Ultrarelativistic Quantum Molecular Dynamics Model Research Articles

Momentum correlation of light nuclei in Au + Au collisions at [formula omitted] GeV

Within the Ultra-relativistic Quantum Molecular Dynamics model (UrQMD) coupled with nucleon coalescence model and Mini-Spanning-Tree model, the yields of light nuclei have been stimulated in Au + Au collisions over an energy range of sNN=2.0∼7.7GeV and the momentum correlation functions of light nuclei pairs have been calculated by both the Lednický-Lyuboshitz and the Correlation After Burner methods. We compare the yields of light nuclei and their momentum correlation functions at midrapidity in this energy region with experimental data. It is found that there are differences between the results of the two models, and the coalescence method seems less valid at low collision energy. Furthermore, both the peak values of proton-proton correlation functions and the transition point of elliptic flows from out-of-plane to in-plane emission show a turning point around 3-4 GeV, which suggests that there is a relation between momentum correlation function and collective flow of particles.

3-dimensional flow analysis: A novel tool to study the collision geometry and the equation-of-state

We propose to extend the commonly known flow analysis in the transverse px-py plane to novel flow coefficients based on the angular distribution in the px-pz and py-pz planes. The new flow coefficients, called un and wn (in addition to vn), turn out to be also highly sensitive to the nuclear Equation-of-State and can be used to explore the EoS in more detail than is possible using only vn. As an example to quantify the effect of the EoS, the Ultra-relativistic Quantum Molecular Dynamics (UrQMD) model is used to investigate 20-30% central Au+Au collisions at E=lab1.23AGeV.

Enhanced dilepton emission from a phase transition in dense matter

It is demonstrated that the presence of a phase transition in heavy-ion collisions, at beam energies that probe dense quantum chromodynamics (QCD) matter, leads to a significant enhancement of the dilepton yield at low invariant mass and requires the embedding of low beam energies per produced pion due to the extended emission time. In addition, the temperature of low-mass dileptons shows a modest decrease due to the mixed phase. The emission of dileptons in the SIS18–SIS100 beam energy range is studied by augmenting the ultra-relativistic quantum molecular dynamics (UrQMD) transport model with a realistic density-dependent equation of state, as well as two different phase transitions. This is achieved by extending the molecular dynamics interaction part of the UrQMD model to a density-dependent interaction potential with a high-density minimum, leading to a phase transition and metastable coexisting high-density states. Together with a high-precision measurement, these simulations will be able to constrain the existence of a phase transition in QCD up to densities of several times nuclear saturation density.

Cumulants of net-strangeness multiplicity distributions at energies available at the BNL Relativistic Heavy Ion Collider

The higher-order cumulants of net-proton number, net-charge, and net-strangeness multiplicity distributions are widely studied to search for the quantum-chromodynamics critical point and extract the chemical freeze-out parameters in heavy-ion collisions. In this context, the event-by-event fluctuations of the net-strangeness multiplicity distributions play important roles in extracting the chemical freeze-out parameter in the strangeness sector. Due to having difficulties in detecting all strange hadrons event by event, the kaon ($K$) and lambda ($\Lambda$) particles serve as a proxy for the strangeness-related observables in heavy-ion collisions. We have studied the net-$K$, net-$\Lambda$, and net-($K$ + $\Lambda$) multiplicity distributions and calculated their different order of cumulants using the ultrarelativistic quantum molecular dynamics model and hadron resonance gas calculation. To adequately account for the net-strangeness cumulants, it has been found that the inclusion of resonance decay contributions in $K$ and $\Lambda$ is necessary.

Forward-backward multiplicity correlation and fluctuation in 197Au + 197Au collisions at fixed target Elab = 10A, 20A, 30A and 40A GeV in the UrQMD model

We use the ultra-relativistic quantum molecular dynamics (UrQMD) model to study the multiplicity correlations and fluctuations of charged hadrons emitted in the forward and backward rapidity hemispheres in 197Au + 197Au collisions at four different incident beam energies, namely Elab=10A,20A, 30A and 40A GeV. Dependence of the correlation and fluctuation parameters on the incident beam energy, collision centrality, rapidity gap and rapidity window size are examined. Both short and long-ranged correlations contribute to our UrQMD simulated results. In the framework of the UrQMD model the short-ranged correlations can be interpreted in terms of resonance decays and/or cluster formation. The long-ranged correlations on the other hand, perhaps originate from multiple rescattering suffered by the hadrons and decay of longitudinally stretched strings in the rapidity space. Our simulation based analysis can be used to set a reference base-line for any future experimental study on the forward-backward multiplicity correlation for the colliding system and collision energies involved in the present case.

