Impact of density-dependent symmetry energy and Coulomb interactions on the evolution of intermediate mass fragments

Within the framework of isospin-dependent quantum molecular dynamics (IQMD) model, we demonstrate the evolution of intermediate mass fragments in heavy-ion collisions. In this paper, we study the time evolution, impact parameter, and excitation energy dependence of IMF production for the different forms of density-dependent symmetry energy. The IMF production and charge distribution show a minor but considerable sensitivity towards various forms of density-dependent symmetry energy. The Coulomb interactions affect the IMF production significantly at peripheral collisions. The IMF production increases with the stiffness of symmetry energy.     

Effects of density-and momentum-dependent potentials in Au+Au collisions at intermediate energies

Based on an isospin-dependent transport model, the effects of the density-and momentum-dependent potentials are studied by simulating Au on Au collisions at 90, 120, 150 and 400 MeV/nucleon. It is found that the calculated results overestimate the experimental data on the directed flow and underestimate the data on the elliptic flow for protons. The impact of the density-and momentum-dependent potentials is observed in the mid-rapidity region of the final spectra. At 90 MeV/nucleon, the momentum-dependent potential has a larger impact on the observables than the density-dependent potential, and the elliptic flow has a higher value with the positive effective mass splitting. At 400 MeV/nucleon, however, the opposite is observed. The rapidity dependence of the elliptic flow for protons is sensitive to the symmetry energy. A soft symmetry energy corresponds to a higher value of the proton elliptic flow.     

Optimizing the rapidity limit for nuclear stopping in intermediate energy heavy-ion collisions

A systematic study regarding the role of participant matter and spectator matter in nuclear stopping using isospin-dependent quantum molecular dynamics model is presented. The simulations have been carried out with soft equation of state along with the reduced isospin-dependent cross section to study the effect of different types and sizes of rapidity distributions on nuclear stopping for the whole colliding geometry with density-dependent symmetry energy. In addition to that, we attempt to investigate the role of isospin in heavy-ion collisions by calculating the individual contribution of neutrons and protons in nuclear stopping for different systems having different isotopic content.     

Analyzing fragment production in mass-asymmetric reactions as a function of density dependent part of symmetry energy

We performed a theoretical investigation of different mass-asymmetric reactions to access the direct impact of the density-dependent part of symmetry energy on multifragmentation. The simulations are performed for a specific set of reactions having same system mass and N/Z content, using isospin-dependent quantum molecular dynamics model to estimate the quantitative dependence of fragment production on themass-asymmetry factor (τ) for various symmetry energy forms. The dynamics associated with different mass-asymmetric reactions is explored and the direct role of symmetry energy is checked. Also a comparison with the experimental data (asymmetric reaction) is presented for a different equation of states (symmetry energy forms).     

Assessment of multifragmentation under the effect of symmetry energy

We study the effect of symmetry energy on the fragment production for the reactions ₂₀ ¹⁰ Ne₁₀+ ₂₀ ¹⁰ Ne₁₀ and ₁₉₇ ⁷⁹ Au₁₁₈ + ₁₉₇ ⁷⁹ Au₁₁₈ for the incident energy range of 50–1000 MeV/nucleon using isospin-dependent quantum molecular dynamics (IQMD) model. Our study shows that the density-dependent symmetry energy plays a significant role in multiplicity of fragments produced at low energy. Moreover, sensitivity of density-dependent symmetry energy decreases with increase in neutron content of colliding system. We also compare the symmetry energy suggested by different groups. A comparative study of experimental results with theoretical calculations of IQMD shows that the density-dependent symmetry energy is a good probe to explain the multiplicity of the fragments at low energy.     

Rapidity distribution as a probe for elliptical flow at intermediate energies

The interplay between spectator and participant matter in heavy-ion collisions is investigated within the isospin-dependent quantum molecular dynamics (IQMD) model in terms of the rapidity distribution of light charged particles. The effect of different types and sizes of rapidity distributions is studied in elliptical flow. The elliptical-flow patterns show the important role of nearby spectator matter on the participant zone. This role is further explained on the basis of the passing time of the spectator and the expansion time of the participant zone. The transition from in-plane to out-of-plane emission is observed only when the mid-rapidity region is included into the rapidity bin. Otherwise no transition occurs. The transition energy is found to be highly sensitive to the size of the rapidity bin, while it is only weakly dependent on the type of the rapidity distribution. These theoretical findings are found to be in agreement with experimental results.     

Radial Expansion Flow in Reactions of 40Ca+58Fe and 40Ca+58Ni

By means of using an isospin-dependent Boltzmann-Langevin equation which includes isospin-dependent symmetry energy, Coulomb energy, isospin-dependent nucleon-nucleon cross sections, Pauli blocking, and initialization, the radial expansion flow of reaction systems ⁴⁰Ca+⁵⁸Ni and ⁴⁰Ca+⁵⁸Fe at 53, 100, 150, and 200 MeV/u in the central collisions were studied. It has shown that the more neutron rich system exhibits smaller radial expansion flow. It was found that the neutron rich system had smaller threshold energy which may provide a new method to determine the isospin dependent nuclear equation of state from calculated result and linear fitting result.     

