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Zhuxia Li

Publications and source records attributed to Zhuxia Li.

At least 19 recordsLinked to original sources
arXiv2025

Investigation of the neutron-proton effective mass splitting via heavy ion collisions: Constraints and Implications

The neutron-proton effective mass splitting ($Δm^*_{np}$) is investigated through analyses of heavy-ion collisions using the improved quantum molecular dynamics (ImQMD) model with both standard and extended Skyrme interactions. By uncovering the strong correlation between the slope of the neutron-to-proton yield ratio with respect to the kinetic energy (i.e., $S_{n/p} $) and $Δm^*_{np}$, we reveal that the constraints of the neutron-proton effective mass splitting via heavy ion collisions depend on the kinetic energy region of the emitted nucleons. At low kinetic energies, the data favor $m_n^*>m_p^*$ which is consistent with the nucleon-nucleus scattering analysis, while at high kinetic energies, they favor $m_n^*<m_p^*$. Our findings partly resolve the longstanding discrepancy in the constraints of neutron-proton effective mass splitting with heavy ion collisions and nucleon-nucleus scattering, and significantly advance the understanding of nucleon effective mass splitting through heavy ion collisions.

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arXiv2025

An effective finite-range Gogny-type interaction for the quantum molecular dynamics like model

In this work, we propose an effective finite-range Gogny-type interaction that can be directly used in the quantum molecular dynamics (QMD) like model. Two methods for determining the parameters of the effective interaction are discussed. The first method establishes an approach to connect the conventional Gogny interaction in nuclear structure to that in heavy-ion collisions, the second method allows for the description of the symmetry energy varying from the supersoft to stiff, as well as the momentum-dependent symmetry potential, exhibiting behaviors ranging from monotonic to non-monotonic variations. This effective interaction opens up opportunities for a deeper understanding of finite-range interactions and non-monotonic momentum-dependent symmetry potentials in future studies.

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arXiv2025

Bayesian method for quantifying the non-Gaussian fluctuations in low-intermediate energy heavy ion collisions

In this work, we present a model-independent method to quantify the non-Gaussian fluctuations in the observable distributions, which are assessed by the difference between the measured observable distributions and reconstructed observable distributions via the Bayesian method. Our results indicate that the strength of non-Gaussian fluctuation increases with the beam energy, and is primarily driven by non-central collision mechanisms. The experimental measurement of the strength of non-Gaussian fluctuation of the observable distributions will provide valuable insights into understanding the nonequilibrium effects in heavy ion collisions and the liquid-gas phase transition in finite nuclei.

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arXiv2024

An extended Skyrme momentum dependent potential in asymmetric nuclear matter and transport models

Based on an extended Skyrme momentum-dependent interaction (MDI), we derive an isospin asymmetric equation of state, isospin-dependent single-particle potential and the Hamiltonian which can be used in the Boltzmann-Uehling-Uhlenbeck (BUU) model and the quantum molecular dynamics (QMD) model at the beam energy less than 1 GeV/u. As an example of the applications of extended Skyrme MDI, we also present the results obtained with the extended Skyrme momentum-dependent interaction in the improved quantum molecular dynamics model (ImQMD), and the influence of the effective mass splitting on the isospin sensitive observables, i.e., the single and double neutron-to-proton ratios, is discussed again.

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arXiv2024

Novel Pauli blocking method in quantum molecular dynamics type models

In this work, we propose a novel method for calculating the occupation probability in the Pauli blocking of the quantum molecular dynamics type models. This method refines the description of the Pauli blocking ratio in the nuclear matter and that in the finite nucleus. The influence of the new Pauli blocking method on the heavy ion collisions observables, such as the charge distribution, the free neutron to proton yield ratios, and the extracted physical quantities, such as the in-medium nucleon-nucleon cross sections, are investigated. For the extracted in-medium nucleon-nucleon cross sections, our results show that it will be enhanced 1.1$-$2.5 times than that with the conventional Pauli blocking method at the beam energy less than 150 MeV/u, which highlights the importance of a refined Pauli blocking method for developing an advanced transport model to describe complex heavy ion collisions.

