The dynamical nucleus-nucleus potentials for fusion reactions 40Ca+40Ca, 48Ca+208Pb and 126Sn+130Te are studied with the improved quantum molecular dynamics (ImQMD) model together with the extended Thomas-Fermi approximation for the kinetic energies of nuclei. The obtained fusion barrier for 40Ca+40Ca is in good agreement with the extracted fusion barrier from the measured fusion excitation function, and the depth of the fusion pockets are close to the results of time-dependent Hartree-Fock calculations. The energy dependence of fusion barrier is also investigated. For heavy fusion system, the fusion pocket becomes shallow and almost disappears for symmetric systems and the obtained potential at short distances is higher than the adiabatic potential.
Within the improved quantum molecular dynamics (ImQMD) model incorporating the statistical decay model, the reactions of 238U+238U at an energy of 7.0A?MeV have been studied. The charge, mass, and excitation energy distributions of primary fragments are investigated within the ImQMD model, and de-excitation processes of these primary fragments are described by a statistical decay model. The mass distribution of the final products in 238U+238U collisions is obtained and compared with the recently obtained experimental data.
Mass parameters for the relative and neck motions in fusion reactions of symmetric systems 90Zr+90Zr, 110Pd+110Pd, and 138Ba+138Ba are studied by means of a microscopic transport model. The shape of the nuclear system is determined by an equidensity surface obtained from the density distribution of the system. The relative and neck motions are then studied and the mass parameters for these two motions are deduced. The mass parameter for the relative motion is around the reduced mass when the reaction partners are at the separated configuration and increases with a decrease of the distance between two reaction partners after the touching configuration. The mass parameter for the neck motion first decreases slightly up to the touching configuration and then increases with the neck width, and its magnitude is from less than a tenth to several times more than the total mass of the system. The mass parameters obtained from the microscopic transport model are larger than the ones obtained from the hydrodynamic model and smaller than those obtained from the linear response function theory. The mass parameters for both motions depend on the reaction systems, but the one for the relative motion depends on the incompressibility of the EoS more obviously than that for neck motion.
Collisions involving 112Sn and 124Sn nuclei have been simulated with the improved Quantum Molecular Dynamics transport model. The results of the calculations reproduce isospin diffusion data from two different observables and the ratios of neutron and proton spectra. By comparing these data to calculations performed over a range of symmetry energies at saturation density and different representations of the density dependence of the symmetry energy, constraints on the density dependence of the symmetry energy at sub-normal density are obtained. Results from present work are compared to constraints put forward in other recent analysis.
Based on the improved quantum molecular-dynamics (ImQMD) model, the incident energy dependence of dynamic potential barriers is investigated in the entrance channel of fusion reactions. The height of the dynamic barrier increases with the incident energy at energies around the Coulomb barrier. The calculated lowest dynamic barrier approaches to the adiabatic barrier, while the highest one goes up to the sudden potential barrier. To understand the energy dependence of the dynamical barrier we study the neck formation and shape evolution of the system which causes the dynamic lowering of the barrier.
The collision of very heavy nuclei 197Au+197Au at 15 A MeV has been studied within the improved quantum molecular dynamics model. A class of ternary events satisfying nearly complete balance of mass numbers is selected. The experimental mass distributions for the system 197Au+197Au ternary fission fragments, the heaviest (A1), the intermediate (A2) and the lightest (A3), are reproduced well. The mean free path of nucleons in the reaction system is studied and the shorter mean free path is responsible for the ternary fission with three mass comparable fragments, in which the two-body dissipation mechanism plays a dominant role.
The collision of very heavy nuclei 197Au+197Au at 15 A MeV has been studied within the improved quantum molecular dynamics model. A class of ternary events satisfying nearly complete balance of mass numbers is selected. The experimental mass distributions for the system 197Au+197Au ternary fission fragments, the heaviest (A1), the intermediate (A2) and the lightest (A3), are reproduced well. The mean free path of nucleons in the reaction system is studied and the shorter mean free path is responsible for the ternary fission with three mass comparable fragments, in which the two-body dissipation mechanism plays a dominant role.
The mass number distributions of three fragments from the ternary fission of the system 197Au+197Au are reproduced rather well by using the improved quantum molecular dynamics (ImQMD) model without any adjusting parameter. It is found that the probability of ternary fission evidently depends on the incident energy and the impact parameter, and the two-body dissipation is the main mechanism responsible for the formation of the third fragment with comparable mass.