Effects of sequential decay on collective flows and nuclear stopping power in heavy-ion collisions at intermediate energies

In this study, the rapidity distribution, collective flows, and nuclear stopping power in ^{197}Au+^{197}Au collisions at intermediate energies were investigated using the ultrarelativistic quantum molecular dynamics (UrQMD) model with GEMINI++ code. The UrQMD model was adopted to simulate the dynamic evolution of heavy-ion collisions, whereas the GEMINI++ code was used to simulate the decay of primary fragments produced by UrQMD. The calculated results were compared with the INDRA and FOPI experimental data. It was found that the rapidity distribution, collective flows, and nuclear stopping power were affected to a certain extent by the decay of primary fragments, especially at lower beam energies. Furthermore, the experimental data of the collective flows and nuclear stopping power at the investigated beam energies were better reproduced when the sequential decay effect was included.

Elliptic flow in heavy-ion collisions at intermediate energy: The role of impact parameter, mean field potential, and collision term

Within the ultrarelativistic quantum molecular dynamics (UrQMD) model, by reversely tracing nucleons that are finally emitted at mid-rapidity (|y0| < 0.1) in the entire reaction process, the time evolution of elliptic flow (v2) 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 v2 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 v2 (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 v2 of nucleons at mid-rapidity is found to be ∼ 60% of the maximum density reached during the collisions.

Light hypernuclei in heavy-ion collisions

Prediction for hyper nuclei multiplicities from GSI to LHC energies from the Ultra-relativistic Quantum Molecular Dynamics (UrQMD) model combined with a final state coalescence approach is presented and compared to the thermal model. The influence of the coalescence radius on the collision energy and centrality dependence of the Λ3H/Λ ratio is discussed.

Intermittency of charged particles in the hybridUrQMD+CMCmodel at energies available at the BNL Relativistic Heavy Ion Collider

Within the framework of intermittency analysis, a search for critical fluctuations is ongoing to locate the possible critical point in the quantum chromodynamics phase diagram. In this study, self-similar critical fluctuations from a critical Monte Carlo (CMC) model have been incorporated into the cascade ultrarelativistic quantum molecular dynamics (UrQMD) model. This hybrid UrQMD+CMC model exhibits a clear power-law behavior of scaled factorial moment for charged particles in Au+Au collisions at $\sqrt{s_\mathrm{NN}}$ = 7.7-200 GeV. By comparing the UrQMD+CMC model results with those from the STAR experiment, it is found that the value of a calculated scaling exponent falls in the range of the experimental measurement when 1-2 \% signal of intermittency fluctuations is added into the UrQMD sample.

Lambda polarization in 108Ag[formula omitted]Ag and 197Au[formula omitted]Au collisions around a few GeV

Within the framework of Ultra-relativistic Quantum Molecular Dynamics (UrQMD) model, we extract the global spin polarization of Λ hyperon in 108Ag+108Ag and 197 Au+197Au collisions at sNN=2.42–62.4 GeV. We use two different approaches to calculate the Λ polarization Py: approach I is based on equilibrium assumption so that Py is determined by thermal vorticity and approach II assumes a proportional relation between Py and the system's angular momentum in Λ's rest frame. We find that both approaches can describe the experimental data at low energies around a few GeV but only approach I describes well also higher-energy data. This suggests that at higher energies the relativistic effect plays an important role. After taking into such effect properly, the relativity-improved approach II can describe the higher-energy data as well.

Decoding the nuclear symmetry energy event-by-event in heavy-ion collisions with machine learning

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.

Effects of Initial Density Fluctuations on Cumulants in Au + Au Collisions at sNN = 7.7 GeV

Within the ultrarelativistic quantum molecular dynamics (UrQMD) model, the effect of initial density fluctuations on cumulants of the net-proton multiplicity distribution in Au + Au Collisions at sNN = 7.7 GeV was investigated by varying the minimum distance dmin between two nucleons in the initialization. It was found that the initial density fluctuations increased with the decrease of dmin from 1.6 fm to 1.0 fm, and the influence of dmin on the magnitude of the net-proton number fluctuation in a narrow pseudorapidity window (Δη≤ 4) was negligible even if it indeed affected the density evolution during the collision. At a broad pseudorapidity window (Δη≥ 4), the cumulant ratios were enlarged when the initial density fluctuations were increased with the smaller value of dmin, and this enhancement was comparable to that observed in the presence of the nuclear mean-field potential. Moreover, the enhanced cumulants were more evident in collisions with a larger impact parameter. The present work demonstrates that the fingerprint of the initial density fluctuations on the cumulants in a broad pseudorapidity window is clearly visible, while it is not obvious as the pseudorapidity window becomes narrow.

