Improved Quantum Molecular Dynamics Model Research Articles

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 an 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 (σA>100), the difference of σA>100 between 132Sn + 124Sn and 124Sn + 124Sn systems (δσA>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.

The description of dynamical fission process using improved quantum molecular dynamics model incorporated with microscopic potential energy surface

A new method, namely the improved quantum molecular dynamics model incorporated with the microscopic potential energy surface, is proposed to simulate the dynamical evolution from saddle to scission point and to calculate the isotope yields of fission fragments in thermal neutron-induced fission of actinide nuclei near 236U. With this approach, the shell and pairing effects are introduced by the microscopic potential energy, while the isospin effect, the dynamical effects of fluctuations and correlations in fission process are automatically included in the improved quantum molecular dynamics model. These two aspects eventually influence the productions of fission fragments. The calculated both charge and mass distributions of fission fragments for a series of actinide nuclei are in overall agreement with the evaluated data from JEFF-3.3 and ENDF/B-VIII.0. The isotope distributions of fission fragments in the fission of 236U reproduce the data reasonable well, from which we extract the relationship between peak mass number of the isotope distributions and the charge number of fission fragments. We find that this relationship deviates linear relation slightly at certain cases, which indicates the isospin nonequilibrium effect. By tracking back to the fission process on the two dimension plane of elongation and mass asymmetry of prefragments, we find that the necked-in shape and the separation of two parts happen much faster for the 132Sn than 128,136Sn in the time evolution of the distance R between the centers of two parts of the fissioning system. The events producing 128,132,136Sn and 136,140,144Xe present two kinds of average fission paths with bypassing and going through the minimum-energy valley of the microscopic potential energy surface, respectively.

Dynamics of charge equilibration and effects on producing neutron-rich isotopes around N=126 in multinucleon transfer reactions

The dynamics of the charge equilibration (CE) and the effects on the production of the neutron-rich isotopes around $N = 126$ in multinucleon transfer reactions are still not well understood. In this Letter, we investigate the mechanism of the CE from different viewpoints by using the extended version of the dinuclear system model (DNS-sysu) and the improved quantum molecular dynamics (ImQMD) model. From the macroscopic and microscopic dynamical viewpoints, we find incomplete CE for the mass asymmetry reaction systems even in the very deep collisions, and the behavior of "inverse CE" that the tendency of the fragments is away from the $N/Z$ value of the compound system in the reaction $^{140}$Xe + $^{198}$Pt. Unlike the slow process presented in the ImQMD model, the behavior of fast equilibration with the characteristic time $\sim$ 0.52 zs is obtained based on the DNS-sysu model, which is consistent with the experimental data. By performing the systematic calculation, the correlation between the CE and the mass asymmetry of the reaction systems is clarified, which not only accounts for the observed intriguing phenomena of the CE but also provides essential information for producing the neutron-rich isotopes around $N = 126$.

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.

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.

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.

Determination of the impact parameter distribution of low-intermediate energy heavy ion collisions using machine learning

<p indent="0mm">The impact parameter is an important quantity for reasonably simulating heavy ion collisions (HIC) using the transport model, because many HIC observables obviously depend on it in the simulation. However, the impact parameter cannot be directly measured or determined from HIC observables, so reconstructing impact parameter distributions from HIC observables is highly desired. For intermediate energy HICs, impact parameters distribute in a wide range for the selected events due to the strong fluctuation mechanism. In this work, three methods for reconstructing impact parameter distributions are discussed, namely sharp cut-off approximation, Bayesian estimation, and neural network estimation of impact parameters. The dataset used for reconstructing the impact parameter distribution by machine learning methods are generated from an improved quantum molecular dynamics model (ImQMD). Finally, we propose to use an unsupervised machine learning method, namely the K-means algorithm, to sort the centrality of heavy ion collisions and its validity is also proved in theory.

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

In this work, we first 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 $^{124}\mathrm{Sn}+^{112}\mathrm{Sn}$ 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.

Study of neutron-rich nuclei reaction using ImQMD ‎model

In the present study, the fusion reactions induced by neutron-rich nuclei have been investigated using the improved quantum molecular-dynamics (ImQMD) model. First, the accuracy of the results was determined by using a set of parameters IQ3a for 16O+92Zr, 40Ca+46Ti and 16O+154Sm fusion excitation functions. The obtained results revealed that the measured fusion excitation function can be reasonably well reproduced. A comparison was also performed with the theoretical results based on the coupled-channel calculations. Then, the time evolution of densities for the 16O+59Co and 32S+92Zr reactions in which the target nuclei were neutron-rich were studied and the fusion cross sections were calculated dynamically. It was found that the fusion cross sections of these reactions at energies around the Coulomb barrier can be well reproduced by using the ImQMD modle.

