DESCRIPTIONS OF THE EQUILIBRATION PROCESS OF THE INTRINSIC DEGREES OF FREEDOM AND DISSIPATIVE PROCESS OF THE NUCLEAR COLLECTIVE MOTION

In this paper the Hamiltonian model is used for studying the nuclear dynamics by taking both the one-body and two-body interaction mechanisms into account. On the basis of the Von Neuman equation the coupling between the collective motion and the single particle degrees of freedom is discussed. Thus, the equations obtained are physically transparent and easy for numerical computations. They may be useful for describing the dissipative process of the nuclear collective motion as well as the equilibration process of the intrinsic degrees of freedom.     

One-body dynamics modified by collective fluctuations

We show how the fluctuating part of the residual coupling between collective and intrinsic motion of a dissipative heavy-ion collision induces correlations in either subspace. They lead in general to a transport equation for the collective motion, and to a new term in the equation for the one-body density which describes collisions with the collective fluctuations. The resulting redistribution of the single-particle occupation numbers ρ_α and the evolution of the fluctuations are coupled with each other due to the dependence of the transition rates in the master equation on the fluctuations, and of the transport coefficients on ρ_α. Considering the special case of a long contact phase, we find the fluctuations to be most effective, with respect to a randomization of ρ_α, within a certain critical region where they pass from stable to unstable behaviour. Estimates are made for the corresponding relaxation times employing a schematic model.     

The adiabatic cranking model for large amplitudes

A simple model of slow large scale collective nuclear motion is developed. Starting with the equation for the single-particle density matrix extended by approximate incorporation of particle collisions in the relaxation time approach the classical equation of motion for the collective variables specifying the shape of nuclear surface is derived. The coefficients of equation of motion are related to the microscopic quantities: single-particle energies, occupation numbers, derivatives of s.-p. energies with respect to the deformation parameters. The one- and two-body contributions to the collective mass and friction parameters are discussed.     

Damping of nuclear collective motion in the extended mean-field theory

The dissipation mechanism in slow nuclear collective motion is studied in the frame of the extended mean-field theory. The collective motion is treated explicitly by employing a travelling single-particle representation in the semi-classical approximation. The rate of change of the collective kinetic energy is determined by: (i) one-body dissipation, which reflects uncorrelated particle-hole excitations as a result of the collisions of particles with the mean field, (ii) two-body dissipation, which consists of simultaneous 2 particle-2 hole excitations via direct coupling of the residual two-body interactions, and (iii) potential dissipation due to the redistribution of the single-particle energies as a result of the random two-body collisions. In contrast to the first two processes the potential dissipation exhibits memory effects due to the large values of the local equilibration times.     

A solvable version of the collisional random phase approximation

We derive the markovian limit of the collisional Random Phase Approximation (CRPA) by resort to the linearization of the Collisional Time-Dependent-Hartree-Fock (CTDHF) equation of motion for the one-body density matrix. The CRPA spectral problem is numerically solved in the frame of a model consisting of a finite fermion system with axial symmetry interacting by means of a separable force. Calculations are performed within a range of interaction strengths, temperature and size parameters and it is shown that both the centroids and the widths of the high energy collective modes exhibit the trend of experimental data.     

Dynamics of nuclear fluid: (I). Foundation

Starting with the time-dependent Hartree-Fock (TDHF) formulation of the many-body problem, we cast the equation into a set of conservation laws of classical type. Besides the equation of continuity, TDHF leads to an equation of motion which is analogous to the Euler equation in classical fluid dynamics. The forces do not come from the collective kinetic stress alone, but also from a density-dependent chemical potential, the surface tensional force which depends on density differences and the Coulomb interaction. With an assumed Navier-Stokes generalization of the stress tensor, such a set of differential equations provides a powerful tool for the study of complicated collective motions of nuclear systems such as those involved in heavy-ion reactions and nuclear fission. In the static case, the equation of motion leads to the Thomas-Fermi model of a finite nucleus as formulated by Bethe.     

Application of a fusion model using collective variables and microscopically related mass parameters

A calculation of nucleus-nucleus collisions is presented, using a model which starts from a TDHF equation and leads to classical equations of motion for a set of four collective variables. Restricting to axial symmetry and assuming the liquid drop mass formula to hold, a differential equation is derived, which describes nuclear deformations and energies and is used to construct a potential energy surface for the collective variables. The nuclear deformations are obtained without the need of shape parameters. The equations of motion for the collective variables are solved numerically.     

Effects of the mean-field dynamics and the phase-space geometry on the cluster formation

A model allowing to simulate the production of clusters is developed and applied to heavy-ion reactions at intermediate energies. The model investigates the geometrical properties of the dynamically generated one-body phase space. The collision process is entirely governed by the Landau-Vlasov model, which provides the time evolution of the one-body phase-space distribution. Particles emitted during successive time intervals of the dynamics are gathered together into subensembles to which a clusterization procedure is applied. Comparison with the experimental data for the Ar(65 MeV/nucleon) + Al reaction shows that the average behaviour of particle-dependent global observables is correctly reproduced within this framework. These results point out that the studied global properties of heavy-ion collisions greatly rely on the dynamical effects of the primary non-steady stage of the nuclear reaction.     