Accessing the in-medium effects on nucleon-nucleon elastic cross section with collective flows and nuclear stopping

A systematic study of the in-medium correction factor (F) on nucleon-nucleon elastic cross section is performed within the Ultra-relativistic Quantum Molecular Dynamics (UrQMD) model. The effects of the beam energy dependence of F on the directed, elliptic flow and nuclear stopping in 197Au+197Au collisions with energy ranging from 0.09 to 0.8A GeV are explored. It is found that the directed, elliptic flow and nuclear stopping at relatively low energies are very sensitive to F, and the sensitivity gradually weakens with increasing beam energy. The beam energy dependent in-medium correction factor F is deduced from the comparison of the excitation functions of the directed, elliptic flow and nuclear stopping between the calculated results and the FOPI experimental data.

Flavor hierarchy at the chemical freeze-out from UrQMD

We introduce a novel approach based on elastic and inelastic scattering rates to extract the hyper-surface of the chemical freeze-out from a hadronic transport simulation. We use the Ultra-relativistic Quantum Molecular Dynamics (UrQMD) model to extract the chemical freeze-out hyper-surface of pions and kaons in the energy range from Elab = 1:23A GeV to √SNN = 7.7 GeV. By employing a coarse-graining procedure, we can extract the local temperature T and baryo-chemical potential μB on the chemical freeze-out surface and compare them to results from statistical model analysis. We find good agreement between the pion chemical freeze-out line extracted from the simulation and the freeze-out line from the statistical model extracted from data. In addition the simulations also hint towards the existence of a flavor hierarchy similar to the one observed in recent lattice QCD calculations.

Quantifying the Effect of Initial Fluctuations on Isospin-Sensitive Observables from Heavy-Ion Collisions at Intermediate Energies

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 Nn/Np, 3H/3He yield ratio, the yield ratio between charged pions π−/π+, and the elliptic flow ratio or difference between free neutrons and protons v2n/v2p (v2n-v2p), are studied within the ultrarelativistic quantum molecular dynamics (UrQMD) model. In practice, Au + Au collisions with impact parameter b = 5 fm and beam energy Elab = 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 Nn/Np and 3H/3He is negligible, while π−/π+ and v2n/v2p (v2n-v2p) display a distinct difference among different initializations. The fingerprints of symmetry energy on π−/π+ and v2n/v2p can be either enhanced or reduced when different initializations are utilized.

Finding signatures of the nuclear symmetry energy in heavy-ion collisions with deep learning

A deep convolutional neural network (CNN) is developed to study symmetry energy (Esym(ρ)) effects by learning the mapping between the symmetry energy and the two-dimensional (transverse momentum and rapidity) distributions of protons and neutrons in heavy-ion collisions. Supervised training is performed with labeled data-set from the ultrarelativistic quantum molecular dynamics (UrQMD) model simulation. It is found that, by using proton spectra on event-by-event basis as input, the accuracy for classifying the soft and stiff Esym(ρ) is about 60% due to large event-by-event fluctuations, while by setting event-summed proton spectra as input, the classification accuracy increases to 98%. The accuracies for 5-label (5 different Esym(ρ)) classification task are about 58% and 72% by using proton and neutron spectra, respectively. For the regression task, the mean absolute errors (MAE) which measure the average magnitude of the absolute differences between the predicted and actual L (the slope parameter of Esym(ρ)) are about 20.4 and 14.8 MeV by using proton and neutron spectra, respectively. Fingerprints of the density-dependent nuclear symmetry energy on the transverse momentum and rapidity distributions of protons and neutrons can be identified by convolutional neural network algorithm.

