Quantum Molecular Dynamics Model Research Articles

Onset of pressure gradient on collective flow through balance and transition geometry

The impression of mean field and spectator matter has been studied through the collision geometry dependence of reduced flow and elliptical flow in heavy-ion collisions (HICs) at intermediate energies using Isospindependent Quantum Molecular Dynamics (IQMD) model for the reaction of $$_{20}^{50}{\rm{Cu + }}_{20}^{50}{\rm{and}}_{79}^{197}{\rm{Au + }}_{79}^{197}{\rm{Au}}$$ at incident energy between 50 MeV/nucleon and 450 MeV/nucleon. The collision geometry at which the reduced flow and elliptical flow changes its sign is termed as balance geometry $$({\hat b_{bal}})$$ and transition geometry $$({\hat b_{trans}})$$ of flow, respectively. Our study reveals that $$({\hat b_{bal}})$$ and $$({\hat b_{trans}})$$ increases with increase in incident energy. In addition to this, the effect of nuclear charge radius has also been studied by using the isospin-independent as well dependent nuclear charge radii parameterizations.

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.

Development of a more accurate Geant4 quantum molecular dynamics model for hadron therapy

Objective. Although in heavy-ion therapy, the quantum molecular dynamics (QMD) model is one of the most fundamental physics models providing an accurate daughter-ion production yield in the final state, there are still non-negligible differences with the experimental results. The aim of this study is to improve fragment production in water phantoms by developing a more accurate QMD model in Geant4. Approach. A QMD model was developed by implementing modern Skyrme interaction parameter sets, as well as by incorporating with an ad hoc α-cluster model in the initial nuclear state. Two adjusting parameters were selected that can significantly affect the fragment productions in the QMD model: the radius to discriminate a cluster to which nucleons belong after the nucleus–nucleus reaction, denoted by R, and the squared standard deviation of the Gaussian packet, denoted by L. Squared Mahalanobis’s distance of fragment yields and angular distributions with 1, 2, and the higher atomic number for the produced fragments were employed as objective functions, and multi-objective optimization (MOO), which make it possible to compare quantitatively the simulated production yields with the reference experimental data, was performed. Main results. The MOO analysis showed that the QMD model with modern Skyrme parameters coupled with the proposed α-cluster model, denoted as SkM* α, can drastically improve light fragments yields in water. In addition, the proposed model reproduced the kinetic energy distribution of the fragments accurately. The optimized L in SkM* α was confirmed to be realistic by the charge radii analysis in the ground state formation. Significance. The proposed framework using MOO was demonstrated to be very useful in judging the superiority of the proposed nuclear model. The optimized QMD model is expected to improve the accuracy of heavy-ion therapy dosimetry.

Improved Quantum Molecular Dynamics Model and Its Application to Ternary Breakup Reactions

Collisions of very heavy nuclei 197Au+197Au at the energy range of 5–30 A MeV have been studied within the improved quantum molecular dynamics (ImQMD) model. A class of ternary events satisfying a nearly complete balance of mass numbers is selected and we find that the probability of ternary breakup depends on the incident energy and the impact parameter. It is also found that the largest probability of ternary breakup is located at the energy around 24 A MeV for the system 197Au+197Au. The experimental mass distributions and angular distributions for the system 197Au+197Au ternary breakup fragments can be reproduced well by the calculation with the ImQMD model at the energy of 15 A MeV. The modes and mechanisms of ternary and quaternary breakup are studied by time-dependent snapshots of ternary events. The direct prolate, direct oblate, and cascade ternary breakup modes, are manifested and their production probabilities are obtained. The characteristic features in ternary breakup events, three mass-comparable fragments, and the very fast, nearly collinear breakup, account for the two-preformed-neck shape of the composite system. The mean free path of nucleons in the reaction system is studied and the shorter mean free path is responsible for the ternary breakup with three mass comparable fragments, in which the two-body dissipation mechanism plays a dominant role.

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.

