密度相关袋常数的夸克介子耦合模型关于核物质和有限核的研究

由满足手征对称的Nambu-Jona-Lasinio(NJL)模型出发, 计算得到袋常数的密度相关性, 并将其与夸克介子耦合(QMC)模型相结合, 研究核物质和有限核的性质. 结果表明, 该模型能够成功地描述核物质的性质, 但得到的有限核结合能过大, 其中重整势起了非常关键的作用.     

Radial Dependence of the Static and Dynamical Properties of Finite Nuclei

Both the static and dynamical properties of finite nuclei are evaluated in the framework of self-consistent semiclassical (SCSC) approach. The present results are compared with those of the quantum mechanics. The comparison ehows that the SCSC approach can reproduce the average and collective properties of the finite nuclei very well.     

Self-consistent approaches in the microscopic theory of the nucleus: Static moments of odd-odd nuclei

Self-consistent mean-field theory and the method of the energy density functional, which are two modern self-consistent approaches in the microscopic theory of the nucleus that possess the highest predictive power for describing unstable nuclei, are briefly discussed. Themost recent results of calculations performed within these approaches are presented. The mean energies of E1 excitations in the range of 0–30 MeV are calculated for 15 stable and unstable tin isotopes (A = 100–176) on the basis of the self-consistent version of the generalized theory of finite Fermi systems by employing SLy4 Skyrme forces. A parameter-dependent expression that takes into account the existence of a pygmy dipole resonance is obtained for this quantity. The density-functional method is used within the self-consistent theory of finite Fermi systems on the basis of the Fayans-Tolokonnikov-Trykov-Zawischa functional in order to calculate the ground-state static quadrupole and magnetic moments of odd and odd-odd stable and unstable spherical near-magic nuclei. Good agreement with available experimental data is attained. The respective features are predicted for unstable nuclei.     

Statistical multifragmentation of nuclei: (I). Formulation of the model

A statistical formulation of the multifragmentation of finite nuclei is given. The approach considers the generalization of the liquid-drop model for hot nuclei and allows one to calculate thermodynamic quantities characterizing the nuclear ensemble at the disassembly stage. It is shown how to determine probabilities of definite partitions of finite nuclei and how to apply a Monte Carlo method. The importance of including finite-size effects is shown by comparison with infinite-like systems.     

On the second moment of the single-hole strength distribution

The second moment of the strength distribution of single-hole states in finite nuclei is discussed. Theoretical estimates for the second moment of single-hole states near the top of the Fermi sea appear to be larger than experimental values that can be derived from data on knock-out reactions; this indicates that experimentally a part of the single-hole strength has not been observed.     

Spherical time dependent Thomas-Fermi calculation of the dynamical evolution of hot and compressed nuclei

We have used a self-consistent time dependent Thomas-Fermi model at finite temperature to calculate the dynamical evolution of hot and compressed nuclei. It has been found that nuclei can accomodate more thermal energy than compressional energy before they break.     

New method for calculating the potential energy of deformed nuclei within the liquid-drop model

The method that we previously developed for going over from double volume integrals to double surface integrals in calculating the Coulomb energy of nuclei that have a sharp surface is generalized to the case of nuclei where the range of nuclear forces is finite and where the nuclear surface is diffuse. New formulas for calculating the Coulomb and the nuclear energy of deformed nuclei are obtained within this approach. For a spherically symmetric nucleus, in which case there is an analytic solution to the problem in question, the results are compared with those that are quoted in the literature, and it is shown that the respective results coincide identically. A differential formulation of the method developed previously by Krappe, Nix, and Sierk for going over from double volume integrals to double surface integrals is proposed here on the basis of the present approach.     

Finite nuclei in the reggeon “toy model”

Hadron–nucleus amplitudes at high energies are studied in the “toy” Regge model in zero transverse dimension for finite nuclei, when the standard series of fan diagrams is converted into a finite sum and loses physical sense at quite low energies. Taking into account all the loop contributions by numerical methods we find a physically meaningful amplitudes at all energies. They practically coincide with the amplitudes for infinite nuclei. A surprising result is that for finite nuclei and small enough triple pomeron coupling the infinite series of fan diagrams describes the amplitude quite well in spite of the fact that in reality the series should be cut and as such deprived of any physical sense at high energies.     

