Progress of quantum molecular dynamics model and its applications in heavy ion collisions

In this review article,we first briefty 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 transrer,fragmentation,collective flow and particle production are reviewed and discussed within the framework of the two models.The constraints on the isospin asymmetric muclear 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.

A possible probe to neutron-skin thickness by fragment parallel momentum distribution in projectile fragmentation reactions

Neutron-skin thickness is a key parameter for a neutron-rich nucleus;however,it is difficult to determine.In the framework of the Lanzhou Quantum Molecular Dynamics(LQMD)model,a possible probe for the neutron-skin thickness(δ_(np))of neutron-rich ^(48)Ca was studied in the 140A MeV ^(48)Ca+^(9)Be projectile fragmentation reaction based on the parallel momentum distribution(p∥)of the residual fragments.A Fermi-type density distribution was employed to initiate the neutron density distributions in the LQMD simulations.A combined Gaussian function with different width parameters for the left side(Γ_(L))and the right side(Γ_(R))in the distribution was used to describe the p∥of the residual fragments.Taking neutron-rich sulfur isotopes as examples,Γ_(L) shows a sensitive correlation withδ_(np) of ^(48)Ca,and is proposed as a probe for determining the neutron skin thickness of the projectile nucleus.

Secondary decay effects of the isospin fractionation in the projectile fragmentation at GeV/nucleon

The isospin fractionations in 124Sn,107Sn+120Sn at 600 MeV/nucleon,and 136Xe,124Xe+208Pb at 1000 MeV/nucleon are investigated by the isospin-dependent quantum molecular dynamics model coupled with the statistical code GEMINI.The yield ratio as a function of the binding energy difference for light mirror nuclei 3H/3He,7Li/7Be,11B/11C,and 15N/15O is applied to estimate the ratio between neutrons and protons in the gas of the fragmenting system.By comparing the estimated values resulting from the simulations with and without the GEMINI code,it was found that the secondary decay distorts the signal of the isospin fractionation.To minimize the secondary decay effects,the yield ratio of the light mirror nuclei 3H/3He as well as its double ratio between two systems with different isospin asymmetries of the projectiles is recommended as robust isospin observables.

Production of high-energy neutron beam from deuteron breakup

The deuteron breakup on heavy targets has been investigated in the framework of an improved quantum molecular dynamics model,focusing on the production of neutrons near zero degrees.The experimental differential cross sections of neutron production in the 102 MeV d+C reactions were reproduced by simulations.Based on the consistency between the model prediction and experiment,the feasibility of producing a neutron beam through the breakup of deuteron on a carbon target was demonstrated.Because of the nucleon Fermi motion inside the deuteron,the energy spectrum of the inclusive neutron near 0°in the laboratory exhibits considerable energy broadening in the main peak,whereas the long tail on the low-energy side is suppressed.By coincidentally measuring the accompanying deuteron breakup proton,the energy of the neutron can be tagged with an intrinsic uncertainty of approximately 5%(1σ).The tagging efficiency of the accompanying proton on the forward-emitted neutron can reach 90%,which ensures that the differential cross section in the(d,np)channel remains two orders higher than that in(p,n)after considering the measurement of accompanying protons.This enables the application of a well-defined energy neutron beam in an event-by-event scheme.

Sigma Meson Production in Nuclear Reactions

The sigma meson production in p ＋ ^12C and p A- ^40Ca reactions at the incident energy Ep = 1.5 GeV is investigated within the Quantum Molecular Dynamics model. The simulation results indicate a distinctive A dependence of the sigma production, that is, the increase of A is followed by an increase of the production cross sections. We find that the σ meson production in proton-induced reactions is strongly medium-dependent, and the produced σ mesons decaying in a denser medium experience a stronger mass shift towards lower masses. This mass shift is an experimentally accessible observable in the final state pion pairs, which do not suffer from reabsorption by the surrounding nucleons. It is pointed out that the ratio of measured sigma cross sections as a function of the sigma invariant-mass from various reactions is a good probe to explore the existence of the σ meson in a dense nuclear environment.

