron scattering, dipole responses, coherent elastic neutrino-nucleus scattering, SRC-induced proton skins in momentum space, and neutron-star observables are also explored. Finally, we highlight opportunities from radioactive beams, improved collision experiments, microscopic many-body and transport calculations, and Bayesian inference. Combining multiple reaction systems and observables with complementary nuclear-structure and astrophysical information will be essential for quantitatively constraining neutron skins and the density dependence of the symmetry energy.

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arXiv2026

An Effective Upper Bound on the Pressure-to-Energy Density Ratio in Neutron Stars

The equation-of-state (EOS) parameter $ϕ\equiv P/\varepsilon$, defined as the ratio of pressure to energy density, encapsulates the fundamental response of matter under extreme compression. Its value at the center of the most massive neutron star (NS), $\x \equiv P_{\rm c}/\varepsilon_{\rm c}$, provides an upper bound on the maximum attainable central EOS parameter of cold visible matter. Remarkably, owing to the intrinsically nonlinear structure of the EOS in General Relativity (GR), this bound lies far below the naive Special Relativity (SR) limit of unity. In this work, we refine the theoretical upper bound on $\x$ in a self-consistent manner by incorporating, in addition to the causality constraint from SR, the mass-sphere stability condition associated with the mass evolution pattern in the vicinity of the NS center. This condition is formulated within the intrinsic and perturbative analysis of the dimensionless Tolman--Oppenheimer--Volkoff equations (IPAD-TOV) framework. The combined constraints yield an improved bound, $\x \lesssim 0.385$, which is slightly above but fully consistent with the previously derived causal-only limit, $\x \lesssim 0.374$. We further derive an improved scaling relation for NS compactness and demonstrate its robustness across a broad set of 284 realistic EOSs, including models with first-order phase transitions, exotic degrees of freedom, continuous crossover behavior, and deconfined quark cores. Within the IPAD-TOV framework, the resulting bound on $\x$ provides a new EOS-insensitive probe of the microphysics of cold superdense matter compressed by strong-field gravity in GR.

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arXiv2026

A New Scaling of Neutron Star Tidal Deformability for Directly Probing the Core Equation of State

The dimensionless tidal deformability, $Λ$, of neutron stars (NSs), inferred from gravitational-wave (GW) observations, has thus far been used primarily to constrain the pressure of dense matter near twice nuclear saturation density, leaving the core equation of state (EOS) largely inaccessible to inspiral-phase GW observations. We show that the core EOS can be probed directly through $Λ$ using a perturbative analysis of the dimensionless stellar-structure and tidal-response equations formulated in terms of scaled intrinsic variables, without invoking any specific EOS model. We uncover a remarkable EOS-insensitive scaling relation between $Λ$ and the central EOS parameter $\mathrm{X}\equiv P_{\rm c}/\varepsilon_{\rm c}$, where $P_{\rm c}$ and $\varepsilon_{\rm c}$ denote the central pressure and energy density, respectively. The relation is validated against a broad ensemble of physically viable EOSs. Applying it to tidal deformabilities inferred from events such as GW170817 enables a direct determination of $\mathrm{X}$. We further derive a tight lower bound, $Λ_{\rm{TOV}}\gtrsim 9.2^{+1.2}_{-1.2}$, for maximum-mass NSs along stable mass-radius sequences, quantitatively demonstrating that even the most compact stable NSs remain distinctly separated from black holes, for which $Λ_{\rm{BH}}=0$. These findings reveal a previously unrecognized connection between inspiral-phase tidal deformability and the core EOS, establishing a direct link between GW observables and the microphysics of ultradense matter in the strong-gravity regime. The resulting scaling establishes inspiral-phase tidal deformability as a direct and largely model-insensitive probe of the EOS of NS cores.

