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.     

Multi-nucleon transfer reactions and fusion with unstable nuclei

We show that a large number of neutrons are expected to be transferred from the projectile to the target if a neutron rich unstable nucleus with a neutron skin is used as the projectile in heavy-ion collisions at energies about twice the Coulomb barrier. We then show that though the neutron halo enhances the fusion cross section through the size effect, the additional effect due to the molecular bond formation is not significant in the fusion between ¹¹Li and ⁹Li at energies near and below the Coulomb barrier.     

Neutron excess in analytical expressions for fusion barrier parameters

The neutron excess dependence of heavy-ion fusion barriers is investigated, guided by predictions of different ion-ion potentials. We develop phenomenological expressions for the fusion barrier radii and heights, involving both the entrance channel mass asymmetry and neutron excess of the projectile and target. Compared to commonly used formulas, the developed expressions reproduce theoretical barrier parameters with a higher accuracy. Furthermore, they provide a means to assess the importance of the neutron excess degree of freedom implied by each potential.Received: 1 April 2003, Revised: 31 January 2004, Published online: 10 August 2004PACS: 24.10.-i Nuclear reaction models and methods - 25.70.-z Low and intermediate energy heavy-ion reactions - 25.70.Jj Fusion and fusion-fission reactions - 25.60.Pj Fusion reactions     

Octupole Deformations of Even-Even Rn,Th, and U Nuclei in Relativistic Mean Field Theory

The octupole deformations and other ground state properties of even-even Rn, Th and U isotopes are investigated systematically within the framework of the reflection asymmetric relativistic mean field （RAS-RMF） model. The calculation results reproduce the binding energies and the quadrupole deformations well. The calculation results indicate these nuclei at ground states evolve from neaxly-spherical （N = 130） shape to quadrupole deformation shape with the increase of the neutron number. It is also found that among the Rn isotopes, only^222,224 Rn axe oetupole deformed and the octupole deformations for them are small. However, more nuclei （N ≌ 134 148） in Th and U isotopes are octupole deformed and the octupole deformations for some of them are significant （｜β3｜- 0.1 or even larger）.     

Heavy-ion fusion at low energies

Through precision measurements of fusion cross sections at energies close to the Coulomb barrier and through the application of the method of “experimental barrier distributions” which these permit, many recent advances have been made in our understanding of the dynamical processes occurring during a heavy-ion collision. It is now clear that the target and projectile reach one another in superpositions of states which correspond to different orientations for rotational nuclei or to different induced deformations for vibrational nuclei. The creation of a neck of neutron matter has also long been postulated and by studying the isotopic dependence of the fusion reaction, some recent results in the ¹⁰Ca+^90,96Zr systems appear to confirm this result. For large Z ₁ Z ₂ a type of extra-push effect can arise from the same inelastic entrance-channel effects which enhance the fusion of lighter systems, though this will be absent in cases where the enhancement arises from neutron transfers. The existence of different barriers will of course influence all other reaction channels. Fusion simply allows one to visualise the barriers most easily, since for this process, the total cross section is an incoherent sum of the contributions from all relevant eigenchannels. Some effects in other channels have already been observed. Other possible effects will be discussed. These include; the exploitation of the lowest-energy barrier to produce exotic evaporation residues and strongly deformed high-spin states at low excitation energy.     

Heavy-ion fusion: Comparison of experimental data with classical trajectory models

Currently available data on fusion excitation functions for heavy-ion induced reactions over a wide mass range are compared to results calculated with a classical dynamical model based on the proximity nuclear potential of Blocki et al., the Coulomb potential of Bondorf et al., and one-body nuclear friction in the proximity formalism of Randrup. With these conservative and dissipative forces and the radial parameters of Myers, overall good agreement is obtained between the theoretical excitation functions and most of the available data. Extensive calculations have been performed to test the sensitivity of the calculated fusion cross-sections to a number of parameters, including the radial dependence of the Coulomb and nuclear potentials, the radial and tangential friction form factors as well as the projectile and target radii. The theoretical excitation functions for the lighter heavy-ion systems are rather insensitive to changes in either the conservative or dissipative forces. The calculations show that tangential friction sufficient to produce the rolling condition is necessary to explain the magnitude of the fusion cross-sections at high energies, which are also sensitive to the magnitude of the radial friction component. This is in contrast to the fusion cross-sections at low energies which are determined by the nuclear potential at larger separations, and to a lesser extent by tangential friction. The low energy fusion data are most sensitive to the nuclear radii. The calculations reveal the importance of more experimental measurements of fusion cross-sections at high energies, especially for heavy systems where the magnitudes of the fusion cross-sections are the most sensitive to the assumed forces. However, even for these cases the effects of the conservative and dissipative forces are similar and difficult to separate. These studies indicate, however, that it is possible to construct a conservative potential that will give calculated fusion excitation functions which are in good agreement with all experimental data over the entire mass range. The maximum fusion cross-sections as defined here exceed considerably the liquid-drop limiting value for heavy systems.     

