Isospin-dependent Quantum Molecular Dynamics Research Articles

Scaling of anisotropic flow and momentum-space densities for light particles in intermediate energy heavy ion collisions

Abstract Anisotropic flows ( v 2 and v 4 ) of light nuclear clusters are studied by isospin-dependent quantum molecular dynamics model for the system of 86 Kr + 124 Sn at intermediate energy and large impact parameters. Number-of-nucleon scaling of the elliptic flow ( v 2 ) are demonstrated for the light fragments up to A = 4 , and the ratio of v 4 / v 2 2 shows a constant value of 1/2. In addition, the momentum-space densities of different clusters are also surveyed as functions of transverse momentum, in-plane transverse momentum and azimuth angle relative to the reaction plane. The results can be essentially described by momentum-space power law. All the above phenomena indicate that there exists a number-of-nucleon scaling for both anisotropic flow and momentum-space densities for light clusters, which can be understood by the coalescence mechanism in nucleonic degree of freedom for the cluster formation.

Surveying the nucleon-nucleon momentum correlation function in the framework of quantum molecular dynamics model

Momentum correlation functions of nucleon-nucleon pairs are presented for reactions with C isotopes bombarding a ${}^{12}C$ target within the framework of the isospin-dependent quantum molecular dynamics model. The binding-energy dependence of the momentum correlation functions is also explored, and other factors that have an influence on momentum correlation functions are investigated. These factors include momentum-dependent nuclear equations of state, in-medium nucleon-nucleon cross sections, impact parameters, total pair momenta, and beam energy. In particular, the rise and the fall of the strength of momentum correlation functions at lower relative momentum are shown with an increase in beam energy.

Entrance channel effects on the role of isospin-dependent momentum interaction in isospin fractionation in heavy ion collisions

An isospin degree of freedom is inserted into the momentum dependent interaction in the quantum molecular dynamics model to obtain an isospin dependent momentum interaction given in a form practically usable in isospin dependent quantum molecular dynamics model. We investigate the entrance channel effects for the role of isospin momentum dependent interaction on the isospin fractionation ratio and its dynamical mechanism in the intermediate energy heavy ion collisions. It is found that the isospin dependent momentum interaction induces a significant reduction of isospin fractionation ratio under all entrance channel conditions. However the strong dependence of isospin fractionation ratio on the symmetry potential is preserved after considering the isospin degree of freedom in the momentum dependent interaction.

Nuclear reaction dynamics induced by halo-nuclei at intermediate energy heavy ion collisions

We studied systematically the reaction dynamics induced by neutron-halo nuclei and proton-halo nuclei within the isospin dependent quantum molecular dynamics,such as the effects of loose bound halo-nuclei on the fragmentation reaction and momentum dissipation for different colliding systems with different beam energies and different impact parameters. In order to emphasize the roles of neutron-halo nucleus 19B and proton-halo nucleus 23Al on the reaction dynamics wealso calculated the the reaction dynamics induced by the stable nuclei 19F and 23Na with equal mass under identical incident channel conditions. Based on the comparison of results of reaction dynamics induced by halo-nucleus colliding systems and stable nucleus collidinmg systems we found that the roles of loose bound halo-nucleus structure on the fragmentation multiplicity and nuclear stopping (momentum dissipation) are important for all of colliding systems with different beam energies and minor impact parameters, such as, the loose bound halo-nuclei structure increases the fragmentation multiplicity, but reduces the nuclear stopping.

ENTRANCE CHANNEL EFFECTS ON THE ISOSPIN FRACTIONATION AT INTERMEDIATE ENERGY HEAVY ION COLLISIONS

We investigate the dependence of isospin fractionation degree on the entrance channel condition, which includes the impact parameter, the beam energy, the mass and the neutron–proton ratio of the colliding system as well as quantifying the gas phase and the liquid phase by using the isospin dependent quantum molecular dynamics model. We found that the isospin fractionation degree increases markedly with the enhancements of the neutron–proton ratio of system and the beam energy; however, it decreases with increasing system mass as well as slowly increases with the enhancement of the impact parameter. In particular, the property for the sensitive dependence of isospin fractionation degree on the symmetry potential and its weak dependence on the in-medium nucleon–nucleon cross-section is preserved for all the neutron-rich systems and all the impact parameters in the relative lower beam energy region. In this case, the isospin fractionation degree for all the neutron-rich systems can be directly compared with the experimental data to extract the information on the symmetry potential in the relative lower beam energy region.