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arXiv2023

Bayesian reconstruction of impact parameter distributions from two observables for intermediate energy heavy ion collisions

To reconstruct the impact parameter distributions from the selected events sample or centrality, which is defined by two-observables, at intermediate energy heavy ion collisions, we extend the approach proposed by Das \textit{et al.} [Phys. Rev. C 97, 014905 (2018)], Rogly \textit{et al.} [Phys. Rev. C 98, 024902 (2018)], and Frankland \textit{et al.} [Phys. Rev. C 104, 034609 (2021)]. Based on deep investigations of the fluctuation mechanism, we found that the intrinsic fluctuations are mainly generated in the microscopic stochasticity of initialization and nucleon-nucleon collisions in the nonequilibrium process of heavy ion collisions, and this leads the observables to fluctuate with respect to impact parameter in a Gaussian form. In this work, the multiplicity of the charged particles and the total transverse momentum of the light charged particles are used simultaneously to model-independently reconstruct the impact parameter distributions for selected events or centrality based on the Bayesian method. For sorting the centrality with two observables, we propose to use the $K$-means clustering method (an unsupervised machine learning algorithm), which can automatically sort events when the class number is given. Furthermore, the reconstructed impact parameter distributions from data of the two observables can be used to learn the correlation between multiplicity and transverse momentum at different centralities, which may be useful for understanding the fragmentation mechanism.

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arXiv2023

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 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 $A>100$ ($σ_{A>100}$), the difference of $σ_{A>100}$ between $^{132}$Sn+$^{124}$Sn and $^{124}$Sn+$^{124}$Sn systems ($δσ_{A>100}$), 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.

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arXiv2023

Impacts of momentum dependent interaction, symmetry energy and near-threshold $NN\to NΔ$ cross sections on isospin sensitive flow and pion observables

Based on the ultra-relativistic quantum molecular dynamics (UrQMD) model, the impacts of momentum dependent interaction, symmetry energy and near-threshold $NN\to NΔ$ cross sections on isospin sensitive collective flow and pion observables are investigated. Our results confirm that the elliptic flow of neutrons and charged particles, i.e. $v_2^n$ and $v_2^{ch}$, are sensitive to the strength of momentum dependence interaction and the elliptic flow ratio, i.e., $v_2^n/v_2^{ch}$, is sensitive to the stiffness of symmetry energy. For describing the pion multiplicity near the threshold energy, accurate $NN\to NΔ$ cross sections are crucial. With the updated momentum dependent interaction and $NN\to NΔ$ cross sections in UrQMD model, seven observables, such as directed flow and elliptic flow of neutrons and charged particles, the elliptic flow ratio of neutrons to charged particles, charged pion multiplicity and its ratio $π^-/π^+$, can be well described by the parameter sets with the slope of symmetry energy from 5 MeV to 70 MeV. To describe the constraints of symmetry energy at the densities probed by the collective flow and pion observables, the named characteristic density is investigated and used. Our analysis found that the flow characteristic density is around 1.2$ρ_0$ and pion characteristic density is around 1.5$ρ_0$, and we got the constrains of symmetry energy at characteristic densities are $S(1.2ρ_0)=34\pm 4$ MeV and $S(1.5ρ_0)=36\pm 8$ MeV. These results are consistent with previous analysis by using pion and flow observable with different transport models, and demonstrate a reasonable description of symmetry energy constraint should be presented at the characteristic density of isospin sensitive observables.

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arXiv2022

How Do Constraints of Nuclear Symmetry Energy Reconcile with Different Models?

By simultaneously describing the data of isospin sensitive nucleonic flow and pion observables, such as $v_2^n/v_2^{ch}$ and $π^-/π^+$, with ultra-relativistic quantum molecular dynamics (UrQMD) model, we got the symmetry energy at flow and pion characteristic densities which are $S(1.2ρ_0)=34\pm 4$ MeV and $S(1.5ρ_0)=36\pm 8$ MeV. Within the uncertainties, the constraints of symmetry energy at characteristic densities are consistent with the previous constraints by using other transport models. The consistency suggests that the reliable constraints on symmetry energy should be presented at the characteristic density of isospin sensitive observables. By using the constraints of symmetry energy at two different characteristic densities, the extrapolated value of $L$ is provided. Within $2σ$ uncertainty, the extrapolated value of $L$ is in $5-70$ MeV which is consistent with the recent combination analysis from PREX-II and astrophyiscs data. Further, the calculations with the constrained parameter sets can describe the data of charged pion multiplicities from S$π$RIT collaboration.

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arXiv2021

The influence of $δ$ meson on the isospin splitting of in-medium $NN\to NΔ$ cross sections

The isospin splitting of the in-medium $NN\rightarrow NΔ$ cross sections in asymmetric nuclear medium are investigated in the framework of the one-boson exchange model by including $δ$ and $ρ$ mesons. Our results show that the medium correction factors $R=σ_{ NN\rightarrow NΔ}^*/σ_{NN\rightarrow NΔ}^{\text{free}}$ have $R_{pp \to nΔ^{++}} < R_{nn \to pΔ^{-}}$ and $R_{NN \to NΔ^{+}} R_{nn \to pΔ^{-}}$ and $R_{NN \to NΔ^{+}} >R_{NN \to NΔ^{0}}$.

