Impact Parameter Dependence of the Double Neutron/Proton Ratio of Nucleon Emissions in Isotopic Reaction Systems

Within the transport model IBUU04, we investigate the double neutron/proton ratio of free nucleons taken from two reaction systems using two Sn isotopes at a beam energy of 50 MeV/nucleon and with impact parameters 2fm, 4fm and 8fm, respectively. It is found that the double neutron/proton ratio from peripheral collisions is more sensitive to the density dependence of the symmetry energy than those from mid-central and central collisions.     

Double neutron/proton ratio of nucleon emissions in isotopic reaction systems as a robust probe of nuclear symmetry energy

The double neutron/proton ratio of nucleon emissions taken from two reaction systems using four isotopes of the same element, namely, the neutron/proton ratio in the neutron-rich system over that in the more symmetric system, has the advantage of reducing systematically the influence of the Coulomb force and the normally poor efficiencies of detecting low energy neutrons. The double ratio thus suffers less systematic errors. Within the IBUU04 transport model the double neutron/proton ratio is shown to have about the same sensitivity to the density dependence of nuclear symmetry energy as the single neutron/proton ratio in the neutron-rich system involved. The double neutron/proton ratio is therefore more useful for further constraining the symmetry energy of neutron-rich matter.     

INDRA 能区重离子输运过程的系统研究及对称能探测

基于改进的极端相对论量子分子动力学(UrQMD) 输运模型,通过细致考察初始化、状态方程及两体碰撞等系统研究了INDRA 能区重离子碰撞后出射的自由核子及轻粒子的集体流和核阻止本领等观测量。研究发现,一个采用带动量依赖的软的状态方程及动量修正的密度依赖的核子核子弹性散射截面的动力学输运过程能够很好描述INDRA 全能域内实验获得的中心快度区的氢同位素的直接流。利用该套输运系统还研究了直接流平衡能对对称势能密度依赖强度因子的敏感性。发现,出射的自由中子平衡能敏感依赖于对称势能的密度依赖,而自由质子却不会。同时还发现,利用两Sn 同位素系列反应出射的自由中子直接流的平衡能与初始中子/质子比的关系可以很好地探测对称能的密度依赖。The terms of initialization, equation of state (EoS), and two-body collision in the updated ultrarelativistic quantum molecular dynamics (UrQMD) model are examined in details so as to systematically study the collective flows and the nuclear stopping of free nucleons and light clusters from heavy-ion collisions at INDRA energies. It is seen that at INDRA energies the dynamic transport with a soft EoS with momentum dependence and with the momentum-modified density-dependent nucleon-nucleon elastic cross sections describes the directed flow exhibited by hydrogen isotopes (Z= 1) emitted at midrapidity fairly well. The sensitivity of the balance energy (Ebal) of the directed flow to the strength parameter of the density dependence of symmetry potential energy is further studied with the same parameter set. It is found that the Ebal of neutrons from HICs is particularly sensitive to the density dependence of the symmetry potential energy, while that of protons is not. And, the initial neutron/proton ratio dependence of the balance energy of neutrons from Sn isotopes can be taken as a useful probe to constrain the stiffness of the nuclear symmetry energy.     

Neutron Skin Thickness of Nuclei and Effective Nucleon-Nucleon Interactions

The Skyrme energy density functional is applied to study the ground state properties of a series of finite nuclei. The charge rms radii, neutron rms radii, and the neutron skin thickness for some nuclei are calculated and compared with the experimental data. The constraint on the effective interactions, especially, the density dependence of the isospin-dependent. part of Skyrme interactions is extracted by the data of neutron skin thicknesses of ^208Pb and isotopes of Sn.     

Nuclear symmetry energy effects in finite nuclei and neutron star

Within a relativistic mean-field model with nonlinear isoscalar–isovector coupling, we explore the possibility of constraining the density dependence of nuclear symmetry energy from a systematic study of the neutron skin thickness of finite nuclei and neutron star properties. We find the present skin data supports a rather stiff symmetry energy at subsaturation densities that corresponds to a soft symmetry energy at supranormal densities. Correlation between the skin of ²⁰⁸Pb and the neutron star masses and radii with kaon condensation has been studied. We find that ²⁰⁸Pb skin estimate suggest star radii that reveals considerable model dependence. Thus precise measurements of neutron star radii in conjunction with skin thickness of heavy nuclei could provide significant constraint on the density dependence of symmetry energy.     