The influence of isospin dependence of in-medium nucleon-nucleon cross sections on the n/p ratios for emitted nucleons in reactions 96Zr+96Zr and 96Ru+96Ru at Eb=400AMeV is investigated by means of an improved quantum molecular dynamics model. Our results show that the high energy part of the spectra of the n/p ratios for emitted nucleons is sensitive to the isospin dependence of in-medium nucleon-nucleon cross sections for neutron-rich reaction systems. Therefore, we propose that the n/p ratio of emitted high energy nucleons in a very neutron-rich reaction system at several hundreds of AMeV can be taken as sensitive observables to constrain the isospindependence of in-medium nucleon-nucleon cross sections.
The recent GSI data for proton-induced spallation reactions by using inverse kinematics are analyzed by the improved quantum molecular dynamics model (ImQMD05) merged with the generalized evaporation model (GEM2) and GEMINI model. We find that the model of ImQMD05+GEM2 reproduces the experimental data of mass and charge distributions for proton-induced spallation reactions on heavy targets (208Pb, 238U and 197Au) well and the model of ImQMD05+GEMINI reproduces the ones on light targets (56Fe) well. The experimental data for double differential cross sections of emitted neutrons and protons in intermediate energy proton-induced spallation reactions can also be reproduced well with the same models and this shows that they are not very sensitive to the merged statistical model.
The emissions of neutrons, protons and bound clusters from central 124Sn + 124Sn and 112Sn + 112Sn collisions are simulated using the Improved Quantum Molecular Dynamics model for two different density-dependent symmetry-energy functions. The calculated neutron–proton spectral double ratios for these two systems are sensitive to the density dependence of the symmetry energy, consistent with previous work. Cluster emission increases the double ratios in the low energy region relative to values calculated in a coalescence-invariant approach. To circumvent uncertainties in cluster production and secondary decays, it is important to have more accurate measurements of the neutron–proton ratios at higher energies in the center of mass system, where the influence of such effects is reduced.
The isospin effects in proton-induced reactions on isotopes of 112-132Sn and the corresponding β-stable isobars are studied by means of the improved quantum molecular dynamics model and some sensitive probes for the density dependence of the symmetry energy at subnormal densities are proposed. The beam energy range is chosen to be 100–300 MeV. Our study shows that the system size dependence of the reaction cross sections for p+112-132Sn deviates from the Carlson's empirical expression obtained by fitting the reaction cross sections for proton on nuclei along the β-stability line and sensitively depends on the stiffness of the symmetry energy. We also find that the angular distribution of elastic scattering for p+132Sn at large impact parameters is very sensitive to the density dependence of the symmetry energy, which is uniquely due to the effect of the symmetry potential with no mixture of the effect from the isospin dependence of the nucleon-nucleon cross sections. The isospin effects in neutron-induced reactions are also studied and it is found that the effects are just opposite to that in proton-induced reactions. We find that the difference between the peaks of the angular distributions of elastic scattering for p+132Sn and n+132Sn at Ep,n=100 MeV and b=7.5 fm is positive for soft symmetry energy Usymsf and negative for super-stiff symmetry energy Usymnlin and close to zero for linear density dependent symmetry energy Usymlin, which seems very useful for constraining the density dependence of the symmetry energy at subnormal densities.
Five sets of isospin-dependent in-medium nucleon–nucleon cross sections obtained by means of many-body theories with different approaches or calculation details are tested by comparing the calculated reaction cross sections of proton-induced reactions on various targets with the experimental data. The calculations are performed by using the improved quantum molecular dynamics model. The comparison indicates that these theoretically predicted isospin-dependent in-medium nucleon–nucleon cross sections can reasonably describe the medium suppression effect on the nucleon–nucleon cross sections when the medium densities are at the range of ρ < 0.5ρ0. But it seems that the medium suppression effect in-medium density range of 0.5ρ0 < ρ < ρ0 provided by these in-medium nucleon–nucleon cross sections is too weak to reproduce the experimental data.