Production of neutron-deficient nuclei around N = 126 by proton-induced spallation* *Supported by the Open Project of Guangxi Key Laboratory of Nuclear Physics and Nuclear Technology (NLK2020-02), the National Natural Science Foundation of China (11875328, 12075327) and the Fundamental Research Funds for the Central Universities, Sun Yat-Sen University (22qntd1801)

Many isotopes of Np, Pu, Am, and Cm around the N = 126 shell still have not been produced in the laboratory. This study aims to investigate the cross sections and yields of the neutron-deficient nuclei of Np, Pu, Am, and Cm produced in the proton-induced spallations of transuranium elements. The isospin-dependent quantum molecular dynamics (IQMD) model is applied to study the dynamical process of reaction, and the subsequent decay process is simulated by the GEMINI++ model. The IQMD-GEMINI++ model is applied to calculate the cross section, kinetic energy, and angular distribution of the isotopic productions around N = 126. The Lindhand, Scharff, and Schiott theory is applied to calculate the energy loss of different heavy nuclei in the target material. A comparison between the data and the calculations shows that the IQMD-GEMINI++ model can reproduce the production cross sections of the neutron-deficient nuclei in spallation within approximately 1.5 orders of magnitude. The maximum cross section of the undiscovered isotopes of Np, Pu, Am, and Cm is about 10−5 mb, while the kinetic energies of the productions are all less than 16 MeV. The angular distribution shows that the emission direction of production is mostly at a backward angle. The range of production in the target is within the range of 10−7 to 10−5 cm. This range is the effective target thickness for the online identification of undiscovered isotopes. Based on the effective thickness of the target and assuming an intensity of 120 μA for the proton beam, the yields of the undiscovered neutron-deficient nuclei are calculated. Productions of the undiscovered isotopes of Np, Pu, Am, and Cm by the proton-induced spallations of transuranium elements are feasible. However, experimental techniques for online identification of neutron-deficient nuclei produced in proton-induced spallation should be developed.

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.

Distinct sequential and massive transfer processes for production of neutron-rich N≈126 nuclei in U238+Pt198 reactions

To investigate the underlying mechanisms responsible for the enhanced production of new neutron-rich $N\ensuremath{\approx}126$ nuclei in the reaction $^{238}\mathrm{U}+^{198}\mathrm{Pt}$, detailed simulations of the system at an incident energy of 8 MeV/nucleon using the improved quantum molecular dynamics model have been performed. Sequential and massive transfer processes, responsible for the production of targetlike and projectilelike $n$-rich $N\ensuremath{\approx}126$ fragments, respectively, have been recognized. Compared to sequential transfer, the contribution from the massive transfer process plays an almost equal role for the production of new nuclei with atomic number $Z\ensuremath{\le}76$. The two processes show distinct features in the angular and kinetic energy distributions in the laboratory system and hopefully can be disentangled experimentally.

Correlation between nuclear temperature and symmetry energy in subsaturation nuclear matter density

Herein, a study of the correlation between nuclear temperature and symmetry energy is presented for heavy ion collisions at intermediate energies via the isospin-dependent quantum molecular-dynamics model. It is found that different symmetry energy parameters change the density and kinetic energy distribution of the hot nuclei. More importantly, nuclear temperatures that are based on kinetic energy properties can be used to study symmetry energy information.

Impact of magnetic field on the giant dipole resonance ofCa40using an extended quantum molecular dynamics model

By taking into account the magnetic field in the extended quantum molecular dynamics model, we analyzed its effects on giant dipole resonance (GDR) by studying the responses and strengths of the dipole moments. The selected system is the $^{40}\mathrm{Ca}$ nucleus which is excited through the Coulomb interaction by $^{16}\mathrm{O}$. The particle acceleration term in the Li\'enard-Wiechert potential is discussed which, however, has small impact on the magnetic field. The peak energy, strength, and width of GDR, temperature, and angular momentum of $^{40}\mathrm{Ca}$ as a function of beam energy are investigated. It is found that the magnetic field enhances the peak energy, strength, and width of GDR which is not only due to the temperature effects, but also due to the enhancement of the angular momentum of nucleus. At beam energy $E >$ 200 MeV/nucleon, the magnetic field maintains a constant value for the strength of GDR. The paper sheds light on examining important roles of the magnetic field on the nuclear structure in low-intermediate energy heavy-ion collisions.

Low Density Neutron Star Matter with Quantum Molecular Dynamics: The Role of Isovector Interactions

The effect of isospin-dependent nuclear forces on the inner crust of neutron stars is modeled within the framework of Quantum Molecular Dynamics (QMD). To successfully control the density dependence of the symmetry energy of neutron-star matter below nuclear saturation density, a mixed vector-isovector potential is introduced. This approach is inspired by the baryon density and isospin density-dependent repulsive Skyrme force of asymmetric nuclear matter. In isospin-asymmetric nuclear matter, the system shows nucleation, as nucleons are arranged into shapes resembling nuclear pasta. The dependence of clusterization in the system on the isospin properties is also explored by calculating two-point correlation functions. We show that, as compared to previous results that did not involve such mixed interaction terms, the energy symmetry slope L is successfully controlled by varying the corresponding coupling strength. Nevertheless, the effect of changing the slope of the nuclear symmetry energy L on the crust-core transition density does not seem significant. To the knowledge of the authors, this is the first implementation of such a coupling in a QMD model for isospin asymmetric matter, which is relevant to the inner crust of neutron and proto-neutron stars.