Symmetry energy effect on emissions of light particles in coincidence with fast fission

The emission of light particles in coincidence with fast fission in near peripheral reactions of 40Ar+197Au at 30 MeV/u beam energy has been studied by using the Improved Quantum Molecular Dynamics Model (ImQMD). It is demonstrated that in the symmetrical fast fission of the heavy target-like fragment (TLF), the emission of the coalescence-invariant neutrons (CIN) is enhanced particularly at large angles in comparison to that in the events without fission. Due to the enhanced CIN emission and the accumulation of the isospin effect in the long-time process, the yield ratio of the CIN to the coalescence-invariant protons (CIP) in the fission events exhibits significant dependence on the symmetry energy Esym(ρ) varying with density. Considering that the large angle neutrons are experimentally advantageous to measure for the lower flying velocity and lower multiplicity, we emphasize that the yield ratio RCINP at large angles in the fast fission events can be used as a novel probe of the nuclear symmetry energy at sub-saturation densities.

Dynamical Properties of the New Ternary Fission in Collisions of 197Au+197Au at 15 MeV/Nucleon

The dynamical properties of the new ternary fission in heavy 197Au+197Au at 15 MeV/nucleon have been investigated by using the improved quantum molecular dynamics model. The dependencies of the production probability, lifetime, the time interval, and angular distribution on the impact parameter are carefully studied. The calculation results show that the characteristics of these are very different between the small and the large impact parameter. Comparing the theoretical results with the experimental data, one can obtain that the fast ternary breakup likely occurs at the impact parameter region b = 7 ‐ 9 fm. The nonisotropic of angular distribution and the short time interval among two fissions indicates that the fast ternary fission is a nonequilibrium and violent process.

Orientation dichroism effect of proton scattering on deformed nuclei * * Supported by the National Natural Science Foundation of China (11875174, 11890712, 11965004, 11947413, U1867212, 11711540016), Natural Science Foundation of Guangxi (2016GXNSFFA380001, 2017GXNSFGA198001), Foundation of Guangxi innovative team and distinguished scholar in institutions of higher education

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.

Production mechanism of the neutron-rich nuclei in multinucleon transfer reactions: A reaction time scale analysis in energy dissipation process

The energy dissipation processes in multinucleon transfer reactions of 136Xe+198Pt at incident energies Elab=5.59 and 7.98 MeV/nucleon are investigated by using the improved quantum molecular dynamics model. The total-kinetic-energy-mass (TKE-Mass) distributions, the total kinetic energy loss (TKEL) distributions, and the excitation energy distributions of the primary binary products under different contact time scales of the reaction partners are analyzed. It shows that the value of the energy dissipation has an increasing trend over contact time. The quasielastic, the deep-inelastic, and the quasifission events can be roughly distinguished by the contact time. By analysing the correlation between the isotopic cross sections and the contact time, we find that the neutron-rich nuclei are produced in the deep-inelastic collisions.

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.

Shielding effects in fusion reactions with a proton-halo nucleus * * Supported by National Natural Science Foundation of China (11965004, U1867212, 11711540016, 11847317, 11947413), Natural Science Foundation of Guangxi province (2016GXNSFFA380001, 2017GXNSFGA198001), Foundation of Guangxi innovative team and distinguished scholar in institutions of higher education, and Innovation project of Guangxi Graduate Education (XYCSZ2018051)

To explain the experimental observation that the fusion cross-section of a proton-halo nucleus with a heavy target nucleus is not enhanced as expected, the shielding hypothesis was proposed, where the proton-halo nucleus is polarized and the valence proton shielded by the core. In the frame of the improved quantum molecular dynamics model, the fusion reaction 17F on 208Pb around the Coulomb barrier is simulated. The existence of the shielding effect is verified by the microscopic dynamics simulations. Its influence on the effective interaction potential is also investigated.

New probe to study the symmetry energy at low nuclear density with the deuteron breakup reaction

The reactions of nucleon and polarized deuteron scattered off a heavy target at large impact parameter with intermediate energies have been investigated by using the improved quantum molecular dynamics model. It is found that, due to the difference effect of isovector potential on proton and neutron, there is a significant difference between the angle distribution of elastic scattering protons and neutrons. To overcome the lack of monochromatic neutron beam, the reaction of polarized deuteron peripherally scattered off the heavy target is used to replace the reaction of individual proton and neutron scattered off heavy target to study the isospin effect. It is found that the distributions of elastic scattering angle of proton and neutron originating from the breakup of deuteron are very similar to the results of the individual proton- and neutron-induced reaction. A new probe more effective and more clean, namely the difference between elastic scattering angle of proton and neutron originating from the breakup of polarized deuteron, is promoted to constrain the symmetry energy at subsaturation density.