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arXiv2021

Influence of the treatment of initialization and mean-field potential on the neutron to proton yield ratios

In this work, we firstly investigate how to reproduce and how well one can reproduce the Woods-Saxon density distribution of initial nuclei in the framework of the improved quantum molecular dynamics model. Then, we propose a new treatment for the initialization of nuclei which is correlated with the nucleonic mean-field potential by using the same potential energy density functional. In the mean field potential, the three-body force term is accurately calculated. Based on the new version of the model, the influences of precise calculations of the three-body force term, the slope of symmetry energy, the neutron-proton effective mass splitting, and the width of the wave packet on heavy ion collision observables, such as the neutron to proton yield ratios for emitted free nucleons [$R(n/p)$] and for coalescence invariant nucleons [$R_{ci}(n/p)$] for $^{124}$Sn+$^{112}$Sn at the beam energy of 200 MeV per nucleon, are discussed. Our calculations show that the spectra of neutron to proton yield ratios [$R(n/p)$] can be used to probe the slope of symmetry energy ($L$) and the neutron-proton effective mass splitting. In detail, the $R(n/p)$ in the low kinetic energy region can be used to probe the slope of symmetry energy ($L$). With a given $L$, the inclination of $R(n/p)$ to kinetic energy ($E_k$) can be used to probe the effective mass splitting. In the case where the neutron-proton effective mass splitting is fixed, $R(n/p)$ at high kinetic energy can also be used to learn the symmetry energy at suprasaturation density.

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arXiv2021

In-medium pion dispersion relation and medium correction of $Nπ\leftrightarrow Δ$ near the threshold energy of pion production

Transport models cannot simultaneously explain very recent data on pion multiplicities and pion charged ratios of Sn+Sn in the reaction at 0.27 A GeV. This stimulates further investigations on the pion dispersion relation, in-medium $Nπ\to Δ$ cross sections and $Δ\to N π$ decay widths near the threshold energy or at subthreshold energy of pion production in isospin asymmetric nuclear matter. In this study, the pion dispersion relation, in-medium $Nπ\to Δ$ cross section and $Δ\to N π$ decay width near the threshold energy are investigated in isospin asymmetric nuclear matter by using the one-boson-exchange model. With the consideration of the energy conservation effect, the in-medium $Nπ\toΔ$ cross sections are enhanced at $s^{1/2}<1.11$ GeV in nuclear medium. The prediction of pion multiplicity and $π^-/π^+$ ratios near the threshold energy can be modified if this effect is considered in transport model simulations.

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arXiv2021

Effects of Pauli blocking and in-medium nucleon-nucleon cross sections on the stopping power at low-intermediate energy heavy ion collisions

Three typical algorithms of Pauli blocking in the quantum molecular dynamics type models are investigated in the nuclear matter, the nucleus and the heavy ion collisions. The calculations in nuclear matter show that the blocking ratios obtained with the three algorithms are underestimated 13-25\% compared to the analytical values of blocking ratios. For the finite nucleus, the spurious collisions occur around the surface of the nucleus owing to the defects of Pauli blocking algorithms. In the simulations of heavy ion collisions, the uncertainty of stopping power from different Pauli blocking algorithms is less than 5\%. Furthermore, the in-medium effects of nucleon-nucleon ($NN$) cross sections on the nuclear stopping power are discussed. Our results show that the transport models calculations with free $NN$ cross sections result in the stopping power decreasing with the beam energy at the beam energy less than 300 MeV/u. To increase or decrease the values of stopping power, an enhanced or suppressed model dependent in-medium $NN$ cross section is required.