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arXiv2026

Nucleon Short-Range Correlations and High-Momentum Dynamics: Implications on the Equation of State of Dense Matter

Nucleon short-range correlations (SRCs) and their high-momentum tails (HMTs) encode key short-range dynamics in nuclei and dense matter. This review provides a concise overview of SRC features relevant to the Equation of State (EOS) of isospin-asymmetric nuclear matter. We summarize empirical and theoretical properties of the single-nucleon momentum distribution $n(k)$, emphasizing the role of the neutron--proton tensor force, the dominance of correlated np pairs, and the enhancement of minority-species HMTs. Links to nucleon effective E-masses, quasi-deuteron components, and orbital entanglement are briefly noted. We examine how SRC-induced HMTs modify kinetic and potential contributions to the EOS in both non-relativistic and relativistic frameworks, including the softening of the kinetic symmetry energy and departures from the isospin parabolic approximation of asymmetric nuclear EOS. Sensitivity to high-momentum components and generalizations to arbitrary dimensions are also highlighted. Implications for heavy-ion reactions are summarized, including effects on particle yields, collective flows, deeply sub-threshold particle production and hard photon emission, driven by modified initial nucleon momentum distributions and abundant high relative-momentum np pairs during the reaction. Finally, we outline SRC-HMT consequences for neutron-star matter, covering proton fractions, tidal deformabilities, $Z$-factors, cooling, and the core--crust transition, as well as possible connections to dark-matter interactions in dense environments.

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arXiv2025

Neutron Star Equation of State with Nucleon Short-Range Correlations: A Concise Review and Open Issues

Nucleon short-range correlations (SRCs) and the associated high-momentum tail (HMT) in its momentum distribution $n(k)$ represent a universal feature of strongly interacting Fermi systems. In nuclear matter, SRCs arise primarily from the spin-isospin dependence of the tensor and short-range components of the nucleon-nucleon interaction, leading to a substantial depletion of its Fermi sea and a characteristic $k^{-4}$ tail populated predominantly by isosinglet neutron-proton pairs. These microscopic structures modify both the kinetic and interaction contributions to the Equation of State (EOS) of dense matter and thereby influence a broad range of neutron-star (NS) properties. This short review provides a streamlined overview of how SRC-induced changes in $n(k)$ reshape the kinetic EOS, including its symmetry energy part and how these effects propagate into macroscopic NS observables, including mass-radius relations, tidal deformabilities, direct Urca thresholds and core-crust transition. We summarize key existing results, highlight current observational constraints relevant for testing SRC-HMT effects, and outline open questions for future theoretical, experimental, and multimessenger studies of dense nucleonic matter.

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arXiv2025

Is The Trace Anomaly at its Minimum Value at Neutron Star Centers?

While the equation of state (EOS) $P(\varepsilon)$ of neutron star (NS) matter has been extensively studied, the EOS-parameter $ϕ= P/\varepsilon$ or equivalently the dimensionless trace anomaly $Δ= 1/3 - ϕ$, which quantifies the balance between pressure $P$ and energy density $\varepsilon$, remains far less explored, especially in NS cores. Its bounds and density profile carry crucial information about the nature of superdense matter. Physically, the EOS-parameter $ϕ$ represents the mean stiffness of matter accumulated from the stellar surface up to a given density. Based on the intrinsic structure of the Tolman--Oppenheimer--Volkoff equations, we show that $ϕ$ decreases monotonically outward from the NS center, independent of any specific input NS EOS model. Furthermore, observational evidence of a peak in the speed-of-sound squared (SSS) density-profile near the center effectively rules out a valley and a subsequent peak in the radial profile of $ϕ$ at similar densities, reinforcing its monotonic decrease. These model-independent relations impose strong constraints on the near-center behavior of the EOS-parameter $ϕ$, particularly demonstrating that the mean stiffness (or equivalently $Δ$) reaches a local maximum (minimum) at the center.

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arXiv2025

Revisiting the Possibility of a Sharp Phase Transition in Cold Neutron Stars

First-order phase transitions (FOPTs) in cold neutron stars (NSs) have been extensively studied and have provided valuable insights into the behavior of the densest matter visible in our Universe, although a strong consensus has yet to emerge. Revisiting the possibility of a hadron-quark FOPT from a new perspective, we examine the interplay between the coupled nature of gravity and microscopic interactions in Tolman--Oppenheimer--Volkoff (TOV) equations and the fundamental requirements of thermodynamic consistency in NSs. We demonstrate that a sharp FOPT manifested as a plateau in the equation of state (EOS) $P(\varepsilon)$, i.e., pressure $P$ versus energy density $\varepsilon$, is intrinsically incompatible with the regularity conditions of the TOV solutions. Although numerical integrations of the TOV equations with EOSs incorporating FOPTs may yield seemingly reasonable mass-radius relations consistent with current observations, such results can mask underlying inconsistencies. Our analysis thus establishes a structural consistency criterion for constraining dense-matter EOSs using NS observables, complementing existing studies of possible phase transitions in NS interiors.