Target dependence of isotopic cross sections in the spallation reactions 238U + p, d and 9Be at 1 AGeV * *Supported by the National Natural Science Foundation of China (11875328, 12075327)

The spallation of 238U is an important way to produce rare isotopes. This work aims at studying the cross sections of isotopes produced in 238U + p, d and 9Be reactions at 1 A GeV and their target dependence. (1) A physical model dependent (Bayesian neural network) BNN, which includes the details of IQMD-GEMINI++ model and BNN, was developed for a more accurate evaluation of production cross sections. The isospin-dependent quantum molecular dynamics (IQMD) model is used to study the non-equilibrium thermalization of the 238U nuclei and fragmentation of the hot system. The subsequent decay of the pre-fragments is simulated by the GEMINI++ model. The BNN algorithm is used to improve the prediction accuracy after learning the residual error between experimental data and calculations by the IQMD-GEMINI++ model. It is shown that the IQMD-GEMINI++ model can reproduce the available experimental data (3282 points) within 1.5 orders of magnitude. After being fine tuned by the BNN algorithm, the deviation between calculations and experimental data were reduced to within 0.4 order of magnitude. (2) Based on the predictions by the IQMD-GEMINI++-BNN framework, the target dependence of isotopic cross sections was studied. The cross sections to produce the rare isotopes by the 238U + p, d and 9Be reactions at 1 A GeV are compared. For the generation of neutron-rich fission products, the cross sections for the 238U + 9Be are the largest. For the generation of neutron-deficient nuclei in the region of A = 200–220, the cross sections for 238U + p reaction are the largest. Considering the largest cross sections and the atomic density, the beryllium target is recommended to produce the neutron-rich fission products by the 238U beam at 1 A GeV, while the liquid-hydrogen target is suggested to produce the neutron-deficient nuclei in the region of A = 200–220.

Characteristics of Fragments Produced by Ternary Fission in Intermediate Energy

The characteristics of fragments produced in the ternary fissions have been researched by using the improved quantum molecular dynamics model in heavy 197Au+197Au at 15 MeV/nucleon. The physical quantities of Z, n/z, θ, ptrans/plong about the nuclear fragments have strong dependencies on the impact parameters, and their curves are systematically drawn. By the study of these theoretical results above, we have concluded that there is a cut-off point at b =6 fm, which divides the impact parameters into two regions: the central or semi-peripheral and peripheral regions, and the ternary breakup mechanisms should be very different at these two impact parameter regions. Further research has showed that the regional property of n/z is related to the isospin symmetry of nuclear products, and the conclusion reflects the properties of nuclear fragments may be an observable probe into the nucleon interactions during heavy ion collisions.

Dissipation of energy and higher-order fluctuations of the largest fragment charge in projectile fragmentation

Abstract The higher-order fluctuations of the largest fragment charge were found to exhibit the signatures of a second-order phase transition in experimental data and simulations of the statistical multifragmentation model recently (Pietrzak et al 2020 Phys. Lett. B 809 135763). This work is devoted to study the dissipation of energy and higher-order fluctuations of the largest fragment charge in projectile fragmentation. The isospin-dependent quantum molecular dynamics (IQMD) model is used to study the non-equilibrium thermalization and fragmentation. The statistical code GEMINI is applied to simulate the second decay of the pre-fragments. To reveal how the incident energy dissipates into the excitation energy of the projectile-like system, the time evolution of the density, collective velocity, and random kinetic energy are displayed. It is found that the competition between the heat conduction and heat flux affects the excitation energy of the projectile-like system, which is the key variable in the fragmenting process. Displaying the mean multiplicity of the intermediate mass fragments and the higher-order fluctuations of the largest fragment charge, it is found that the decay mechanism of the projectile-like system transfers from the multi-fragmentation at mid-peripheral collision into the nucleon-evaporation at peripheral collision. The pseudo-critical point of this transition can be indicated by the zero of third order fluctuation together with the minimum of fourth order fluctuation. The calculations of the pseudo-critical point by the IQMD + GEMINI model agree with that extracted from the experimental data. Finally, the influences of the pseudo-critical point by the second decay, the mass number of the colliding system, and the incident energy are studied.