Microscopic description of giant resonances in highly excited nuclei

Giant resonances of general multipolarity in highly excited nuclei, which are produced in compound nuclear and deep inelastic heavy ion reactions, are described microscopically in the finite temperature linear response formalism. The linear response function is calculated in the finite temperature (FT) quasi-particle RPA approximation (FT-HFB-RPA) and is based on the corresponding self-consistent quasi-particle basis (FT-HFB). The theory is derived from the small amplitude limit of FT-TDHFB. The inclusion of cranking constraints allows the investigation of giant resonances in nuclei with large intrinsic excitation energy and high spin. A schematic model for the FT-HFB-RPA is developed and applied to the isovector giant dipole resonance in hot spherical nuclei. It is shown that the energy of the resonance depends only weakly on temperature in these systems. The experimentally observed lowering of the giant mode in highly excited nuclei is to be attributed to different effects. The descritpion of resonance damping lies beyond the scope of the random phase approximation. Possible extensions in this direction and qualitative features of the width of giant resonances at finite temperature are discussed.     

Mean field approach to the momentum distribution

Momentum distributions resulting from mean field theories are studied. It is found that their main features depend little on the effective mean field considered. Simple parametrizations of this rather universal curve are proposed to replace the standard distribution of the Fermi gas model, which is found to be quite unrealistic for finite nuclei. Simple approximations to the Wigner transform are used to understand the structure of the momentum distributions, and particularly to identify their deviation from the nuclear matter momentum distribution due to finite size effects.     

基于有限核性质确定核物质对称能的密度依赖性

密度依赖的对称能作为核物质状态方程的同位旋相关部分,是当前核物理和天体物理两个领域共同关注的重要热点问题之一。人们在实验和理论两方面对此进行了大量的探索,然而由于问题的困难性,对其研究尚未达成共识。目前,研究对称能的方法有很多,其中包括微观和唯像核多体理论、重离子碰撞、原子核的巨共振等。近年来,低密对称能的研究已经取得了重要进展。本文综述了利用有限核的信息来约束核物质对称能的密度依赖性方面的研究工作,这一研究途径尽可能地降低了理论分析的模型依赖性。研究表明,208Pb对称能(系数)asym(A)等于参考密度ρA=0.55ρ0处的核物质对称能(系数)。这个关系将有限核与核物质的对称能联系了起来,借此可以探究亚饱和密度核物质对称能的密度依赖性,因此核心目标是准确确定208Pb对称能(系数)。我们通过重核β-衰变能和质量差来提取208Pb对称能(系数),进而约束亚饱和密度下核物质对称能的密度依赖行为。     

The breathing mode and the nuclear surface

The role of the nuclear surface in the breathing mode of nuclei is analyzed. We discuss a simple model in which the density varies according to a scaling of the coordinates. We show that this model reproduces accurately the results of microscopic calculations in heavy nuclei, and we use it to estimate the contribution of the surface to the effective compression modulus of semi-infinite nuclear matter. The calculation is performed in the framework of an extended Thomas-Fermi approximation and using several effective interactions. It is shown that the surface energy is maximum with respect to variations of the density around saturation density. The reduction of the effective compression modulus due to the surface turns to be proportional to the bulk compression modulus. The magnitude of the effect is compared with results of RPA calculations. Other contributions to the effective compression modulus of finite nuclei are also discussed.     

Self-consistent theory of finite Fermi systems and Skyrme–Hartree–Fock method

Recent results obtained on the basis of the self-consistent theory of finite Fermi systems by employing the energy density functional proposed by Fayans and his coauthors are surveyed. These results are compared with the predictions of Skyrme–Hartree–Fock theory involving several popular versions of the Skyrme energy density functional. Spherical nuclei are predominantly considered. The charge radii of even and odd nuclei and features of low-lying 2⁺ excitations in semimagic nuclei are discussed briefly. The single-particle energies ofmagic nuclei are examined inmore detail with allowance for corrections to mean-field theory that are induced by particle coupling to low-lying collective surface excitations (phonons). The importance of taking into account, in this problem, nonpole (tadpole) diagrams, which are usually disregarded, is emphasized. The spectroscopic factors of magic and semimagic nuclei are also considered. In this problem, only the surface term stemming from the energy dependence induced in the mass operator by the exchange of surface phonons is usually taken into account. The volume contribution associated with the energy dependence initially present in the mass operator within the self-consistent theory of finite Fermi systems because of the exchange of high-lying particle–hole excitations is also included in the spectroscopic factor. The results of the first studies that employed the Fayans energy density functional for deformed nuclei are also presented.