Transport model studies on the fast fission of the target-like fragments in heavy ion collisions

The fission of the target-like fragments (TLF) in heavy ion collisions (40Ar+197Au, b=8 fm) at beam energies from 20 to 40 MeV/u has been studied by an improved quantum molecular dynamics model (ImQMD). The time scale at a few 100 fm/c (10−21 s) of the TLF fission is consistent with the picture that fast fission occurs. The dynamic feature of the fast fission is illustrated by the mass asymmetry and the angular distribution of the fission axis. The effect of the surface energy coefficient and the beam energy on the dynamic feature of the fission is demonstrated. At higher beam energy, or with larger surface energy coefficient, the mass asymmetry of the fission fragments is larger and the angular distribution of the fission axis shows a more pronounced peak near beam direction, coincidentally the fission time scale is shorter. The variation suggests that the fission observables can be used as sensitive probes to the surface energy coefficient of nucleus. Irrelevant to the beam energy or the surface energy coefficient, the mean value of the relative velocity of the fission fragments situates in the vicinity of 2.4 cm/ns, in accordance with the Viola systematics applied in statistic fission. This value can be used as a calibration constant in all heavy ion fission experiments. The studies demonstrate the applicability of the transport model in the description of fast fission as a large amplitude collective motion mode in heavy ion collisions.

Production of exotic neutron-deficient isotopes near N, Z = 50 in multinucleon transfer reactions * * Supported by National Natural Science Foundation of China (11635003, 11025524, 11161130520), the National Basic Research Program of China (2010CB832903) and the European Commissions 7th Framework Programme (FP7-PEOPLE-2010-IRSES) (269131)

The multinucleon transfer reaction in the collisions of 40Ca+ 124Sn at MeV is investigated using the improved quantum molecular dynamics model. The measured angular distributions and isotopic distributions of the products are reproduced reasonably well by the calculations. The multinucleon transfer reactions of 40Ca + 112Sn, 58Ni + 112Sn, 106Cd + 112Sn, and 48Ca + 112Sn are also studied. This demonstrates that the combinations of neutron-deficient projectile and target are advantageous for the production of exotic neutron-deficient nuclei near N, Z = 50. The charged particles' emission plays an important role at small impact parameters in the de-excitation processes of the system. The production cross sections of the exotic neutron-deficient nuclei in multinucleon transfer reactions are much larger than those measured in the fragmentation and fusion-evaporation reactions. Several new neutron-deficient nuclei can be produced in the 106Cd + 112Sn reaction. The corresponding production cross sections for the new neutron-deficient nuclei, 101, 112Sb, 103Te, and 106, 107I, are 2.0 nb, 4.1 nb, 6.5 nb, 0.4 b and 1.0 b, respectively.

The Xe136+Pt198 reaction: A test of models of multi-nucleon transfer reactions

The yields of 42 projectile-like fragments (PLFs) and fission fragments and 36 target-like fragments (TLFs) were measured using off-line $\ensuremath{\gamma}$-ray spectroscopy in a thin target experiment involving the $^{136}\mathrm{Xe}+^{198}\mathrm{Pt}$ reaction. The center of target beam energy was 760.5 MeV $({\mathrm{E}}_{\mathrm{c}.\mathrm{m}.}=450$ MeV). The reported yields are compared with those from previous measurements for this reaction and with predictions of the GRAZING, di-nuclear systems (DNS), and improved quantum molecular dynamics (ImQMD) models. The yields of the TLFs and PLFs are, in general, substantially smaller than those previously observed at a beam energy of 1085 MeV. Neither the GRAZING nor the DNS model correctly describes the measured TLF and PLF yields in this lower- energy reaction but the ImQMD model describes these yields adequately.

Constraints on symmetry energy and n/p effective mass splitting with improved quantum molecular dynamics model

A new version of improved quantum molecular dynamics model that includes standard Skyrme interactions has been developed. Based on the new code,four commonly used parameter sets,SLy4,SkI2,SkM*and Gs are adopted in the improved quantum molecular dynamics model and the isospin sensitive observables,namely isospin transport ratios,single and double ratios of the yields of neutrons and protons are investigated. The isospin transport ratios are strongly sensitive to the slope of symmetry energy,and are not very sensitive to the nucleon effective mass splitting. On the other hand,the high energy neutrons and protons yields ratios from reactions at different incident energies provide a good observable to the momentum dependence of nucleon effective mass splitting. By comparing our calculations with the data,we find that the constrained L value(the slope of density dependence of symmetry energy) is about ~46 MeV when the Skyrme type interaction is considered in transport models,and the isospin diffusion data prefer to mn*mp*,but it is not a strong constraint with deep χ2minimum.