Probing the high density behavior of the nuclear symmetry energy with high energy heavy-ion collisions

High energy heavy-ion collisions are proposed as a novel means to constrain stringently the high density (HD) behavior of nuclear symmetry energy. Within an isospin-dependent hadronic transport model, it is shown for the first time that the isospin asymmetry of the HD nuclear matter formed in high energy heavy-ion collisions is uniquely determined by the HD behavior of the nuclear symmetry energy. Experimental signatures in two sensitive probes, i.e., pi(-) to pi(+) ratio and neutron-proton differential collective flow, are also investigated.     

中能重离子碰撞中集体流的同位旋效应

在同位旋相关的量子分子动力学模型的基础上,利用Skyrme–Hartree–Fock计算所得的中子、质子密度,同时利用费米气体模型得到相应的中子、质子费米面,抽样出稳定的⁵⁸Fe和⁵⁸Ni初始核.仔细研究了55MeV/u ⁵⁸Fe+⁵⁸Fe和55MeV/u⁵⁸Ni+⁵⁸Ni两个反应中集体流的同位旋效应.在不同碰撞参数下对不同类型的碎块,观察到丰中子反应系统⁵⁸Fe+⁵⁸Fe比⁵⁸Ni+⁵⁸Ni有更强的集体流,并能与实验结果定性符合.同时,研究了同位旋相关的对称能与核子–核子碰撞截面对集体流的影响.     

Covariance analysis of an isospin-dependent probe

Based on a modified quantum molecular dynamics model,we calculate the neutron-proton ratio and the nuclear stopping of reaction systems with different symmetry potentials and collision cross sections.We perform correlations of several probes using the covariance data processing method.It is shown that the correlation between the nuclear stopping and the isospin-dependent nucleon-nucleon cross sections is strong,but the nuclear stopping and symmetry potentials have a weak correlation.The correlation between neutron-proton ratio and symmetry potentials in the case of low energy is stronger.The correlation between neutron-proton ratio and isospin-dependent collision cross sections is enhanced with the increase of energy,but remains weak.In addition,the correlations of the emission numbers of the deuteron with the symmetry potentials and collision cross sections at different beam energies are not obvious compared to two prior physical quantities.In this paper,we define a parameter to quantitatively describe the sensitivity of isospin-dependent probes.By analyzing this parameter,one can extract more information about the isospin effects of the physical quantity.     

重离子反应中核子前平衡发射的同位旋效应

考虑了同位旋相关的对称能、库仑能及核子—核子碰撞截面，对反应４０Ａｒ＋４０Ａｒ（Ｅ＝２５ＭｅＶ／ｕ，ｂ＝０）进行了量子分子动力学模拟，讨论了同位旋效应对核子发射的影响．观察到前平衡发射的中子和质子的比率大于反应系统的中质比，发现对称能有利于中子的发射而阻碍质子的发射，而同位旋相关的核子—核子碰撞截面对中子和质子的发射都有利，但似乎更有利于质子的发射。     

Probing Balance Energy Using Momentum- and Isospin-Dependent Potential

Using the momentum- and isospin-dependent Boltmann-Uehling-Uhlenbeck （BUU） model, we investigate the transverse flow and balance energy in two isotopic colliding systems ^48Ca＋^58Fe and ^48Cr＋^58Ni by adopting different symmetry potentials. By comparing the results between the two colliding systems, we find that the difference between the balance energies of two isotopic systems can be considered as a sensitive probe to the density dependence of symmetry energy.     

在相对论平均场框架下研究同位旋依赖的高阶核子-ω-ρ介子耦合(英文)

在相对论平均场的框架下,对208Pb中子皮对新的同位旋依赖的高阶核子-ω-ρ介子耦合项的敏感性进行了研究。计算表明,高阶同位旋依赖的核子-ω-ρ介子耦合能够进一步软化对称能,因而能够在不影响其它基态可观测量的情况下,进一步减小208Pb的中子半径。The sensitivity of the neutron skin thickness S in ^208Pb to the new addition of the high order isospin-dependent nucleon-ω-ρ coupling term in the relativistic mean field model is studied. Calculations show that the high order isospin-dependent nucleon-ω-ρ coupling term can further soften the symmetry energy, and thus further decrease the neutron radius of ^208Pb without affecting other ground-state observables     

On the role of density-dependent symmetry energy and momentum dependent interactions in multi-fragmentation

We study the multi-fragmentation for the different parameterizations of the density dependent symmetry energy using an isospin-dependent quantum molecular dynamics (IQMD) model. We analyze the sensitivity of fragment production towards various forms of the density dependent symmetry energy. The inclusion of momentum dependent interactions (MDI) results in a larger variation of fragment production. We here highlighted the collective response of the MDI and symmetry energy towards the fragmentation of colliding nuclei at intermediate energies.     

Re-visit N/Z Ratio of Free Nucleons from Collisions of Neutron-Rich Nuclei as a Probe of EoS of Asymmetric Nuclear Matter

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.     