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arXiv2025

Unraveling Trace Anomaly of Supradense Matter via Neutron Star Compactness Scaling

The trace anomaly $Δ\equiv 1/3-P/\varepsilon=1/3-ϕ$ quantifies the possibly broken conformal symmetry in supradense matter under pressure $P$ at energy density $\varepsilon$. Perturbative QCD (pQCD) predicts a vanishing $Δ$ at extremely high energy or baryon densities when the conformal symmetry is realized but its behavior at intermediate densities reachable in neutron stars (NSs) are still very uncertain. The extraction of $Δ$ from NS observations strongly depends on the employed model for nuclear Equation of State (EOS). Using the IPAD-TOV method based on an Intrinsic and Perturbatively Analysis of the Dimensionless (IPAD) Tolman-Oppenheimer-Volkoff (TOV) equations that are further verified numerically by using $10^5$ EOSs generated randomly with a meta-model in a very broad EOS parameter space constrained by terrestrial nuclear experiments and astrophysical observations, here we first show that the compactness $ξ\equiv GM_{\rm{NS}}/Rc^2\equiv M_{\rm{NS}}/R$ of a NS with mass $M_{\rm{NS}}$ and radius $R$ scales very accurately with $\overlineΠ_{\rm{c}}\equivΠ_{\rm{c}}\cdot(1+18\x/25)\equiv\x/(1+3\x^2+4\x)\cdot(1+18\rm{X}/25)$ where $\x\equivϕ_{\rm{c}}= P_{\rm{c}}/\varepsilon_{\rm{c}}$ is the ratio of pressure over energy density at NS centers. The scaling of NS compactness thus enables one to readily read off the central trace anomaly $Δ_{\rm{c}}=1/3-\x$ directly from the observational data of either the mass-radius or red-shift measurements. We then demonstrate indeed that the available NS data themselves from recent X-ray and gravitational wave observations can determine model-insensitively the trace anomaly as a function of energy density in NS cores, providing a stringent test of existing NS models and a clear guidance in a new direction for further understanding the nature and EOS of supradense matter.

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arXiv2025

Novel Scalings of Neutron Star Properties from Analyzing Dimensionless Tolman--Oppenheimer--Volkoff Equations

The TOV equations govern the radial evolution of pressure and energy density in static neutron stars (NSs) in hydrodynamical equilibrium. Using the reduced pressure and energy density with respect to the NS central energy density, the original TOV equations can be recast into dimensionless forms. While the traditionally used integral approach for solving the original TOV equations require an input nuclear Equation of State (EOS), the dimensionless TOV equations can be anatomized by using the reduced pressure and energy density as polynomials of the reduced radial coordinate without using any input nuclear EOS. Interesting and novel perspectives about NS core EOS can be extracted directly from NS observables using this new approach based on Intrinsic and Perturbative Analyses of the Dimensionless (IPAD) TOV equations (IPAD-TOV). In this review, we first discuss the length and energy density scales of NSs as well as the dimensionless TOV equations for scaled variables and their perturbative solutions near NS cores. We then review several new insights into NS physics gained from using the IPAD-TOV. We also demonstrate that the strong-field gravity plays a fundamental role in extruding a peak in the density/radius profile of the speed of sound squared (SSS) in massive NS cores independent of the nuclear EOS. Finally, some future perspectives of NS research using the IPAD-TOV are outlined.

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arXiv2024

New Insights into Supradense Matter from Dissecting Scaled Stellar Structure Equations

The strong-field gravity in General Relativity (GR) realized in neutron stars (NSs) renders the Equation of State (EOS) $P(\varepsilon)$ of supradense neutron star (NS) matter to be essentially nonlinear and refines the upper bound for $ϕ\equiv P/\varepsilon$ to be much smaller than the Special Relativity (SR) requirement with linear EOSs, where $P$ and $\varepsilon$ are respectively the pressure and energy density of the system considered. Specifically, a tight bound $ϕ\lesssim0.374$ is obtained by anatomizing perturbatively the intrinsic structures of the scaled Tolman--Oppenheimer--Volkoff (TOV) equations without using any input nuclear EOS. New insights gained from this novel analysis provide EOS-model independent constraints on properties (e.g., density profiles of the sound speed squared $s^2=\d P/\d\varepsilon$ and trace anomaly $Δ=1/3-ϕ$) of cold supradense matter in NS cores. Using the gravity-matter duality in theories describing NSs, we investigate the impact of gravity on supradense matter EOS in NSs. In particular, we show that the NS mass $M_{\rm{NS}}$, radius $R$ and its compactness $ξ\equiv M_{\rm{NS}}/R$ scale with certain combinations of its central pressure and energy density (encapsulating its central EOS). Thus, observational data on these properties of NSs can straightforwardly constrain NS central EOSs without relying on any specific nuclear EOS-model.