Application of machine learning in the determination of impact parameter in the Sn132+Sn124 system

Background: $^{132}$Sn+$^{124}$Sn collisions at the beam energy of 270 MeV$/$nucleon have been performed at the Radioactive Isotope Beam Factory (RIBF) in RIKEN to investigate the nuclear equation of state. Reconstructing impact parameter is one of the important tasks in the experiment as it relates to many observables. Purpose: In this work, we employ three commonly used algorithms in machine learning, the artificial neural network (ANN), the convolutional neural network (CNN) and the light gradient boosting machine (LightGBM), to determine impact parameter by analyzing either the charged particles spectra or several features simulated with events from the ultra-relativistic quantum molecular dynamics (UrQMD) model. Method: To closely imitate experimental data and investigate the generalizability of the trained machine learning algorithms, incompressibility of nuclear equation of state and the in-medium nucleon-nucleon cross sections are varied in the UrQMD model to generate the training data. Results: The mean absolute error $\Delta b$ between the true and the predicted impact parameter is smaller than 0.45 fm if training and testing sets are sampled from the UrQMD model with the same parameter set. However, if training and testing sets are sampled with different parameter sets, $\Delta b$ would increase to 0.8 fm. Conclusion: The generalizability of the trained machine learning algorithms suggests that these machine learning algorithms can be used reliably to reconstruct impact parameter in experiment.

Dependence on beam energy and nuclear equation of state of anisotropic flow and particle production in low-energy heavy-ion collisions

We analyze various flow coefficients of anisotropic momentum distribution of final state particles in mid-central ($b=5\text{--}9\phantom{\rule{0.16em}{0ex}}\mathrm{fm}$) $\mathrm{Au}\phantom{\rule{4pt}{0ex}}+\phantom{\rule{4pt}{0ex}}\mathrm{Au}$ collisions in the beam energy range ${E}_{\mathrm{Lab}}=1A\text{--}158A$ GeV. Different variants of the ultrarelativistic quantum molecular dynamics (UrQMD) model, namely the pure transport (cascade) mode and the hybrid mode, are employed for this investigation. In the hybrid UrQMD model, the ideal hydrodynamical evolution is integrated with the pure transport calculation for description of the evolution of the fireball. We opt for the different available equations of state (EoS) replicating the hadronic as well as partonic degrees of freedom together with possible phase transitions, viz., hadron gas, chiral $+$ deconfinement EoS, and bag model EoS, to investigate their effect on the properties of the final state particles. We also attempt to gain insights about the dynamics of the medium by studying different features of particle production such as particle ratios and net-proton rapidity distribution. The results and conclusions drawn here would be useful to understand the response of various observables to the underlying physics of the model as well as to make comparisons with the upcoming measurements of the future experiments at the Facility for Antiproton and Ion Research (FAIR) and the Nuclotron-based Ion Collider fAcility (NICA).

Particle ratios within EPOS, UrQMD and thermal models at AGS, SPS and RHIC energies

The particle ratios [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] measured at AGS, SPS and RHIC energies are compared with large statistical ensembles of 100,000 events deduced from the CRMC EPOS [Formula: see text] and the Ultra-relativistic Quantum Molecular Dynamics (UrQMD) hybrid model. In the UrQMD hybrid model two types of phase transitions are taken into account. All these data are then confronted with the ideal Hadron Resonance Gas Model. The two types of phase transitions are apparently indistinguishable. Apart from [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text], the UrQMD hybrid model agrees well with the CRMC EPOS [Formula: see text]. We also conclude that the CRMC EPOS [Formula: see text] seems to largely underestimate [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text].

Effects of nuclear deformation in U$+$U collisions at the intermediate energy

Nuclear deformation is an important topic in the study of nuclear structure. The influence of nuclear structure on nuclear reactions and heavy-ion collisions has attracted considerable attention recently. Based on the ultra-relativistic quantum molecular dynamics (UrQMD) model, the effect of nuclear deformation in $^{238}$U$+$$^{238}$U at the beam energy of łinebreak 0.4 GeV/nucleon is investigated and several observables, such as the stopping power, collective flow, and $\pi^{-}/\pi^{+}$ yield ratio, are calculated. It is found that the stopping power obtained with tip-tip (the two nuclei with their long axes head-on) collisions is the largest among collisions with different deformations. For belly-belly (the two nuclei with their short axes head-on and long axes parallel in the reaction plane) collisions, the elliptic flow exists even for the most central collision ($b$=0 fm). $\pi^{-}/\pi^{+}$yield ratio obtained with tip-tip collision is larger than that obtained with belly-belly collision. In addition, the influence of nuclear deformation on the elliptic flow of free protons is stronger than that of nuclear symmetry energy in $^{238}$U$+$$^{238}$U collisions at 0.4 GeV/nucleon, while the elliptic flow ratio between neutrons and protons shows hardly any sensitivity to different deformations of uranium.