The dynamic, adiabatic and diabatic entrance potentials in strongly damped reactions of 238U+238U, 232Th+250Cf are calculated and compared. The feature of the dynamical potential implies that it is possible for the composite systems to stick together for a period of time. By means of the improved quantum molecular dynamics model the time evolution of the density and charge distributions of giant composite systems and their fragments for reactions 238U+238U, 232Th+250Cf are investigated, from which the lifetimes of giant composite systems at different energies are obtained. The longest average lifetime of 238U+238U is found when the incident energy is about
The elliptic flow for Z≤2 particles in heavy ion collisions at energies from several tens to several hundreds MeV per nucleon is investigated by means of a transport model, i.e., a new version of the improved quantum molecular dynamics model (ImQMD05). This model employs a complete Skyrme potential energy density functional. The influence of different effective interactions and medium corrections of nucleon-nucleon cross sections on the elliptic flow are studied. Our results show that a soft nuclear equation of state and incident energy dependent in-medium nucleon-nucleon cross sections are required to describe the excitation function of the elliptic flow at intermediate energies. The size dependence of transition energies for the elliptic flow at intermediate energies is also studied. The system size dependence of transition energies fits a power of system size with an exponent of 0.223.
By using the Improved Quantum Molecular Dynamics model, the ^{244}Pu+^{244}Pu, ^{238}U+^{238}U and ^{197}Au+^{197}Au reactions at the energy range of E_{c.m.}=800 MeV to 2000 MeV are studied. We find that the production probability of superheavy fragments (SHFs) with Z≥114 for the ^{244}Pu+^{244}Pu reaction is much higher compared with that for the ^{238}U+^{238}U reaction and no product of SHF is found for the ^{197}Au+^{197}Au. The production probability of SHFs strongly depends on the incident energy and a narrowly peaked energy dependence of production probability is found. The decay mechanism of the composite system of projectile and target is studied and the time scale of decay process is explored. The binding energies and the shapes of SHFs are studied. The binding energies of SHFs are broadly distributed and the shapes of SHFs are strongly deformed.
The peripheral heavy-ion collisions of 112,124Sn+86Kr at Eb=25 A MeV are studied by means of the improved quantum molecular dynamics model (ImQMD). It is shown that the slope of the average N/Z ratio of emitted nucleons versus impact parameters for these reactions is very sensitive to the density dependence of the symmetry energy. Our study also shows that the yields of 3H and 3He decrease with impact parameters and that the slope of the yield of 3H versus impact parameters as well as the ratio of Y(3H)/Y(3He) depends strongly on the symmetry potential for peripheral heavy-ion collisions.
The improved quantum molecular dynamics model is further developed by introducing new parameters in interaction potential energy functional based on Skyrme interaction of SkM* and SLy series. The properties of ground states of selected nuclei can be reproduced very well. The Coulomb barriers for a series of reaction systems are studied and compared with the results of the proximity potential. The fusion excitation functions for a series of fusion reactions are calculated and the results are in good agreement with experimental data.
By using the updated improved quantum molecular dynamics model in which a surface-symmetry potential term has been introduced, the excitation functions for fusion reactions of 40,48Ca+90,96Zr at energies around the Coulomb barrier have been studied. The experimental data of the fusion cross sections for 40Ca+90,96Zr have been reproduced remarkably well without introducing any new parameters. The fusion cross sections for the neutron-rich fusion reactions of 48Ca+90,96Zr around the Coulomb barrier are predicted to be enhanced compared with a non-neutron-rich fusion reaction. In order to clarify the mechanism of the enhancement of the fusion cross sections for neutron-rich nuclear fusions, we pay great attention to studying the dynamic lowering of the Coulomb barrier during a neck formation. The isospin effect on the barrier lowering is investigated. It is interesting that the effect of the projectile and target nuclear structure on fusion dynamics can be revealed to a certain extent in our approach. The time evolution of the N/Z ratio at the neck region has been firstly illustrated. A large enhancement of the N/Z ratio at neck region for neutron-rich nuclear fusion reactions is found.
The neck dynamics and nucleon transfer through the neck in fusion reactions 40Ca+90,96Zr are studied by applying the improved quantum molecular dynamics model. A special attention is paid to the dynamic behaviour of the neck development at touching point and to the contribution of excess neutrons in a neutron-rich target (or projectile) to neck formation and nucleon transfer.
An improved quantum molecular dynamics model is developed. By using this model, the properties of ground state of nuclei from 6Li to 208Pb are described very well with one set of parameters. The fusion reactions for 40Ca+90Zr, 40Ca+96Zr, and 48Ca+90Zr at energies near the barrier are studied by this model. The experimental data of the fusion cross sections for 40Ca+90,96Zr at energies near the barrier are reproduced remarkably well without introducing any new parameters. The mechanism for the enhancement of the fusion cross sections for neutron-rich nuclear reaction near barrier is analyzed.