Azimuthal-sensitive three-dimensional HBT radius in Au–Au collisions at $$E_{beam} = 1.23A$$ GeV by the IQMD model

We used an Isospin dependent Quantum Molecular Dynamics (IQMD) model to simulate Au + Au collisions at beam energy $$E_{beam}$$ = 1.23A GeV, which corresponds to center of mass energy $$\sqrt{s_{NN}} = 2.4$$ GeV. Firstly, we obtained reasonable rapidity and transverse mass spectra of $$\pi ^-$$ and $$\pi ^+$$ as well as “apparent” temperature parameters in comparison with the HADES data. Then by calculating three-dimensional Hanbury Brown and Twiss (HBT) radius of same charged pion-pairs, we obtained the square difference of outward radius and sideward radius, i.e. $$R_{out}^{2}-R_{side}^{2}$$ , as well as the freeze-out volume ( $$V_{fo}$$ ), which were basically consistent with the trend of HADES experimental results. The azimuthal dependence of the HBT radii was also calculated by a matrix method, and corrected by the rotation matrix. In addition, the eccentricities of the xy- and zy- planes of pion-pair emissions were also extracted for different pair transverse momentum and collision centrality, which show that the xy-eccentricity increases with pair transverse momentum as well as centrality but not for zy-eccentricity, indicating a more asymmetric transverse emission of particle-pairs with higher transverse momentum in off-central collisions.

Effects of neutron-skin thickness on direct hard photon emission from reactions induced by the neutron-rich projectile Ca50

Direct hard photon emissions from incoherent proton-neutron bremsstrahlung in collisions of the neutron-rich projectile $^{50}$Ca with $^{12}$C and $^{40}$Ca targets are simulated in the framework of the isospin-dependent quantum molecular dynamics (IQMD) model. By adjusting the diffuseness parameter of neutron density in the droplet model to obtain different neutron skin thicknesses for $^{50}$Ca, the effects of neutron skin thickness on direct hard photon emission are investigated via several probes. The results show that more direct hard photons are produced with increasing neutron skin thickness in peripheral collisions. Meanwhile, we find that the multiplicity yield ratio $R_{cp}(\sigma_{\gamma})$ between central collisions and peripheral collisions as well as the rapidity dependence of multiplicity for direct hard photons are sensitive to neutron skin thickness. The results indicate that direct hard photon emission can be taken as an experimental observable to extract information on neutron skin thickness.

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.

利用机器学习研究原子核四极形变在中能重离子碰撞中的效应

The influence of quadrupole deformation on the projectile and target nucleus in $^{238}$U + $^{238}$U collisions at beam energies of 0.4, 1.0, and 1.5 GeV/nucleon is investigated using the ultra relativistic quantum molecular dynamics (UrQMD) model. The effect of quadrupole deformation is investigated using the LightGBM decision tree algorithm. LightGBM's ability to identify nuclear deformation from particle spectra is demonstrated on an event-by-event basis by learning the two-dimensional (transverse momentum and rapidity) distributions of free protons, charged fragments (mass number $A>$1), and charged $\pi$ mesons produced in $^{238}$U + $^{238}$U collisions with and without deformed initializations. Using the important characteristic analysis of LightGBM, the yield of charged fragments around target/projectile rapidities is found to be sensitive to the quadrupole deformation of both the projectile and the target.It can be used as a promising observable to probe quadrupole deformation with heavy-ion collision.

Short-range correlations in the extended quantum molecular dynamics model

Short-range potential has been added into an extended quantum molecular dynamics (EQMD) model. The rms radius, binding energy, and momentum distribution of $^{12}\mathrm{C}$ with different initial structures and short-range potential parameters have been checked. The separation energy of $^{12}\mathrm{C}(p,2p)^{11}\mathrm{B}$ reaction is calculated and compared with the experimental data, which indicates that our modified EQMD model can be taken as a reliable tool for studying proton pair knock-out reaction. Furthermore, the short-range correlation effects on emission time and momentum spectrum of two protons are discussed. Finally, the momentum correlation function of the emitted proton pair is calculated by Lednicky and Lyuboshitz's analytical method. The result explains that short-range repulsion causes high momentum tail and weakens the momentum correlation function.