QMD模型的改进及其在低能重离子反应中的应用

丰中子核以及重核熔合机制的研究以及中能重离子碰撞中多重碎裂的研究都迫切需要一个统一的、自洽的微观动力学模型.经过对量子分子动力学模型进行根本的改进,发展了一个新的、适用于低能以及中能重离子反应的统一描述的微观动力学模型.改进的量子分子动力学(ImQMD)模型能够将整个熔合反应过程中的动力学效应、同位旋效应以及弹靶质量不对称效应等比较全面地、自洽地考虑进来,从而给熔合反应的研究提供了一个新的途径.ImQMD模型能够很好地再现一系列核的基态性质以及10多个熔合反应的激发函数(包括丰中子核熔合体系以及实验最新测量的132Sn+64Ni熔合体系).此外还运用该模型初步探索了重核熔合过程中复合体系的寿命与体系的入射能量、体系大小以及体系的中子质子比的依赖关系. We have developed a new microscopic dynamical model called improved quantum molecular dynamical model (ImQMD). This model can describe the fusion process at energies near the Coulomb barrier as well as the multifragmentation process at intermediate energies in heavy-ion collision (HIC) uniformly. By using this model, fusion cross sections (including some of neutron-rich nuclei reactions and that of newly measured~(132)Sn+~(64)Ni fusion reaction) of tens reactions can be reproduced remarkably well. In fusi...     

Dynamical calculations of the cross section for heavy-ion fusion with allowance for tunneling

The surface-friction model was proposed for describing reactions induced by deep-inelastic heavy-ion interactions. Its use in describing heavy-ion fusion was restricted to the case of energies above the fusion barrier. An attempt is made here to extend the use of the model to subbarrier energies via the inclusion of the tunneling effect. A method for taking into account the tunneling effect in dynamical calculations on the basis of Langevin’s equations is proposed. It is shown that, at energies in the barrier region and at high angular momenta, this effect leads to an increase in the cross section for touching of ions.     

Analysis of autoionization resonances in the Hg 6s 2-photoionization by measurements of photoelectron polarization

It is shown that nuclear target fragmentation in proton and heavy ion induced reactions, in particular the following experimental facts concerning the mass-yield distribution can be understood in terms of a semiclassical model:(i) its independence on the mass of the projectile at approximately the same incident energies,(ii) its trend of approaching a limit at higher bombarding energies,(iii) its “U-formed” shape at sufficiently high bombarding energies. Standard methods in statistical theory of chemical equilibrium are used to calculate the mass-yield distribution for medium and heavy target nuclei in high-energy nuclear reactions where the Coulomb interaction between the fragments is taken into account selfconsistently. The result shows: The fact that the decaying rest target nucleus and its fragments are bounded objects of finite size and finite charge have significant influences, especially on the form of the mass-yield distributions.     

Ground state properties of La isotopes in reflection asymmetric relativistic mean field theory

The ground state properties of La isotopes are investigated with the reflection asymmetric relativistic mean field(RAS-RMF) model.The calculation results of binding energies and the quadrupole moments are in good agreements with the experiment.The calculation results indicate the change of the quadrupole deformation with the nuclear mass number.The "kink" on the isotope shifts is observed at A = 139 where the neutron number is the magic number N = 82.It is also found that the octupole deformations may exist...     

Preequilibrium proton and α emission from neutron induced reactions in CsI

Angle integrated energy spectra of protons (plus deuterons) andα particles have been obtained from neutron bombardment of a CsI crystal serving both as detector and target. Measurements were performed for neutron energies between 14 and 32 MeV. An explanation of proton andα yields cannot be given by statistical evaporation, but requires the assumption of a preequilibrium mechanism dominating for projectile energies in excess of 20 MeV. For these neutron energies the hard components of the proton andα particle spectra can be described quantitatively with the hybrid and the quasi free scattering preequilibrium model, respectively.     

Systematics of the power law parameter and minimum angular momenta for fragment production

The element yield distributionsσ(Z) of intermediate mass fragments from proton, helium, and heavy-ion induced reactions exhibit a universal behaviour as a function of the bombarding energy. The power law parameterτ, obtained from fits withσ(Z)∝σ ^-τ, falls monotonically with increasing projectile energy E_lab and reaches a saturation valueτ?2.0 atE _lab?2GeV. It is suggested that the behaviour at low bombarding energies is caused by a dynamical hindrance of the fragment emission at low angular momentum.     

Production mechanism of neutron-rich nuclei around N =126 in the multi-nucleon transfer reaction ~(132)Sn+~(208)Pb

The time-dependent Hartree-Fock approach in three dimensions is employed to study the multi-nucleon transfer reaction~(132) Sn +~(208) Pb at various incident energies above the Coulomb barrier. Probabilities for different transfer channels are calculated by using the particle-number projection method. The results indicate that neutron stripping(transfer from the projectile to the target) and proton pick-up(transfer from the target to the projectile)are favored. De-excitation of the primary fragments is treated by using the state-of-art statistical code GEMINI++.Primary and final production cross sections of the target-like fragments(with Z =77 to Z =87) are investigated. The results reveal that fission decay of heavy nuclei plays an important role in the de-excitation process of nuclei with Z 82. It is also found that the final production cross sections of neutron-rich nuclei depend only slightly on the incident energy, while those of neutron-deficient nuclei depend strongly on the incident energy.     