Special roles of loose neutron-halo nucleus structure on the fragmentation and momentum dissipation in heavy ion collisions

We studied the special roles of loose neutron-halo structure of 19B on the fragmentation and momentum dissipation by using isospin dependent quantum molecular dynamics. In order to protrude the special roles of neutron-halo structure on the reaction dynamics we compared the fragmentation multiplicity and nuclear stopping (momentum dissipations) induced by neutron-halo nucleus 19B with those induced by a same mass stable nucleus 19F under the same incident channel condition. We found that the loose neutron-halo structure of 19B increases the fragmentation multiplicity in lower beam energy region. On the contrary, the special halo structure of 19B weakens the nuclear stopping, compared to those induced by stable nucleus 19F. However both fragmentation multiplicity-difference and nuclear stopping-difference between the reactions induced by 19B and 19F gradually decrease and finally disappear as the increase of beam energy. These results suggest a good project for the experimental measurements of the fragmentation multiplicity and nuclear stopping to study the reaction dynamics induced by neutron-halo nuclei.

Improved isospin dependent quantum molecular dynamics model and its application to fusion reactions near Coulomb barrier

The isospin dependent quantum molecular dynamics model is developed by introducing switch function method which deals with correctly the surface interaction and shell effect in the process of projectile and target approaching. The fusion excitation functions for 40Ca + 40Ca, 40Ca + 48Ca and 48Ca + 48Ca at energies in the vicinity of the Coulomb barrier are studied. The experimental data of the fusion cross sections for these three systems can be regenerated very well. It is found that the fusion cross sections for neutron-rich system increase obviously. The static and dynamical Coulomb barriers are studied in order to clarify the phenomena. The neutron to proton ratio (N/Z ratio) at neck region is also studied, which apparently presents isospin effects of projectile-target combinations.

The isospin effects on the momentum dissipation induced by the Coulomb interacti on in the process of heavy-ion collissions

The isospin effects of Coulomb interaction on the momentum dissipation in the heavy ion collissions at an intermediate energy has been studied carefully within the isospin dependent quantum molecular dynamics model. The results show that Co ulomb interaction induces the reduction of momentum dissipation because it leads the shrinking of the mechanical and chemical instability domains, and the degre e of reduction depends sensitively on the form and strength of symmetry potentia l. However, the property that the momentum dissipation depends sensitively on th e isospin dependences of in-medium nucleon_nucleon cross section and insensitiv ely on the symmetry potential, is true for the cases with and without the Coulom b interaction.

Systematic studies of binding energy dependence of neutron–proton momentum correlation function

Hanbury Brown–Twiss (HBT) results of the neutron–proton correlation function have been systematically investigated for a series of nuclear reactions with light projectiles with the help of the isospin-dependent quantum molecular dynamics model. The relationship between the binding energy per nucleon of the projectiles and the strength of the neutron–proton HBT at small relative momentum has been obtained. Results show that neutron–proton HBT results are sensitive to the binding energy per nucleon.

Isospin Effect of Coulomb Interaction on Momentum Dissipationin Intermediate Energy Heavy Ion Collisions

We investigate the isospin effect of Coulomb interaction on the momentumdissipation or nuclear stopping in the intermediate energy heavy ioncollisions by using the isospin-dependent quantum molecular dynamics model.The calculated results show that the Coulomb interaction inducesobviously the reductions of the momentum dissipation. We also find thatthe variation amplitude of momentum dissipation induced by the Coulombinteraction depends sensitively on the form and strength of symmetrypotential. However, the isospin effect of Coulomb interaction on themomentum dissipation is less than that induced by the in-medium nucleon–nucleon cross section. In this case, Coulomb interaction does not changeobviously the isospin effect of momentum dissipation induced by thein-medium two-body collision. In particular, the Coulomb interaction ispreferable for standing up the isospin effect of in-medium nucleon–nucleon cross section on the momentum dissipation and reducing theisospin effect of symmetry potential on it, which is important forobtaining the feature about the sensitive dependence of momentumdissipation on the in-medium nucleon–nucleon cross section and weakly onthe symmetry potential.