Probing the nuclear symmetry energy with heavy-ion reactions induced by neutron-rich nuclei

Heavy-ion reactions induced by neutron-rich nuclei provide a unique means to investigate the equation of state of isospin-asymmetric nuclear matter, especially the density dependence of the nuclear symmetry energy. In particular, recent analyses of the isospin diffusion data in heavy-ion reactions have already put a stringent constraint on the nuclear symmetry energy around the nuclear matter saturation density. We review this exciting result and discuss its implications on nuclear effective interactions and the neutron skin thickness of heavy nuclei. In addition, we also review the theoretical progress on probing the high density behaviors of the nuclear symmetry energy in heavy-ion reactions induced by high energy radioactive beams.      

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.     

低SIS能区重离子碰撞过程的系统性研究

在极端相对论量子分子动力学(UrQMD)模型中加入势能密度泛函形式的势修正、核子-核子弹性散射截面的更细致的介质修正以及碎片重构模式中的同位旋效应后,重点研究低SIS能区(约40～400 MeV/u)重离子碰撞的动力学过程。在较系统地研究此能区重离子碰撞后的轻碎片产生及集体流后,重点研究对高密区对称能密度依赖敏感的观测量。发现:(1)质量对称的Sn系列同位素反应系统,其中子平衡能的系统N/Z分布能敏感探测对称能密度依赖;(2)横速度/动量分布的中子和质子及氢同位素的椭圆流比vn2/vp,H2敏感依赖于对称能。经采用多组核物质标量不可压缩系数K0值差别很小、对称能斜率参数L值相差较大的Skyrme势参数计算并对FOPI/LAND相应数据做χ2分析后抽取的L值为(89±45)MeV。     

Ground-state properties of light kaonic nuclei signaling symmetry energy at high densities

A sensitive correlation between the ground-state properties of light kaonic nuclei and the symmetry energy at high densities is constructed under the framework of relativistic mean-field theory. Taking oxygen isotopes as an example, we see that a high-density core is produced in kaonic oxygen nuclei, due to the strongly attractive antikaonnucleon interaction. It is found that the 1 S_(1/2) state energy in the high-density core of kaonic nuclei can directly probe the variation of the symmetry energy at supranormal nuclear density, and a sensitive correlation between the neutron skin thickness and the symmetry energy at supranormal density is established directly. Meanwhile, the sensitivity of the neutron skin thickness to the low-density slope of the symmetry energy is greatly increased in the corresponding kaonic nuclei. These sensitive relationships are established upon the fact that the isovector potential in the central region of kaonic nuclei becomes very sensitive to the variation of the symmetry energy. These findings might provide another perspective to constrain high-density symmetry energy, and await experimental verification in the future.     

Probing the structure of exotic nuclei by transfer reactions

Low energy single nucleon transfer reactions are proposed as a tool to investigate the structure of nuclei far off stability. Experimental concepts and conditions are discussed, in particular high resolution γ-ray spectroscopy after single nucleon pickup reactions. Nuclear structure is described by Skyrme Hartree-Fock calculations including pairing. As representative examples, binding energies, radii and wave functions for Mg and Sn isotopes are calculated. In the neutron deficient Mg isotopes a proton skin is found. At the neutron driplines the Mg and Sn isotopes develop extended neutron skins. The nuclear structure results are used in DWBA and EFR-DWBA transfer calculations. Single nucleon transfer reactions of ^32,36Mg and exotic Sn beams on targets ranging from ²H to ²⁴Mg in inverse kinematics are explored. The one-nucleon transfer cross sections decrease strongly for high-Z targets. An impact parameter analysis shows that the transfer process is selective on the tails of the wave functions. The largest cross sections are obtained for ²H and ⁹Be targets at incident energies of E _lab = 2-5 MeV/u. The energy-momentum dependence is closely related to the special properties of wave functions of weakly bound states. Two-neutron (p,t) stripping reactions are studied for a ⁶He projectile. A strong competition of sequential and direct processes is found at low energies. Received: 1 October 1997 / Revised version: 25 November 1997     

Effect of entrance-channel asymmetry on the isospin dependence of nucleon emission in heavy ion collisions

Using the isospin- and momentum-dependent hadronic transport model IBUU04, we have in-vestigated the influence of the entrance-channel isospin asymmetry on the sensitivity of the pre-equilibrium neutron/proton ratio to symmetry energy in central heavy-ion collisions induced by high-energy radioactive beams. Our analysis and discussion are based on the dynamical simulations of the three isotopic reaction systems 132Sn+124Sn, 124Sn+112Sn and 112Sn+112Sn which are of the same total proton number but different isospin asymmetry. We find that the kinetic-energy distributions of the pre-equilibrium neutron/proton ratio are quite sensitive to the density-dependence of symmetry energy at incident beam energy E/A = 400 MeV,and the sensitivity increases as the isospin asymmetry of the reaction system increases.     