Equation of state for warm dense lithium： A first principles investigation

The quantum molecular dynamics based on the density functional theory has been adopted to simulate the equation of state for the shock compressed lithium. In contrary to some earlier experimental measurement and theoretical simulation,there is not any evidence of the ‘kink＇ in the Hugoniot curve in our accurate simulation. Throughout the shock compression process, only a simple solid-to-liquid melting behavior is demonstrated, instead of complicated solid–solid phase transitions. Moreover, the x-ray absorption near-edge spectroscopy has been predicted as a feasible way to diagnose the structural evolution of warm dense lithium in this density region.

Phase transition and chemical decomposition of liquid carbon dioxide and nitrogen mixture under extreme conditions

Thermodynamic and chemical properties of liquid carbon dioxide and nitrogen（CO_（2~–）N_2） mixture under the conditions of extremely high densities and temperatures are studied by using quantum molecular dynamic（QMD） simulations based on density functional theory including dispersion corrections（DFT-D）. We present equilibrium properties of liquid mixture for 112 separate density and temperature points, by selecting densities ranging from ρ = 1.80 g/cm^3 to 3.40 g/cm^3 and temperatures from T = 500 K to 8000 K. In the range of our study, the liquid CO_（2~–）N_2 mixture undergoes a continuous transition from molecular to atomic fluid state and liquid polymerization inferred from pair correlation functions（PCFs）and the distribution of various molecular components. The insulator–metal transition is demonstrated by means of the electronic density of states（DOS）.

Car-Parinello molecular dynamics simulations of thionitroxide and S-nitrosothiol in the gas phase,methanol,and water——A theoretical study of S-nitrosylation

A dilemma about whether thionitroxide radical (RSNHO) or S-nitrosothiol (RSNO) is observed in protein S-nitrosylation has arisen recently. To illustrate the effect of chemical environment on these structures, this paper presents quantum mechanical molecular dynamics of thionitroxide, and cis-and trans-S-nitrosothiols in the gas phase, methanol, and water. By using Car-Parrinello molecular dynamics (CPMD), we have observed that there is free rotation about the S-N bond at 300 K in thionitroxide, but no such rotation is observed for S-nitrosothiol. The C-S-N-O torsion angle distribution in thionitroxide is s-ignificantly dependent upon the surrounding environment, leading to either gauche-, cis-, or trans-conformation. In the case of S-nitrosothiol the C-S-N-O plane is twisted slightly by 5°-15° in the cis-isomer, while the periplanar structure is well-retained in the trans-isomer. The calculated results are in agreement with the X-ray crystallographic data of small molecular RSNO species. Interestingly, for both compounds, the CPMD simulations show that solvation can cause a decrease in the S-N bond length. Moreover, the oxygen atom of thionitroxide is found to be a good hydrogen-bond acceptor, forming an oxyanion-hole-like hydrogen bonding network.

Uncertainties of critical temperatures based on higher-order fluctuations of the largest fragment charge

The new signature of liquid-gas phase transition has been well indicated by the higher-order fluctuations of the largest fragment charge,but the uncertainties of critical temperatures based on this signature have not been revealed.This study extracts the critical temperatures of liquid-gas phase transition in nuclear reactions and investigates their uncertainties.Utilizing the isospin-dependent quantum molecular dynamics model in conjunction with the statistical model GEMINI enables us to describe the dynamical path from the initial to the final state.An isotope thermometer and a quantum fluctuation thermometer are employed to extract the nuclear temperature.The higher-order fluctuations of the largest fragment charge and critical temperatures are studied in^(124)Sn+^(120)Sn collisions ranging from 400 to 1000 MeV/nucleon and^(124)Sn+AZ collisions at 600 MeV/nucleon.Observations revealed that the pseudo-critical point is robustly indicated by the higher-order fluctuations of the largest fragment charge.The critical temperatures extracted by the isotope thermometer are relatively consistent,with an uncertainty of 15%,while those obtained by the quantum fluctuation thermometer are heavily influenced by the incident energy and mass number of target nuclei.The excitation energy E∗and bound charge Zbound are used for event-sorting.These two ensembles represent the statistical properties of the initial and final states of the system,respectively.The initial-final correlations of statistical properties might lead to two phenomena.First,the size distribution of the largest fragment at the pseudo-critical point based on the Zbound ensemble is wide,while that based on E∗ensemble exhibits bimodality,which is a typical characteristic in the liquid-gas coexistence of a finite system.Second,the temperature at the pseudo-critical point based on the Zbound ensemble is higher than that based on the E∗ensemble.Furthermore,the projectile-like system exhibits a significant dynamical effect in its evolution path from the initial to final state,closely associated with the fluctuation of critical temperature.