Isospin effect of Coulomb interaction on the dissipation and fragmentation in intermediate energy heavy ion collisions

We investigate separately the isospin effects of Coulomb interaction and symmetry potential on the dissipation and fragmentation in the intermediate energy heavy ion collisions by using isospin-dependent quantum molecular dynamics model. The calculated results show that the Coulomb interaction induces the reductions of both isospin fractionation ratio and nuclear stopping (momentum dissipation). However, the Coulomb interaction not only does not change obviously the strong isospin effect of the symmetry potential on the isospin fractionation ratio but also does not change obviously that of in-medium two-body collision on the nuclear stopping. On the contrary, the symmetry potential induces the enhancement of the isospin fractionation ratio but it is insensitive to the nuclear stopping. Finally, the competition between the Coulomb interaction and symmetry potential induces the reductions of both isospin fractionation ratio and nuclear stopping for two forms of symmetry potentials in this paper.

Effect of Coulomb Interaction on the Isospin FractionationProcess

We studied the effect of Coulomb interaction on the isospinfractionation in the intermediate energy heavy ion collisions by usingthe isospin-dependent quantum molecular dynamics model. The calculatedresults show that Coulomb interaction induces the reduction of the isospinfractionation process with the evolutions of neutron–proton ratio andmass of system. Because Coulomb interaction is repulsive for the proton,more binding protons become free, which produces the neutron-poor gasphase and neutron-rich liquid phase, compared to the neutron–protonratio of the system. The isospin fractionation degree is weakened by theCoulomb term. In contrast, the symmetry potential is repulsive forneutrons and attractive for protons in the neutron-rich system, and thenthe binding neutrons more than the protons become free, which produces aneutron-rich gas phase and neutron-poor liquid phase, so that theisospin fractionation degree is increased. The competition between theeffects from the Coulomb interaction and the symmetry potential inducesthe reduction of the isospin fractionation degree for all the systemmasses. The properties for the sensitive dependence of isospinfractionation degree on the symmetry potential and weak dependence onthe nucleon–nucleon cross section are preserved for all theneutron-rich systems.

Re-visit N/Z Ratio of Free Nucleons from Collisions of Neutron-Rich Nuclei as a Probe of EoS of Asymmetric Nuclear Matter**The project supported by National Natural Science Foundation of China under Grant Nos. 10175093 and 10235030, the Science Foundation of Chinese Nuclear Industry and the State Key Basic Research Development Program under Contract No. G20000774, the Knowledge Innovation Project of the

The N/Z ratio of free nucleons from collisions of neutron-rich nuclei as a function of their momentum is studied by means of isospin-dependent Quantum Molecular Dynamics. We find that this ratio is not only sensitive to the form of the density dependence of the symmetry potential energy but also its strength determined by the symmetry energy coefficient. The uncertainties about the symmetry energy coefficient influence the accuracy of probing the density dependence of the symmetry energy by means of the N/Z ratio of free nucleons of neutron-rich nuclei.

Exploring binding energy and separation energy dependences of HBT strength

Hanbury Brown–Twiss (HBT) results of the nucleon–nucleon correlation function have been presented for the nuclear reactions with neutron-rich projectiles (Be isotopes) using an event-generator, the Isospin-Dependent Quantum Molecular Dynamics model. We explore that the relationship between the binding energy per nucleon of the projectiles and the strength of the neutron–proton HBT at small relative momentum. Moreover, we reveal the relationship between the single neutron separation energy and the strength of the halo neutron–proton HBT. Results show that neutron–proton HBT results are sensitive to binding energy or separation energy.

Dependences of isospin fractionation degree on the mass and beam energy of a colliding system

Based on the isospindependent quantum molecular dynamics model, we have invest igated the dependences of isospin fractionation degree (N/Z)n/(N/Z)fragon the mass and the beam energy of colliding system. The (N/Z)n a nd (N/Z)frag are the neutron proton ratio of the nucleon emission (gas-phase) and that of the fragment emission (liquid phase) respectively. The isosp in fractionation degree is a sensitive func tion to the mass and beam energy of the colliding system. The (N/Z)n/(N/Z)frag reduces with increasing mass of the colliding system when the beam energy and n eutron proton ratio of the colliding system are fixed. This is due to the larg er compr ession, small heating energy and larger critical temperature of the gasliquid phase transition for the heavy colliding system, compared to those of the light colliding system. We also found that (N/Z)n/(N/Z)frag enhances wit h increasing beam energy due to the increase of excitation energy of the collidi ng system which leads to larger nucleon transport and isospin fractionation. But the isospin frac tionation only occurr in the energy region for producing the liquidgas phase t r ansition. In this case, we propose that (N/Z)n/(N/Z)frag can be directly compa red with the experimental data to get the information about symmetry potential.