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arXiv2024

Strong Gravity Extruding Peaks in Speed of Sound Profiles of Massive Neutron Stars

The speed of sound squared (SSS) $s^2$ in massive neutron stars (NSs) characterizes not only the stiffness of supradense neutron-rich matter within but also equivalently properties of the curved geometry due to the strong-field gravity and matter-geometry coupling. A peaked density or radius profile of $s^2$ has been predicted for massive NSs using various NS Equation of State (EOS) models. However, the nature, cause, location and size of the peak in $s^2$ profiles are still very EOS model dependent. In this work, we investigate systematically $s^2$ profiles in massive NSs in a new approach that is independent of the nuclear EOS model and without any presumption about the NS structure and/or composition. In terms of the small quantities (reduced radius, the energy density and pressure scaled by their central values), we perform double-element perturbative expansions in solving perturbatively the scaled Tolman--Oppenheimer--Volkoff (TOV) equations and analyzing $s^2$ profiles from the Newtonian limit to the general relativistic (GR) case. The GR term in the TOV equations plays a twofold role: it compresses NS matter and modifies the pressure/energy density ratio from small values in Newtonian stars showing no $s^2$ peak to large ones for massive NSs possessing a peak in their $s^2$ profiles, and eventually takes away the peak in extremely compact/massive NSs approaching the causality limit. {In particular, the peaked behavior in $s^2$ is expected to emerge near the center of massive NSs like PSR J0740+6620, while a sharp phase transition is unlikely to occur there.} These features revealed from our analyses are universal as they are intrinsic properties of the GR stellar structure equations independent of the still very uncertain EOS of supradense neutron-rich matter in NSs.

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arXiv2024

Bayesian model averaging for nuclear symmetry energy from effective proton-neutron chemical potential difference of neutron-rich nuclei

The data-driven Bayesian model averaging is a rigorous statistical approach to combining multiple models for a unified prediction. Compared with the individual model, it provides more reliable information, especially for problems involving apparent model dependence. In this work, within both the non-relativistic Skyrme energy density functional and the nonlinear relativistic mean field model, the effective proton-neutron chemical potential difference $Δμ^*_{\rm{pn}}$ of neutron-rich nuclei is found to be strongly sensitive to the symmetry energy $E_{\rm{sym}}(ρ)$ around $2ρ_0/3$, with $ρ_0$ being the nuclear saturation density. Given discrepancies on the $Δμ^*_{\rm{pn}}$-$E_{\rm{sym}}(2ρ_0/3)$ correlations between the two models, we carry out a Bayesian model averaging analysis based on Gaussian process emulators to extract the symmetry energy around $2ρ_0/3$ from the measured $Δμ^*_{\rm{pn}}$ of 5 doubly magic nuclei $^{48}$Ca, $^{68}$Ni, $^{88}$Sr, $^{132}$Sn and $^{208}$Pb. Specifically, the $E_{\mathrm{sym}}(2ρ_0/3)$ is inferred to be $E_{\mathrm{sym}}(2ρ_0/3) = 25.6_{-1.3}^{+1.4}\,\mathrm{MeV}$ at $1σ$ confidence level. The obtained constraints on the $E_{\mathrm{sym}}(ρ)$ around $2ρ_0/3$ agree well with microscopic predictions and results from other isovector indicators.

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arXiv2023

Central Speed of Sound, Trace Anomaly and Observables of Neutron Stars from Perturbative Analyses of Scaled TOV Equations