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arXiv2020

Insights on pion production mechanism and symmetry energy at high density

The $NΔ\to NN$ cross sections, which take into account the $Δ$-mass dependence of M-matrix and momentum $p_{NΔ}$, are applied on the calculation of pion production within the framework of the UrQMD model. Our study shows that UrQMD calculations with the $Δ$-mass dependent $NΔ\to NN$ cross sections enhance the pion multiplicities and decrease the $π^-/π^+$ ratios. By analyzing the time evolution of the pion production rate and the density in the overlapped region for Au+Au at the beam energy of 0.4A GeV, we find that the pion multiplicity probes the symmetry energy in the region of 1-2 times normal density. The process of pion production in the reaction is tracked including the loops of $NN\leftrightarrow NΔ$ and $Δ\leftrightarrow Nπ$, our calculations show that the sensitivity of $π^-/π^+$ to symmetry energy is weakened after 4-5 N-$Δ$-$π$ loops in the pion production path, while the $π^{-}/π^{+}$ ratio in reactions at near threshold energies remains its sensitivity to the symmetry energy. By comparing the calculations to the FOPI data, we obtain a model dependent conclusion on the symmetry energy and the symmetry energy at two times normal density is $S(2ρ_0)$=38-73 MeV within $1σ$ uncertainties. Under the constraints of tidal deformability and maximum mass of neutron star, the symmetry energy at two times normal density is reduced to $48-58$ MeV and slope of symmetry energy $L=54-81$ MeV, and it is consistent with the constraints from ASY-EOS flow data.

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arXiv2020

Progress of Quantum Molecular Dynamics model and its applications in Heavy Ion Collisions

In this review article, we first briefly introduce the transport theory and quantum molecular dynamics model applied in the study of the heavy ion collisions from low to intermediate energies. The developments of improved quantum molecular dynamics model (ImQMD) and ultra-relativistic quantum molecular dynamics model (UrQMD), are reviewed. The reaction mechanism and phenomena related to the fusion, multinucleon transfer, fragmentation, collective flow and particle production are reviewed and discussed within the framework of the two models. The constraints on the isospin asymmetric nuclear equation of state and in-medium nucleon-nucleon cross sections by comparing the heavy ion collision data with transport models calculations in last decades are also discussed, and the uncertainties of these constraints are analyzed as well. Finally, we discuss the future direction of the development of the transport models for improving the understanding of the reaction mechanism, the descriptions of various observables, the constraint on the nuclear equation of state, as well as for the constraint on in-medium nucleon-nucleon cross sections.

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arXiv2020

Constraints on the symmetry energy and its associated parameters from nuclei to neutron stars

The symmetry energy obtained with the effective Skyrme energy density functional is related to the values of isoscalar effective mass and isovector effective mass, which is also indirectly related to the incompressibility of symmetric nuclear matter. In this work, we analyze the values of symmetry energy and its related nuclear matter parameters in five-dimensional parameter space by describing the heavy ion collision data, such as isospin diffusion data at 35 MeV/u and 50 MeV/u, neutron skin of $^{208}$Pb, and tidal deformability and maximum mass of neutron star. We obtain the parameter sets which can describe the isospin diffusion, neutron skin, tidal deformability and maximum mass of neutron star, and give the incompressibility $K_0$=250.23$\pm$20.16 MeV, symmetry energy coefficient $S_0$=31.35$\pm$2.08 MeV, the slope of symmetry energy $L$=59.57$\pm$10.06 MeV, isoscalar effective mass $m_s^*/m$=0.75$\pm$0.05 and quantity related to effective mass splitting $f_I$=0.005$\pm$0.170. At two times normal density, the symmetry energy we obtained is in 35-55 MeV. To reduce the large uncertainties of $f_I$, more critical works in heavy ion collisions at different beam energies are needed.

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arXiv2019

Extracting Skyrme energy density functional parameters with Heavy-Ion Collision Data

The effective Skyrme energy density functionals are widely used in the study of nuclear structure, nuclear reaction and neutron star, but they are less established from the heavy ion collision data. In this work, we find 22 effective Skyrme parameter sets, when incorporated in use the transport model, ImQMD, to describe the heavy ion collision data, such as isospin diffusion data at 35 MeV/u and 50 MeV/u. We use these sets to calculate the neutron skin of $^{208}$Pb based on the restricted density variation method, and obtain the neutron skin of $^{208}$Pb in the range of $δR_{np}=0.18\pm0.04$ fm.

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arXiv2019

$Δ$-mass dependence of the M-matrix in the calculation of $\mbox{N}Δ\to \mbox{NN}$ cross sections

Within the one boson exchange model, $Δ$-mass dependent M-matrix and its influence on the calculation of $NΔ\to NN$ cross sections are investigated. Our calculations show that the $m_Δ$ dependence of $|\textbf{p}_{NΔ}|$ and $|\mathcal{M}|^2$ has effects on the calculations of $σ_{NΔ\to NN}$, especially around the threshold energy. We finally provide a table of accurate $σ_{NΔ\to NN}$ which can be used in the transport models.

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