Production of neutron-deficient nuclei around N=126 by proton-induced spallation

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 10-7to 10-5cm.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 120μA 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.

Target dependence of isotopic cross sections in the spallation reactions^(238)U+p,d and^(9)Be at 1 A GeV

The spallation of ^(238)U is an important way to produce rare isotopes.This work aims at studying the cross sections of isotopes produced in ^(238)U+p,d and^9 Be 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 ^(238)U 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 ^(238)U+p,d and^9 Be reactions at 1 A GeV are compared.For the generation of neutron-rich fission products,the cross sections for the ^(238)U+^(9)Be are the largest.For the generation of neutron-deficient nuclei in the region of A=200–220,the cross sections for ^(238)U+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 ^(238)U 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.

Isospin effect of the in-medium nucleon-nucleon cross section in excited nuclear reactions

Using relativistic mean field theory, the neutron and the proton density distribution of 56Ni nuclei could be obtained in the ground state and the excited state. Based on the framework of the quantum molecular dynamics model, the 56Ni nuclei have been simulated in ground state and in the neutron or proton excited state. We then used the three different states of 56Ni to collide with the 56Ni in the ground state. To discuss the evolution of the nuclear stopping in different reactions, two kinds of different excited nuclear reactions were studied at different reaction energies and at different impact parameters. Studies have shown that the nuclear stopping of an excited nuclear reaction is sensitive to the isospin-dependent in-medium nucleon-nucleon cross section, compared with the response value of the ground state nuclear reaction. So, it is better for the excited nuclei to extract the isospin dependence of nucleon-nucleon cross section information.

Probing the symmetry potential with neutron-proton bremsstrahlung in heavy-ion collisions

In the framework of the isospin-dependent quantum molecular dynamics transport model （QMD）, the effects of symmetry potential on the collision number and the neutron-proton bremsstrahlung photon in the reactions of 40Ca＋40Ca, 124Sn＋124Sn, 40Ca＋64Zn, 40Ca＋124Sn at different incident beam energies are studied. It is found that the collision number shows moderate sensitivity to the stiffness of the symmetry potential and the number of hard photons calculated with stiff symmetry potential is obviously smaller than that with soft symmetry potential. Thus, the neutron-proton bremsstrahlung photons produced in heavy-ion collisions may be a useful probe for the high-density behavior of the nuclear symmetry potential.

Isospin dependence of projectile fragmentation at hundreds of MeV/u

By modeling the fragmentation process using a dynamic model and permitting only evaporation in the statistical code,the main features of a projectile fragmentation at 600 MeV/u were considered in our previous study[Phys.Rev.C,98:014610(2018)].In this study,we extend this to the isospin dependence of a projectile fragmentation at several hundreds of MeV/u.We searched for isospin observables related to the isospin fractionation to extract the symmetry energy,and found that at the pre-equilibrium stage of the collisions an isospin diffusion will take place and affect the isospin of the final fragments.The isospin fractionation plays a part during the fragmenting stage.Compared to the soft symmetry energy,the stiff symmetry energy provides a smaller repulsive force for neutrons and an attractive force for the protons in a neutron-rich system at a subnormal density,and hence causes a smaller isospin asymmetry of the gas phase,leaving a more neutron-rich liquid phase.An observable robust isospin is proposed to extract the slope of the symmetry energy at normal density based on the isospin dependence of the projectile fragmentation at hundreds of MeV/u.

