Semiclassical inertia of nuclear collective dynamics

For the low-lying collective excitations in nuclei, the transport coefficients, such as the stiffness, the inertia, and the friction, are derived within the periodic-orbit theory in the lowest orders of semiclassical expansion corresponding to the extended Thomas—Fermi approach. The multipole vibrations near the spherical shape are described in the mean-field approximation through the infinitely deep square-well potential and Strutinsky averaging of the transport coefficients. Owing to the consistency condition, the collective inertia for sufficiently increased particle numbers and temperatures is substantially larger than that of irrotational flow. The average energies of collective vibrations, reduced friction, and effective damping coefficients are in better agreement with experimental data than those found from the hydrodynamic model. The text was submitted by the authors in English.     

Self-consistent transport coefficients for average collective motion at moderately high temperatures

Linear response theory is applied to compute the coefficients for inertia, friction and local stiffness for slow, large scale nuclear collective motion. It is shown how these coefficients can be defined within a locally harmonic approximation. The latter allows to study the implications arising from a finite local collective frequency. It is only for temperatures around 2 MeV that the zero frequency limit becomes a fair approximation. Friction is found to have a marked temperature dependence. The numerical computations are performed on the basis of a two-center shell model, but allowing the particles and holes to become dressed through effects of the medium. The dependence of the transport coefficients on the parameters of these self-energies is studied. It is argued that the uncertainties are smaller than a factor of 2.     

Influence of the quadrupole pairing interaction on the spontaneous fission lifetime of heavy nuclei

The influence of the quadrupole pairing interaction on the value of the collective potential and inertia of fissioning nuclei is presented. The calculation employed a Nilsson potential having quadrupole and hexadecapole deformations. The collective inertia and potential found were then used to estimate the spontaneous fission lifetimes of a number of Fm isotopes. It was found that the calculated lifetimes are very sensitive to the presence of the quadrupole pairing forces.     

MICROSCOPIC CALCULATION OF THE INERTIA IN HEAVY NUCLEI

A realistic calculation of the inertia for ²³⁶U fisson based on the linear response theory is presented, in which the single particle states are provided by Nilsson model. The dependence of the nuclear inertia M_δiδi on the collective variables δ₂, δ₄ is studied at the range of certain nuclear temperature (0—1 MeV). The pairing effect and the shell effect on the nuclear inertia are discussed. The calculated results show a very prominent structure at level crossing points and when acrossing the critical temperature.     

SF6在惰性气体中输运性质的理论研究

利用Tang-Toennies势模型(以下简称TT势),计算了(Ne、Ar、Kr、Xe)-SF6相互作用势,在此基础上得到了SF6在惰性气体中的扩散系数,粘滞系数和热传导系数,通过相互作用势与M3SV势比较及输运性质与实验值的比较,说明了TT势模型是一种简单、可靠的势模型。     

Microscopic transport theory of heavy-ion collisions

Effects from shell structure on mass transport coefficients are studied in a schematic model. The diffusion coefficient is slightly reduced by shell effects, the reduction being less than 20% for realistic cases and reasonably high excitation energies. A much stronger effect results for the drift coefficient. This is due to the rapid variation of the shell correction energy as function of the fragmentation variable. The influence of shell effects on the time-dependent mass distributions is illustrated.     

Shapes and alignments at high spin in some rare-earth nuclei

Properties of quasirotational rare-earth nuclei at high spins are studied with continuum γ-ray spectra. It is shown that the height of these spectra at each rotational frequency gives an effective moment of inertia which includes both collective and alignment effects. At high frequencies it is necessary to correct these spectra for incomplete population of the highest spin states. This feeding correction method is presented and studied in detail. It is shown that, in quasirotational nuclei, it can in general be applied successfully. The results are discussed in terms of an interplay between alignment and deformation effects. At high spins, the highly aligned orbitais from the first empty major shell (above the valence shell) play a major role. When they reach the Fermi surface, they produce large alignments visible in our spectra. The effect of the Fermi level position and of the softness toward deformation are discussed.     

A numerical analysis of the heavy-ion reaction based on the linear response theory

Taking the relative distanceR and the deformationδ of each nucleus as the collective variables, we solve the two dimensional coupled dynamical equations of motion with friction in the framework of the linear response theory. In solving the equations of motion, we approximately replace the inertia tensor with the hydrodynamical one and use the modified liquid-drop one as the collective potential energy. As the frictional coefficients we use the microscopically calculated ones in the previous paper. The calculation is done for the reaction of²⁸Si+²⁰Ne, in which the incident energy of²⁰Ne is 120 MeV. Results show that our microscopically calculated friction gives the large value of energy dissipation which amounts to the “completely damped” collision. Besides it, growths of the oblate deformation in the entrance channel and the prolate deformation in the exit channel are clearly seen. They give a large influence on the time development of the energy dissipation. We compare our calculated results with the experimental data for the reactions of 120 MeV²⁰Ne with²⁷Al. The agreement between them is found to be reasonably good.     

Dynamical effects on the way to fusion of very heavy nuclei

The central collision of ⁴⁰Ar and ²⁰⁸Pb is studied considering the ellipsoidal deformations and isovector dipole mode of motion in the approaching phase. The collective energy dissipation is suggested to originate from the Fermi surface deformation which is treated as a kinematically independent mode of motion within the canonical Lagrange-Rayleigh dynamics. The possible extensions of the approach are discussed. The potential energy surface, calculated using the generalized (folded) surface potential, is studied. The saddle point in the potential energy surface lying at the border of strongly deformed compact configurations is located. The potential energy at this point is about 10MeV smaller than that of the ions touching each other in the spherical shape. The examination of trajectories followed by the system in its evolution shows that the inertia forces strongly hinder the motion of ions along the potential energy valley. The collective energy dissipated during the approach is found to be smaller than the difference in the potential energies at saddle point and at the touching configuration of unpolarized ions.     