The central speed of sound (SS) measures the stiffness of the Equation of State (EOS) of superdense neutron star (NS) matter. Its variations with density and radial coordinate in NSs in conventional analyses often suffer from uncertainties of the specific nuclear EOSs used. Using the central SS and NS mass/radius scaling obtained from solving perturbatively the scaled Tolman-Oppenheimer-Volkoff (TOV) equations, we study the variations of SS, trace anomaly and several closely related properties of NSs in an EOS-model independent manner. We find that the SS increases with the reduced central pressure $\widehat{P}_{\rm{c}}\equiv P_{\rm{c}}/\varepsilon_{\rm{c}}$ (scaled by the central energy density $\varepsilon_{\rm{c}}$), and the conformal bound for SS tends to break down for NSs with masses higher than about 1.9$M_{\odot}$. The ratio $P/\varepsilon$ is upper bounded as $P/\varepsilon\lesssim0.374$ around the centers of stable NSs. We demonstrate that it is an intrinsic property of strong-field gravity and is more relevant than the perturbative QCD bound on it. While a sharp phase transition at high densities characterized by a sudden vanishing of SS in cores of massive NSs are basically excluded, the probability for a continuous crossover signaled by a peaked radial profile of SS is found to be enhanced as $\widehat{P}_{\rm{c}}$ decreases, implying it likely happens near the centers of massive NSs. Moreover, a new and more stringent causality boundary as $R_{\max}/\rm{km}\gtrsim 4.73M_{\rm{NS}}^{\max}/M_{\odot}+1.14$ for NS M-R curve is found to be excellently consistent with observational data on NS masses and radii. Furthermore, new constraints on the ultimate energy density and pressure allowed in NSs before collapsing into black holes are obtained and compared with earlier predictions in the literature.

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arXiv2023

Core States of Neutron Stars from Anatomizing their Scaled Structure Equations

Given an Equation of State (EOS) for neutron star (NS) matter, there is a unique mass-radius sequence characterized by a maximum mass $M_{\rm{NS}}^{\max}$ at radius $R_{\max}$. We first show analytically that the $M_{\rm{NS}}^{\max}$ and $R_{\max}$ scale linearly with two different combinations of NS central pressure $P_{\rm{c}}$ and energy density $\varepsilon_{\rm{c}}$ by dissecting perturbatively the dimensionless Tolman-Oppenheimer-Volkoff (TOV) equations governing NS internal variables. The scaling relations are then verified via 87 widely used and rather diverse phenomenological as well as 17 microscopic NS EOSs with/without considering hadron-quark phase transitions and hyperons by solving numerically the original TOV equations. The EOS of densest NS matter allowed before it collapses into a black hole (BH) is then obtained. Using the universal $M_{\rm{NS}}^{\max}$ and $R_{\max}$ scalings and NICER (Neutron Star Interior Composition Explorer) and XMM-Newton mass-radius observational data for PSR J0740+6620, a very narrow constraining band on the NS central EOS is extracted directly from the data for the first time without using any specific input EOS model.

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arXiv2022

Nuclear Equation of State and Single-nucleon Potential from Gogny-like Energy Density Functionals Encapsulating Effects of Nucleon-nucleon Short-range Correlations

Nucleon-nucleon short-range correlations (SRCs) induce a high momentum tail (HMT) in the single-nucleon momentum distribution function $n_{ǩ}^J(ρ,δ)$ in cold neutron-rich matter. While there are clear experimental evidences that the SRC/HMT effects are different for neutrons and protons and their strengths depend strongly on the isospin asymmetry of finite nuclei mostly based on electron-nucleus scattering experiments, much less is known experimentally about the SRC/HMT effects in the dense neutron-rich matter. To facilitate further explorations of SRC/HMT effects in dense neutron-rich matter especially with heavy-ion reactions involving high-energy radioactive beams as well as multimessenger observations of neutron stars and their mergers, by incorporating the SRC-induced HMT in $n_{ǩ}^J(ρ,δ)$ into a Gogny-like energy density functional we study SRC/HMT effects on the equation of state (EOS) especially its symmetry energy term and single-nucleon potential in the dense asymmetric nucleonic matter (ANM). Using a parametrization as a surrogate for the momentum-dependent kernel in the Gogny-like energy density functional (EDF) we derive analytical expressions for all components of the ANM EOS and their characteristics (e.g., magnitude, slope and curvature as well as nucleon effective mass) at saturation density $ρ_0$ as well as the momentum-dependent single-nucleon optical potential in neutron-rich matter using parameters characterizing nuclear interactions as well as the size, shape and isospin dependence of the HMT at $ρ_0$. Some consequences of the SRC/HMT effects on properties of neutron stars are also studied.