     

Energy density of the glasma

The initial energy density produced in an ultrarelativistic heavy ion collision can, in the color glass condensate framework, be factorized into a product of the integrated gluon distributions of the nuclei. Although this energy density is well defined without any infrared cutoff besides the saturation scale, it is apparently logarithmically ultraviolet divergent. We argue that this divergence is not physically meaningful and does not affect the behavior of the system at any finite proper time.     

On the Liguid-Gas Phase Transition and the Instability of Hot Nuclei

Based on a simple semi-empirical energy density, the free energy density for a hot nucleon system is derived, from which the equations of state P(T, p) and chemical potentials μ_q(T, p) for both finite nucleus and infinite nuclear matter are acquired. The liquid-gas phase transition and the instability of hot nuclei are analysed with these ingredients within the framework of thermodynamic's. Both critical temperature T_c for infinite nuclear matter and limiting temperature T_lim, for finite nuclei are predicted and compared with previous calculations.     

Dirac-Brueckner-Hartree-Fock calculations for isospin asymmetric nuclear matter based on improved approximation schemes

We present Dirac-Brueckner-Hartree-Fock calculations for isospin asymmetric nuclear matter which are based on improved approximations schemes. The potential matrix elements have been adapted for isospin asymmetric nuclear matter in order to account for the proton-neutron mass splitting in a more consistent way. The proton properties are particularly sensitive to this adaption and its consequences, whereas the neutron properties remains almost unaffected in neutron-rich matter. Although at present full Brueckner calculations are still too complex to apply to finite nuclei, these relativistic Brueckner results can be used as a guidance to construct a density-dependent relativistic mean-field theory, which can be applied to finite nuclei. It is found that an accurate reproduction of the Dirac-Brueckner-Hartree-Fock equation of state requires a renormalization of these coupling functions.     

Finite size α-particle calculations of absolute α-decay for spherical nuclei

Recently some important results have been obtained in calculating absolute α-decay widths, the calculations having been performed in the zero range α-particle approximation. In this paper the effects of the finite size of the α-particle are considered. Two important effects have been found: (i) for the finite size calculation, the absolute α-decay widths decrease by 2–3 orders of magnitude, and (ii) the finite size effects are strongly dependent on the shell model configuration of the initial nucleus. In the framework of the superfluid model the absolute probabilities of finite size α-particle emission have been calculated for the favored α-transitions of more than 200 spherical nuclei. The theoretical α-widths turn out to be smaller than the experimental ones by a factor of 10, which is approximately constant for all the nuclei studied.     

A Study of Giant Monopole an. d. Quadrupole States in the Relativistic Thomas-Fermi Approximation

The isoscalar giant monopole and quadrupole states in finite nuclei are studied in a relativistic δ-ω model by making use of a local Lorentz boost and scaling method, and the nuclear surface and the density distribution are treated in the relativistic Thomas-Fekmi approximation.The excitation energies of the giant resonances are self-consistently calculated. It is found that the excitation energies of giant monopole arehbasically in agreement with experimental data for all nuclei and those of giant quadrupole for light nuclei. Coupling constants and δ-meson mass in the theory are chosen to fit static properties of nuclear matter.     

On the calculation of the reaction matrix in finite nuclei

A method is suggested for calculating the reaction matrix in finite nuclei from any local or non-local potential. It employs a harmonic oscillator Pauli operator and purely kinetic particle states. Particle and hole states are properly orthogonalized. Bare reaction matrix elements to be used in shell-model calculations for A = 18 nuclei are given as sample results. They are based on the soft-core Reid potential.