Transport Theory and Collective Modes. I. The Case of Moderately Dense Gases

The complex spectral representation of the Liouville operator introduced by Prigogine and others is applied to moderately dense gases interacting through hard-core potentials in arbitrary d-dimensional spaces. Kinetic equations near equilibrium are constructed in each subspace as introduced in the spectral decomposition for collective, renormalized reduced distribution functions. Our renormalization is a nonequilibrium effect, as the renormalization effect disappears at equilibrium. It is remarkable that our renormalized functions strictly obey well-defined Markovian kinetic equations for all d, even though the ordinary distribution functions obey nonMarkovian equations with memory effects. One can now define transport coefficients associated to the collective modes for all dimensional systems including d = 2. Our formulation hence provides a microscopic meaning of the macroscopic transport theory. Moreover, this gives an answer to the long-standing question whether or not transport equations exist in two-dimensional systems. The non-Markovian effects for the ordinary distribution function, such as the long-time tails for arbitrary n-mode coupling, are estimated by superposition of the Markovian evolutions of the dressed distribution functions.     

Mass transport in anharmonic potentials

We investigate the effect of nuclear shell structure on the mass transport in low-energy heavy-ion collisions. The shell-correction energy leads to anharmonic driving potentials and thus, to nonlinear drift coefficients in the Fokker-Planck equation. Results for²³⁸U (7.42 MeV/nucleon)+²³⁸U are presented. The drift towards the closed Pb-shell enhances the fluctuations in the mass transport and provides an explanation for the large variances found experimentally. Local maxima in the mass distribution at the shell minima disappear due to the temperature dependence of the driving potential.     

Application of the theory of open quantum systems to nuclear physics problems

Quantum diffusion equations with transport coefficients explicitly depending on time are derived from the generalized non-Markovian Langevin equations. The asymptotic behavior of the friction and diffusion coefficients is investigated in the case of the FC and RWA couplings between the collective and internal subsystems. An asymptotic expression is obtained for the propagator of the density matrix of the open quantum system with the general quadratic Hamiltonian, linearly coupled (in coordinate and momentum) to internal degrees of freedom. The effect of different sets of transport coefficients on the decoherence and decay rate of the metastable state is investigated using the master equation for the reduced density matrix of open quantum systems. The developed approach is used to study the capture of the projectile nucleus by the target nucleus at energies near the Coulomb barrier. Capture cross sections in asymmetric reactions are well described with allowance for the calculated capture probabilities. Particular cases where dissipation favors penetration through the potential barrier are found. The generalized Kramers formula for the quasi-stationary decay rate of the quantum metastable systems is analytically derived.     

Electrokinetic and hydrodynamic properties of charged-particles systems

Dynamic processes in dispersions of charged spherical particles are of importance both in fundamental science, and in technical and bio-medical applications. There exists a large variety of charged-particles systems, ranging from nanometer-sized electrolyte ions to micron-sized charge-stabilized colloids. We review recent advances in theoretical methods for the calculation of linear transport coefficients in concentrated particulate systems, with the focus on hydrodynamic interactions and electrokinetic effects. Considered transport properties are the dispersion viscosity, self- and collective diffusion coefficients, sedimentation coefficients, and electrophoretic mobilities and conductivities of ionic particle species in an external electric field. Advances by our group are also discussed, including a novel mode-coupling-theory method for conduction-diffusion and viscoelastic properties of strong electrolyte solutions. Furthermore, results are presented for dispersions of solvent-permeable particles, and particles with non-zero hydrodynamic surface slip. The concentration-dependent swelling of ionic microgels is discussed, as well as a far-reaching dynamic scaling behavior relating colloidal long- to short-time dynamics.     

Transport coefficients in Chiral Perturbation Theory

We present recent results on the calculation of transport coefficients for a pion gas at zero chemical potential in Chiral Perturbation Theory (ChPT) using the Linear Response Theory (LRT). More precisely, we show the behavior of DC conductivity and shear viscosity at low temperatures. To compute transport coefficients, the standard power counting of ChPT has to be modified. The effects derived from imposing unitarity are also analyzed. As physical applications in relativistic heavy-ion collisions, we show the relation of the DC conductivity to soft-photon production and phenomenological effects related to a non-zero shear viscosity. In addition, our values for the shear viscosity to entropy ratio satisfy the KSS bound.     

Hf高自族态推转壳模型PNC方法研究

用推转壳模型ＰＮＣ方法研究了１６６Ｈｆ９４－１７０Ｈｆ９８核，计算了这三个核晕带和次晕带间的带交叉频率、带间互作用强度、顺排角动量和转动惯量等，并与实验值作了比较，结果表明在Ｎｉｌｓｓｏｎ势参数完全按照Ｌｕｎｄ系统学选取的情况下，理论计算值与实验值符合得较好．     

Random alloy diffusion kinetics for the application to multicomponent alloy systems

In this paper, extensive Monte Carlo simulation results are reported on tracer and collective diffusion correlation effects in the random ternary alloy, as an example of a multicomponent alloy system. The problem of analytically describing both collective and tracer diffusion kinetics is also addressed for the random multicomponent alloy by application of a combination of the Manning theory and Holdsworth and Elliott theory. It is found that the overall results from the combined theory agree reasonably well with Monte Carlo results. This combined approach is much more accurate than Manning’s approach itself and much more manageable than the almost exact, but unfortunately difficult to use, self-consistent theory of Moleko, Allnatt and Allnatt. Some relations between the Onsager phenomenological coefficients and tracer diffusion coefficients are derived and are tested with our Monte Carlo data. Good agreement is found.