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In heavy-ion collisions at intermediate energies, the production and propagation of Δ particles are crucial to understanding the nuclear equation of state and inferring the properties of nuclear matter at high densities. Based on the self-consistent relativistic Boltzmann-Uehling-Uhlenbeck (RBUU) transport theory, by introducing the isovector ρ meson exchange into the effective Lagrangian and adopting the density-dependent coupling constants, the detailed expressions for isospin-dependent in-medium N Δ → N Δ elastic cross sections σ N Δ ∗ have been calculated. The energy and density dependence of the isospin-related σ N Δ ∗ as well as the total contributions of σ , ω and ρ meson fields are analyzed. It is found that the total σ N Δ ∗ has a sensitive center-of-mass energy dependence at lower energies while exhibiting a slight increase as the center-of-mass energy increases. The isospin effect between different isospin-separated channels weakens as the energy and/or density increases. The isospin effect on the density- and energy-dependent in-medium N Δ elastic cross sections is dominantly caused by the delicate balance of the isovector ρ meson exchange. [ABSTRACT FROM AUTHOR]

Background: The nuclear incompressibility ( K 0 ) plays a crucial role in understanding diverse phenomena in nuclear structure and reactions, as well as in astrophysics. Heavy-ion-collision measurements in combination with transport model simulations serve as important tools for extracting the nuclear incompressibility. However, uncertainties in transport models (or model dependence) partly affect the reliability of the extracted result. Purpose: In the present work, by using the recently measured data of rapidity-dependent flows, we constrain the incompressibility of nuclear matter and analyze the impact of model uncertainties on the obtained value. Method: The method is based on the newly updated version of the ultrarelativistic quantum molecular dynamics (UrQMD) model in which the Skyrme potential energy-density functional is introduced. Three different Skyrme interactions which give different incompressibilities varying from K 0 = 201 to 271 MeV are adopted. The incompressibility is deduced from the comparison of the UrQMD model simulations and the FOPI data for rapidity-dependent elliptic flow in Au + Au collisions at beam energies 0.4 A –1.0 A GeV. Results: The elliptic flow v 2 as a function of rapidity y 0 can be well described by a quadratic fit v 2 = v 20 + v 22 ⋅ y 0 2 . It is found that the quantity v 2 n defined by v 2 n = | v 20 | + | v 22 | is quite sensitive to the incompressibility K 0 and the in-medium nucleon–nucleon cross section, but not sensitive to the slope parameter L of the nuclear symmetry energy. Conclusions: With the FU3FP4 parametrization of the in-medium nucleon–nucleon cross section, an averaged K 0 = 220 ± 40 MeV is extracted from the v 2 n of free protons and deuterons. However, remaining systematic uncertainties, partly related to the choice of in-medium nucleon–nucleon cross sections, are of the same magnitude ( ± 40 MeV ). Overall, the rapidity dependent elliptic flow supports a soft symmetric-matter equation-of-state. [ABSTRACT FROM AUTHOR]

Within the ultrarelativistic quantum molecular dynamics (UrQMD) model, by reversely tracing nucleons that are finally emitted at mid-rapidity (| y 0 | < 0.1) in the entire reaction process, the time evolution of elliptic flow (v 2) of these traced nucleons is studied in Au+Au collisions at beam energy of 0.4 GeV/nucleon with different impact parameters. The initial value of v 2 is positive and increases with impact parameter, it then decreases as time passes and tends to saturate at a negative value. It is found that nucleon-nucleon collisions always suppress the value of v 2 (enhance the out-of-plane emission), while the nuclear mean field potential effect is more complex, which depends on both impact parameter and reaction time. The most relevant density probed by v 2 of nucleons at mid-rapidity is found to be ∼ 60% of the maximum density reached during the collisions. [ABSTRACT FROM AUTHOR]