基于中能重离子碰撞研究高密对称能

用于描述核物质中子质子单粒子能量之差的对称能，最近20年得到了核物理学界的广泛关注。在饱和核密度附近，对称能的数值及斜率基本得到约束，然而其高密行为至今仍具有很大的不确定性。当前，探测对称能的研究计划正在世界范围内能够提供放射性束流的实验室展开。伴随着对称能相关实验的规划、进行，发展更加先进的同位旋依赖的输运理论模型变得非常必要。我们将核子-核子短程关联及介质中同位旋依赖的重子-重子非弹性散射截面等研究的新进展融入到了同位旋依赖的输运模型里面；探索了新的敏感于高密对称能的可观测量，比如挤出核子的中质比、光子、轻碎片，以及包含奇异隐奇异夸克的介子产生等；提出了高密对称能探测盲点的问题并给出解决办法；对于常见的对称能敏感观测量的模型预言的不确定性进行了彻底细致的研究；提出采用定性观测量，比如高能出射粒子的中质比，将高密对称能进行定性约束；率先提出并研究了对称能敏感观测量的探测密度区间问题，指出对称能敏感观测量的探测密度往往小于核反应最大压缩密度；发现核子-核子短程关联明显削弱观测量的对称能效应；考虑到饱和点处对称能斜率的约束范围，基于输运模型，提出通过探测对称能的曲率来约束高密对称能。除了利用重离子碰撞约束高密对称能之外，人们也可以通过与中子星相关的大量天体观测来间接约束高密对称能。     

Effect of the momentum dependence of nuclear symmetry potential on the transverse and elliptic flows

In the framework of the isospin-dependent Boltzmann-Uehling-Uhlenbeck transport model, the effect of the momentum dependence of nuclear symmetry potential on nuclear transverse and elliptic flows in the neutron-rich reaction ¹³²Sn+¹²⁴Sn at a beam energy of 400MeV/nucleon is studied. We find that the momentum dependence of nuclear symmetry potential affects the rapidity distribution of the free neutron to proton ratio, the neutron and the proton transverse flows as a function of rapidity. The momentum dependence of nuclear symmetry potential affects the neutron-proton differential transverse flow more evidently than the difference of neutron and proton transverse flows as well as the difference of proton and neutron elliptic flows. It is thus better to probe the symmetry energy by using the difference of neutron and proton flows since the momentum dependence of nuclear symmetry potential is still an open question. And it is better to probe the momentum dependence of nuclear symmetry potential by using the neutron-proton differential transverse flow the rapidity distribution of the free neutron to proton ratio.     

Effects of symmetry energy on two-nucleon correlation functions in heavy-ion collisions induced by neutron-rich nuclei

Using an isospin-dependent transport model, we study the effects of nuclear symmetry energy on two-nucleon correlation functions in heavy-ion collisions induced by neutron-rich nuclei. We find that the density dependence of the nuclear symmetry energy affects significantly the nucleon emission times in these collisions, leading to larger values of two-nucleon correlation functions for a symmetry energy that has a stronger density dependence. Two-nucleon correlation functions are thus useful tools for extracting information about the nuclear symmetry energy from heavy-ion collisions.     

Recent progress and new challenges in isospin physics with heavy-ion reactions

The ultimate goal of studying isospin physics via heavy-ion reactions with neutron-rich, stable and/or radioactive nuclei is to explore the isospin dependence of in-medium nuclear effective interactions and the equation of state of neutron-rich nuclear matter, particularly the isospin-dependent term in the equation of state, i.e., the density dependence of the symmetry energy. Because of its great importance for understanding many phenomena in both nuclear physics and astrophysics, the study of the density dependence of the nuclear symmetry energy has been the main focus of the intermediate-energy heavy-ion physics community during the last decade, and significant progress has been achieved both experimentally and theoretically. In particular, a number of phenomena or observables have been identified as sensitive probes to the density dependence of nuclear symmetry energy. Experimental studies have confirmed some of these interesting isospin-dependent effects and allowed us to constrain relatively stringently the symmetry energy at sub-saturation densities. The impact of this constrained density dependence of the symmetry energy on the properties of neutron stars have also been studied, and they were found to be very useful for the astrophysical community. With new opportunities provided by the various radioactive beam facilities being constructed around the world, the study of isospin physics is expected to remain one of the forefront research areas in nuclear physics. In this report, we review the major progress achieved during the last decade in isospin physics with heavy ion reactions and discuss future challenges to the most important issues in this field.     

Entrance-Channel Dependence of Isospin Effects on Double n/p Ratio in HIC

Within the hadronic transport model IBUU04, we investigate the effect of density-dependent symmetry energy on double neutron/proton (n/p) ratio of free nucleons in heavy ion collisions by taking four isotopic Sn+Sn reaction systems. Especially the entrance-channel asymmetry and impact-parameter dependence of the effect of symmetry energy are discussed. It is found that in both central and semi-central collisions the sensitivity of the double n/p ratio to the density-dependent symmetry energy is more pronounced in neutron-richer systems. Our results also indicate clearly that the effect of symmetry energy is stronger in central collisions than that in semi-central collisions.