Theoretical uncertainties on the extraction of in-medium NN cross sections by different Pauli blocking algorithms

Three typical Pauli blocking algorithms in quantum molecular dynamics type models are investigated in the nuclear matter,the nucleus,and heavy ion collisions.In nuclear matter,the blocking ratios obtained with the three algorithms are underestimated by 13%-25%compared to the corresponding analytical values.For a finite nucleus,spurious collisions occur around the surface of the nucleus owing to the defects of the Pauli blocking algorithms.In the simulations of heavy ion collisions,the uncertainty of stopping power arising from the 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 model calculations with free NN cross sections result in the stopping power decreasing with beam energy when the beam energy is less than 300 MeV/u.To increase or decrease the values of the stopping power,the transport model calculations need enhanced or suppressed model dependent in-medium NN cross sections that are expected to be smaller than the true in-medium NN cross sections.

Orientation dichroism effect of proton scattering on deformed nuclei

Proton-induced scattering of 238U nuclei,with spheroidal deformations at beam energies above 100 MeV,is simulated using an improved quantum molecular dynamics model.The angular distribution of the deflected protons is highly sensitive to the orientation of the symmetrical long axis of the target nuclei with respect to the beam direction.As a result,in reverse kinematic reactions,an orientation dichroism effect is predicted,implying that the absorption rate of the 238U beam by a proton target discerns between the parallel and perpendicular orientations of the deformed 238U nuclei.

Equation of State for Shock Compressed Xenon in the Ionization Regime:ab Initio Study

Quantum molecular dynamic (QMD) simulations have been applied to study the thermophysical properties of liquid xenon under dynamic compressions. The equation of state (EOS) obtained from QMD calculations are corrected according to Saha equation, and contributions from atomic ionization, which are of predominance in determining the EOS at high temperature and pressure, are considered. For the pressures below 160 GPa, the necessity in accounting for the atomic ionization has been demonstrated by the Hugoniot curve, which shows excellent agreement with previous experimental measurements, and three levels of ionization have been proved to be sufficient at this stage.

Nuclear dynamical octupole deformation in heavy-ion reactions

Within the quantum molecular dynamics （QMD） model, the dynamical octupole deformation is studied as a function of the central distance between the projectile and target in the approaching process of heavy-ion fusion reactions. The dependence of the maximum dynamical octupole defor- mations on tile incident energies is also investigated. The dynamical octupole deformations can be observed during the approaching process, and the maximum dynamical octupole deformations be- come more significant with decreasing incident energies. The distributions of the proton and neutron centers in the projectile and target are also investigated, respectively. In the approaching process of heavy-ion fusion reactions, the separation between proton centers for two nuclei is larger than that between neutron centers because of the strong Coulomb potential.

Fragment distribution in 78,86Kr+181Ta reactions

Within the framework of the isospin-dependent quantum molecular dynamics model, along with the GEMINI model, the86Kr+181Ta reaction at 80, 120 and 160 MeV/nucleon and the78Kr+181Ta reaction at 160 MeV/nucleon are studied, and the production cross sections of the generated fragments are calculated. More intermediate and large mass fragments can be produced in the reactions with a large range of impact parameter. The production cross sections of nuclei such as the isotopes of Si and P generally decrease with increasing incident energy.Isotopes near the neutron drip line are produced more in the neutron-rich system86Kr+181Ta.

Two-dimensional ultraviolet spectroscopy of proteins

Two-dimensional ultraviolet(2 DUV) spectroscopy is a novel technology for probing molecular structure. We have developed a generalized quantum mechanics/molecular mechanics(QM/MM) approach to simulate the electronic transitions of protein backbones and aromatic amino acids in aqueous solution. These transitions, which occur in the ultraviolet(UV) region, provide a sensitive probe of molecular structure. The features of 2 DUV spectra are accurately characterized and enable us to trace small variations in the structure and dynamics as well as evolution propensity with high accuracy. Various structures and dynamic phenomena are investigated to construct a systematic framework for 2 DUV simulation mechanisms, so as to explore further applications of this technique. In this feature article, we summarize the theory and applications of 2 DUV spectroscopy we have engaged in recently, present the important roles of 2 DUV spectroscopy, and outline directions for future development. We hope this article can offer a platform for more scientists in different research fields to gain a clear overview of 2 DUVand further attract more people to explore this promising field.