Inferences of the nuclear symmetry energy from heavy-ion collisions are currently based on the comparison of measured observables and transport model simulations. Only the expectation values of observables over all considered events are used in these approaches, however, observables can be obtained event-by-event both in experiments and transport model simulations. By using the light gradient boosting machine (LightGBM), a modern machine-learning algorithm, we present a framework for inferring the density-dependent nuclear symmetry energy from observables in heavy-ion collisions on the event-by-event analysis. The ultrarelativistic quantum molecular dynamics (UrQMD) model simulations are used as training data. The symmetry energy slope parameter extracted with LightGBM event-by-event from test data also by UrQMD has an average spread of approximately 30 MeV from the truth, and is found to be robust against variations in model parameters. In addition, LightGBM can identify features that have the greatest effect on the physics of interest, thereby offering valuable insights. Our study suggests that the present framework can be a powerful tool and may offer a new paradigm to study the underlying physics in heavy-ion collisions. [ABSTRACT FROM AUTHOR]

Initial fluctuation is one of the ingredients that washes fingerprints of the nuclear symmetry energy on observables in heavy-ion collisions. By artificially using the same initial nuclei in all collision events, the effect of the initial fluctuation on isospin-sensitive observables, e.g., the yield ratio of free neutrons with respect to protons N n / N p , 3 H/ 3 He yield ratio, the yield ratio between charged pions π − / π + , and the elliptic flow ratio or difference between free neutrons and protons v 2 n / v 2 p ( v 2 n - v 2 p ), are studied within the ultrarelativistic quantum molecular dynamics (UrQMD) model. In practice, Au + Au collisions with impact parameter b = 5 fm and beam energy E lab = 400 MeV/nucleon are calculated. It is found that the effect of the initialization on the yields of free protons and neutrons is small, while for the yield of pions, the directed and elliptic flows are found to be apparently influenced by the choice of initialization because of the strong memory effects. Regarding the isospin-sensitive observables, the effect of the initialization on N n / N p and 3 H/ 3 He is negligible, while π − / π + and v 2 n / v 2 p ( v 2 n - v 2 p ) display a distinct difference among different initializations. The fingerprints of symmetry energy on π − / π + and v 2 n / v 2 p can be either enhanced or reduced when different initializations are utilized. [ABSTRACT FROM AUTHOR]

It is shown that the inclusion of hadronic interactions, and in particular nuclear potentials, in simulations of heavy ion collisions at the SPS energy range can lead to obvious correlations of protons. These correlations contribute significantly to an intermittency analysis as performed at the NA61 experiment. The beam energy and system size dependence is studied by comparing the resulting intermittency index for heavy ion collisions of different nuclei at beam energies of 40 A , 80 A and 150 A GeV. The resulting intermittency index from our simulations is similar to the reported values of the NA61 collaboration, if nuclear interactions are included. The observed apparent intermittency signal is the result of the correlated proton pairs with small relative transverse momentum Δ p t , which would be enhanced by hadronic potentials, and this correlation between the protons is slightly influenced by the coalescence parameters and the relative invariant four-momentum q i n v cut. [ABSTRACT FROM AUTHOR]

The elliptic flow ratio of neutrons versus protons in heavy-ion collisions (HICs) is one of the important probes to constrain the nuclear symmetry energy, however measuring the flow of neutrons with high precision is a great challenge for experimental techniques. In this work, the elliptic flow of protons is studied and it is found that the rapidity at which the sign of v 2 changes from negative to positive is sensitive to the density dependence of the symmetry energy. By comparing the existing FOPI experimental data for proton flows to the calculations with the ultrarelativistic quantum molecular dynamics (UrQMD) model, the slope parameter of the nuclear symmetry energy is extracted to be L 0 = 43 ± 20 MeV at 95% confidence level. This is in good agreement with many recent results from investigations of nuclear structure properties and also partly overlaps with the recent result of the ASY-EOS experiment. [ABSTRACT FROM AUTHOR]