Damping of collective modes in DIC: Quantal versus statistical fluctuations

A model is developed to describe the transformation of relative kinetic energy into intrinsic excitation energy in DIC. Energy dissipation is viewed as an indirect process, in which collective vibrational modes are first excited coherently and then damped due to the coupling to the remaining non-collective degrees of freedom. Both collective and intrinsic degrees of freedom are included explicitly, and the coupling between them is treated in a random-matrix model. Under certain assumptions it is shown that, in the weak-coupling limit, the collective probability distribution in phase space obeys a Fokker-Planek equation. This transport equation is used to derive equations of motion for the expectation values of some “macroscopic” quantities characterizing the process. Some numerical results are presented and a qualitative comparison with the Copenhagen model is attached.     

Two-proton small-angle correlations in central heavy-ion collisions: A beam-energy- and system-size-dependent study

Small-angle correlations of pairs of protons emitted in central collisions of Ca + Ca, Ru + Ru and Au + Au at beam energies from 400 to 1500MeV per nucleon are investigated with the FOPI detector system at SIS/GSI Darmstadt. Dependences on system size and beam energy are presented which extend the experimental data basis of pp correlations in the SIS energy range substantially. The size of the proton-emitting source is estimated by comparing the experimental data with the output of a final-state interaction model which utilizes either static Gaussian sources or the one-body phase-space distribution of protons provided by the BUU transport approach. The trends in the experimental data, i.e. system size and beam energy dependences, are well reproduced by this hybrid model. However, the pp correlation function is found rather insensitive to the stiffness of the equation of state entering the transport model calculations.     

On the description of dissipative collective motion

We use a recently developed time-dependent projection method to describe the dissipation of collective motion coupled to an intrinsic system. The underlying physical picture is similar to that of the linear response approach. Our approach is, however, different from the conceptual point of view. We do not resort to a quasistatic picture but use instead a time-dependent projector. Furthermore, we project on a model space which includes the intrinsic hamiltonian in addition to the collective subspace. In this way we obtain a Fokker-Planck equation for the collective variables which is coupled to a transport equation describing the evolution of the temperature of the intrinsic system.     

Fragmentation,dissipative expansion,and freeze-out in medium energy heavy-ion collisions

The collision dynamics of ⁹⁶Mo + ⁹⁶Mo at 55 A MeV is simulated by solving numerically the Boltzmann-Uehling-Uhlenbeck (BUU) transport equation for the one-body phase-space distribution-function of nucleons with and without Coulomb interaction. A scatter-plot of the one-body density distribution shows an initial compression, subsequent homogeneous expansion, a breaking into “fragments”, a very slow creeping expansion up to a freeze-out and in the case of included Coulomb-interaction a Coulomb-explosion. In the calculation which included Coulomb-interaction the overall shape of the ensemble of dense fragments is spherical. The fragments are created over the entire volume of the dense part of the source and not at the surface only. In the simulation without Coulomb interaction a doughnut-like shape may develop.     

Dissipation of nuclear collective motion

The collective transport theory provides a framework for understanding damped collective motion. The irreversibility of collective motion is traced to the fact that the nucleus is an open system. The finite lifetime of single-particle excitations causes the relaxation of the nuclear collective response. Both vibrational states and damped heavy-ion collisions can be understood quantitatively by computations without free parameters.     

On the competiting role of mean-field and residual interactions in flow observables

Theoretical analyses of heavy-ion reactions are performed in the framework of the semi-classical Landau-Vlasov approach. The incident energies are investigated in the range from intermediate to low energy regimes, where transverse collective motion has been experimentally evidenced. The influence of the equation of state (E.O.S.) parameters on various collective observables is studied in relation with the action of the residual interactions. From the sensitivity to both aspects, and taking into account the experimental biases limitations, our investigation indicates that E.O.S. signatures should be more expected at energies below 100 MeV per nucleon.     

核多体系统输运现象的微观理论

首先回顾了描写核多体系统输运现象的一些主要模型和方法,然后介绍了输运现象微观动力学基础研究上一些新的结果,强调了单粒子运动动力学特征在建立集体输运方程和理解超重核合成机制上的重要作用。能量耗散和熵产生的数值计算结果表明,集体运动耗散过程可分为退相干、弛豫和定态等3 个阶段,弛豫过程通常表现为非常复杂的反常扩散过程。在这些理论工作的基础上,提出了一种自洽地分离核多体系统集体和单粒子变量的可能途径。In this article, I provide a simple review on conventional methods and models on the transport phenomenon of nuclear many-body systems. By exploiting the basic idea of time-dependent projection operator, I recommend a novel method to derive the transport equation for collective motion which is embedded on the microscopic dynamics of timedependent single-particle motion. It is emphasized that the microscopic dynamics of single-particle motion should play an important role for understanding the dynamics of nuclear reaction and the synthesis mechanisms of new superheavy elements. The numerical results of energy dissipation and entropy production indicate that the collective motion passes through three stages, such as dephasing/decoherence, statistical relaxation and stationary state. The statistical relaxation is a complex anomalous diffusion process in general. With the aid of above analysis and results, a possible way to define the collective and single-particle variables for the realistic nuclear many-body systems is proposed.