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arXiv2022

High-order isospin-dependent surface tension contribution to the fourth-order symmetry energy of finite nuclei

The relation between the fourth-order symmetry energy $E_{\rm{sym,4}}(ρ_0)$ of nuclear matter at saturation density $ρ_0$ and its counterpart $a_{\rm{sym,4}}(A)$ of finite nuclei in a semiempirical nuclear mass formula is revisited by considering the high-order isospin-dependent surface tension contribution to the latter. We derive the full expression of $a_{\rm{sym,4}}(A)$, which includes explicitly the high-order isospin-dependent surface tension effects, and find that the value of $E_{\rm{sym,4}}(ρ_0)$ cannot be extracted from the measured $a_{\rm{sym,4}}(A)$ before the high-order surface tension is well constrained. Our results imply that a large $a_{\rm{sym,4}}(A)$ value of several MeVs obtained from analyzing nuclear masses can nicely agree with the empirical constraint of $E_{\rm{sym,4}}(ρ_0)\lesssim 2$ MeV from mean-field models and does not necessarily lead to a large $E_{\rm{sym,4}}(ρ_0)$ value of $\approx 20$ MeV obtained previously without considering the high-order surface tension. Furthermore, we also give the expression for the sixth-order symmetry energy $a_{\rm{sym,6}}(A)$ of finite nuclei, which involves more nuclear matter bulk parameters and the higher-order isospin-dependent surface tension.

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arXiv2022

Equation of State of Neutron-Rich Matter in $d$-Dimensions

Nuclear systems under constraints, with high degrees of symmetries and/or collectivities may be considered as moving effectively in spaces with reduced spatial dimensions. We first derive analytical expressions for the nucleon specific energy $E_0(ρ)$, pressure $P_0(ρ)$, incompressibility coefficient $K_0(ρ)$ and skewness coefficient $J_0(ρ)$ of symmetric nucleonic matter (SNM), the quadratic symmetry energy $E_{\rm{sym}}(ρ)$, its slope parameter $L(ρ)$ and curvature coefficient $K_{\rm{sym}}(ρ)$ as well as the fourth-order symmetry energy $E_{\rm{sym,4}}(ρ)$ of neutron-rich matter in general $d$ spatial dimensions (abbreviated as "$d$D") in terms of the isoscalar and isovector parts of the isospin-dependent single-nucleon potential according to the generalized Hugenholtz-Van Hove (HVH) theorem. The equation of state (EOS) of nuclear matter in $d$D can be linked to that in the conventional 3-dimensional (3D) space by the $ε$-expansion which is a perturbative approach successfully used previously in treating second-order phase transitions and related critical phenomena and more recently in studying the EOS of cold atoms. The $ε$-expansion of nuclear EOS in $d$D based on a reference dimension $d_{\rm{f}}=d-ε$ is shown to be effective with $-1\lesssimε\lesssim1$ starting from $1\lesssim d_{\rm{f}}\lesssim3$ in comparison with the exact expressions derived using the HVH theorem. Moreover, the EOS of SNM (with/without considering its potential part) is found to be reduced (enhanced) in lower (higher) dimensions, indicating in particular that the many-nucleon system tends to be deeper bounded but saturate at higher densities in spaces with lower dimensions. The links between the EOSs in 3D and $d$D spaces from the $ε$-expansion provide new perspectives to the EOS of neutron-rich matter.

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arXiv2022

A theoretical overview of isospin and EOS effects in heavy-ion reactions at intermediate energies

The isospin dependence of in-medium nuclear effective interactions is a fundamental issue in nuclear physics and has broad ramifications in astrophysics. Its uncertainties, especially the difference of neutron-proton interactions in the isosinglet and isotriplet channels, affect significantly the density and momentum dependence of the isovector single-nucleon potential and nucleon-nucleon short-range correlation in neutron-rich matter. Consequently, the neutron-proton effective mass splitting and the density dependence of nuclear symmetry energy are still rather uncertain. Heavy-ion reactions especially those involving rare isotopes is a useful tool for probing the isospin dependence of nuclear effective interactions through (1) the neutron-skin in coordinate and proton-skin in momentum of the initial state of colliding nuclei, (2) the density and momentum dependence of especially the isovector nuclear mean-field as well as (3) the isospin dependence of in-medium nucleon-nucleon cross sections. Observations of neutron stars especially since GW1710817 have also helped us significantly in understanding the isospin dependence of nuclear effective interactions. {\it We summarize here a review talk on these issues given at the 2021 International Workshop on multi-facets of EOS and Clustering. For details we refer the readers to the original publications and references therein}.

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