Symmetry energy and the isoscaling in reactions on enriched tin isotopes

The coefficients of symmetry energy term for fragments with Z = 4, 11, 12 measured in multifragmentation reactions initiated by proton and deuteron with energy of 3.65 A GeV on enriched tin isotopes ^{112,118,120,124}Sn are determined. The dependence of isoscaling parameter on the excitation energy, the temperature of fragmenting systems and the density ratio for heavy mass products are analyzed.     

Effect of entrance-channel asymmetry on the isospin dependence of nucleon emission in heavy ion collisions

Using the isospin- and momentum-dependent hadronic transport model IBUU04, we have investigated the influence of the entrance-channel isospin asymmetry on the sensitivity of the pre-equilibrium neutron/proton ratio to symmetry energy in central heavy-ion collisions induced by high-energy radioactive beams. Our analysis and discussion are based on the dynamical simulations of the three     

质子椭圆流与对称能的密度依赖性

基于同位旋和动量依赖的强子输运IBUU04模型, 研究了¹³²Sn+¹²⁴Sn碰撞系统中的质子椭圆流对对称能的敏感关系. 研究发现入射能量从每核子400MeV到800MeV时质子椭圆流在低横动量端对对称能的敏感性高于高横动量端, 同时发现随着入射能量的增大, 质子椭圆流对对称能的敏感性在降低. 在研究入射能量范围内, 当入射能量为每核子400MeV左右时质子椭圆流对对称能最为敏感.     

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.     

A possible experimental observable for the determination of neutron skin thickness

The dependence between neutron skin thickness and neutron abrasion cross section （σnabr） for neutron-rich nuclei is investigated within the framework of the statistical abrasion ablation model. Assuming that the density distributions for proton and neutron are of Fermi-type, and adjusting the diffuseness parameter of neutron density distribution in the droplet model, we find out the good linear correlation between the neutron skin thickness and the abrasion cross section σnabr for neutron-rich nuclei. The uncertainty of neutron skin thickness determined from σnabr is very small. It is suggested that σnabr can be used as a new experimental observable to extract the neutron skin thickness for neutronrich nucleus. The scaling behaviours between neutron skin thickness and σnabr, separately, for isotopes of ^26-35Na, ^44-56Ar, ^48-60Ca, ^67-78Ni are also investigated.     

Ground-State Properties of Ca Isotopes and the Density Dependence of the Symmetry Energy

A relativistic mean field model is used to study the ground-state properties of neutron-rich nuclei in Ca isotopes. An additional isoscalar and isovector nonlinear coupling has been introduced in the relativistic mean field model, which could soften the symmetry energy, while keep the agreement with the experimental data. The sensitivity of proton and neutron density distributions and single particle states in Ca isotopes to the additional isoscalarisovector nonlinear coupling term is investigated. We found that the binding energies, the density distributions of single particle levels are strongly correlated with the density dependence of the symmetric energy in nuclear matter.     

核物质的对称能与中子皮厚度(英文)

在现有的平均场模型中引入同位旋相关的高阶修正项．研究了核物质对称能的密度依赖性和。^208Pb的中子皮厚度。采用新提出的PK1相互作用以及NL3．S271和Z271相互作用．得到核物质饱和点对称能的范围为29-38MeV以及相应的^208Pb中子皮厚度为0．17—0.28fm．在所有相互作用中，核物质饱和点的对称能与^208Pb的中子皮厚度近似呈线性关系。After adding isospin dependent high order correction terms to existing relativistic mean field models (RMF), the density dependence of symmetry energy and the neutron skin thickness S for 208Pb are studied. Using the new effective interaction PK1, together with NL3, S271 and Z271, a range of 29—38 MeV for the symmetry energy for nuclear matter at saturation point and the corresponding neutron skin thickness S = 0.14—0.28 fm for 208Pb are obtained. For all effective interactions, a linear relation between the symmetry energy at saturation point and the neutron skin thickness for 208Pb is observed.