Isospin fractionation in the nucleon emissions and fragment emissions in the intermediate energy heavy ion collisions

The degree of isospin fractionation is measured by ( N/ Z) n /( N/ Z) N imf , where ( N/ Z) n and ( N/ Z) N imf are the saturated neutron–proton ratio of nucleon emissions (gas phase) and that of fragment emissions (liquid phase) in heavy ion collision at intermediate energy. The calculated results by using the isospin-dependent quantum molecular dynamics model show that the degree of isospin fractionation is sensitive to the neutron–proton ratio of colliding system but insensitive to the difference between the neutron–proton ratio of target and that of projectile. In particular, the degree of isospin fractionation sensitively depends on the symmetry potential. However, its dependences on the isospin dependent in-medium nucleon–nucleon cross section and momentum dependent interaction are rather weak. The nucleon emission (gas phase) mainly determines the dynamical behavior of the degree of isospin fractionation in the isospin fractionation process, compared to the effect of fragment emission. In this case, we propose that ( N/ Z) n /( N/ Z) N imf or ( N/ Z) n can be directly compared with the experimental data so that the information about symmetry potential can be obtained.

Medium Influence of the Nucleon-Nucleon Cross Section on theFragmentation

Based on an isospin-dependent quantum molecular dynamics model westudied the influence of a medium correction of an isospin-dependentnucleon-nucleon cross section on the fragmentation at the intermediateenergy heavy-ion collisions. We found that the medium correction froman isospin-dependent nucleon-nucleon cross section increases thedependence of the fragmentation on the isospin effect of in-mediumnucleon-nucleon cross section, at the same time, the momentum-dependentinteraction also produces an important role for enhancing theinfluence of the medium correction on the isospin effect of two-bodycollisions in the fragmentation process.

Influence of a momentum dependent interaction on the isospin dependence of fragmentation and dissipation in intermediate energy heavy ion collisions

We studied the influence of a momentum dependent interaction in the context of isopspin effects on fragmentation and dissipation in intermediate energy heavy ion collisions by using an isospin dependent quantum molecular dynamics model. It is shown that the nuclear stopping, the number of nucleons emitted ,and the multiplicity of intermediate mass fragments are larger with a momentum dependent interaction than without. In particular, the differences for these observables, when using an isospin dependent in-medium nucleon nucleon cross section versus an isospin independent one, are also larger at high energies for a momentum dependent interaction than without one. Therefore,momentum dependence enhances the sensitivities of those observables to the isospin effect of the in-medium nucleon nucleon cross section towards high beam energies

Total Reaction Cross Section in an Isospin-Dependent QuantumMolecular Dynamics Model

The isospin-dependent quantum molecular dynamics (IDQMD) model is usedto study the total reaction cross section σR. Theenergy-dependent Pauli volumes of neutrons and protons have beendiscussed and introduced into the IDQMD calculation to replace thewidely used energy-independent Pauli volumes. The modified IDQMDcalculation can reproduce the experimental σR well for bothstable and exotic nuclei induced reactions. Comparisons of thecalculated σR induced by 11Li with different initialdensity distributions have been performed. It is shown that thecalculation by using the experimentally deduced density distributionwith a long tail can fit the experimental excitation function betterthan that by using the Skyrme-Hartree-Fock calculated density withoutlong tails. It is also found that σR at high energy is sensitiveto the long tail of density distribution.

Directed and elliptic flows in heavy ion collisions at intermediate energies

A theoretical investigation of directed and elliptic flows for different light particles and fragments in collisions of 40Ca + 40Ca and 112Sn + 112Sn is conducted below 100 MeV/nucleon in the isospin-dependent quantum molecular dynamics model. With increasing incident energy, the directed flow rises from negative to positive, while the elliptic flow decreases with the increasing incident energies. The directed flow for 40Ca + 40Ca system is not sensitive to the nuclear equation of states (EOS), but the directed flow for 112Sn + 112Sn system is sensitive to the EOS. However, the elliptic flows for both 40Ca + 40Ca and 112Sn + 112Sn systems are not sensitive to EOS. A study of the dependence of directed and elliptic flows on fragment charge (mass) is also performed. The information on EOS can be extracted by investigating the directed flow at intermediate energies when the combined mass is large or small.