Experimental investigation of charge-exchange processes involving a target proton in <Superscript>16</Superscript>O<Emphasis Type="Italic">p</Emphasis> collisions at a momentum of 3.25 GeV/<Emphasis Type="Italic">c</Emphasis> per nucleon

For the first time, charge-exchange processes involving a target proton in ¹⁶Op collisions at a momentum of 3.25 GeV/c per nucleon are studied under conditions of 4π geometry. New data on the mean multiplicities fragments and pions, as well as on inelastic cross sections for topological channels of the fragmentation of an oxygen nucleus in charge-exchange reactions involving a target proton that either are accompanied or are not accompanied by charge transfer to a projectile nucleus, are presented. It is shown that, in ¹⁶Op interactions at high energies, charge transfer from a target proton to a projectile nucleus proceeds predominantly via inelastic proton scattering on a neutron of the oxygen nucleus.     

Simple estimates for Fermi jets

The phenomenon of Fermi jets is investigated in the approximation of two colliding potential wells filled with degenerate Fermi gases of nucleons. A model is formulated which largely bypasses the explicit treatment of the relative motion of the nuclei, assumed to be governed by the window friction mechanism. Formulae for the velocity distributions and differential cross sections for neutrons and protons jetting through either target or projectile are derived. The numerical results are investigated systematically over a wide range of nuclear reactions. It is shown that the net linear momentum carried away by Fermi jets accounts for only a rather minor fraction of the observed missing momentum in typical heavy-ion fusion reactions.     

Relating breakup and incomplete fusion of weakly bound nuclei through a classical trajectory model with stochastic breakup

A classical dynamical model that treats breakup stochastically is presented for low energy reactions of weakly bound nuclei. The three-dimensional model allows a consistent calculation of breakup, incomplete, and complete fusion cross sections. The model is assessed by comparing the breakup observables with continuum discretized coupled-channel quantum mechanical predictions, which are found to be in reasonable agreement. Through the model, it is demonstrated that the breakup probability of the projectile as a function of its distance from the target is of primary importance for understanding complete and incomplete fusion at energies near the Coulomb barrier.     

Special features of nuclear reactions induced by loosely bound <Superscript>6</Superscript>He and <Superscript>6,7</Superscript>Li nuclei in the vicinity of the Coulomb barrier height

Excitation functions are measured for complete-fusion and transfer reactions induced by the interaction of ⁶He and ⁶Li with ²⁰⁶Pb, ²⁰⁹Bi, and Pt. Data obtained for fusion reactions induced by ⁶He ions deviate from the predictions of the statistical model of compound-nucleus decay at projectile energies in the vicinity of the Coulomb barrier height. A strong enhancement of cross sections for fusion reactions induced by the interaction of ⁶He with target nuclei is observed. The cross sections for reactions of cluster transfer, neutron transfer from ⁶He, and deuteron transfer from ⁶Li at deep-subbarrier energies are also found to be enhanced. These results are discussed from the point of view of the effect of the cluster structure of nuclei on the interaction probability at energies in the vicinity of the Coulomb barrier height.     

超重核合成时的驱动势与热熔合反应截面

在双核模型框架下,双核系统生成超重复合核的机理是由双核中的弹核的核子全部转移到靶核产生的,而核子转移是由双核系统驱动势确定的.对有的反应道,核子转移与中质比变化路径之间有比较复杂的关系.原则上动力学方程与驱动势都应该是中子和质子的二维显函数.为处理方便,采用与中质比相关的核子转移路径的选择来取驱动势,得到了接近实验值的超重核合成蒸发剩余截面. 关键词： 超重核 熔合反应 驱动势 激发函数     

Dynamical fluctuations in fragmentation reactions in a Boltzmann–Langevin approach

Based on the isospin-dependent Boltzmann–Langevin model, the dynamical fluctuations in the fragmentation reaction of ¹¹²Sn+¹¹²Sn are investigated. The quadrupole moment and octupole moment with zero magnetic quantum number have large fluctuations in the early time of the collisions. The dynamical fluctuations in momentum space show a strong dependence on the incident energy. The effects of using different fluctuations on the fragment cross sections are also studied in the fragmentation reactions. The results by using Q₂₀ + Q₃₀ fluctuation have a better agreement with the experimental data. Calculations using Q₂₀ + Q₃₀ fluctuation produce more proton-rich and neutron-rich nuclei than those using Q₂₀ fluctuation only. Besides, the difference between the production cross sections of fragments calculated by using Q₂₀ and Q₂₀ + Q₃₀ fluctuations is larger in the vicinity of the projectile. These results present that the dynamical fluctuations may affect the whole dynamical process of fragmentation reactions including the production of fragments, due to the nonlinear nature of the Boltzmann–Langevin equation.