Modern energy density functional for nuclei and the nuclear matter equation of state

We discuss a method of determining a modern energy density functional (EDF) in nuclei. We adopt a Skyrme type EDF and fit the Skyrme parameters to an extensive set of experimental data on the ground-state binding energies, radii, and the breathing mode energies of a wide range of nuclei. We further constrain the values of the Skyrme parameters by requiring positive values for the slope of the symmetry energy S, the enhancement factor κ, associated with the isovector giant dipole resonance, and the Landau parameter G ₀^′. This is done within the approaches of Hartree-Fock (HF) and HF with the inclusion of correlation effects, using a simulated-annealing based algorithm forminimizing χ ².We also present results of HF based random phase approximation for the excitation strength function of the breathing mode and discuss the current status of the nuclear matter incompressibility coefficient.     

A phenomenological equation of state for isospin asymmetric nuclear matter

A phenomenological momentum-independent(MID) model is constructed to describe the equation of state(EOS) for isospin asymmetric nuclear matter,especially the density dependence of the nuclear symmetry energy Esym(ρ).This model can reasonably describe the general properties of the EOS for symmetric nuclear matter and the symmetry energy predicted by both the sophisticated isospin and momentum dependent MDI model and the Skyrme-Hartree-Fock approach.We find that there exists a nicely linear correlation betwee...     

A simple semiempirical equation of state for cold nuclear matter

On the basis of gross properties of nuclei, a simple semiempirical equation of state is developed for cold hadronic matter composed of light quarks of two flavors. The source of binding energy in the model is the decreasing asymmetry between the number of up and down quarks in extended regions of overlapping nucleons. The resulting incompressibility of symmetric nuclear matter at equilibrium density is K=324 MeV. The incompressibility decreases rapidly with decreasing density but increases only slowly with increasing density until homogenous quark matter is reached at a density just above three times ordinary nuclear matter density.     

A simplified equation of state near nuclear density

The equation of state near nuclear density influences shock formation in stellar collapse Supernovae. The drop in the adiabatic index below $\text{4}\text{3}$ in this region, due to the negative nuclear pressure, disturbs the homology of the inner core and decreases its size. The initial shock energy and formation dynamics are particularly sensitive to matter in this regime.Only matter at low entropies (S ? 1.5) in the unshocked inner core approaches nuclear densities. We derive a simple equation of state for this material and find that nuclear properties are close to those at S = 0. The entropy associated with the nuclear surface can be absorbed into an “effective mass” which decreases towards one with increasing density, giving an accurate accounting for the storage of entropy in the excitation of the large nuclei. Such thermal excitation drains energy with little contribution to the pressure and thus may have important effects on the launching of the shock.Two phase transitions are considered. The first, from the heavy nucleus to the “bubble” phase, occurs at half nuclear matter density and is accomplished by use of simple expressions for the energy and pressure that include effects of the transition implicitly. The second, that to uniform nuclear matter, is done by requiring continuity of the pressure and entropy at the transition. The density at which this transition takes place is calculated and is found to decrease with entropy in a simple manner.With the use of suitable approximations, the equation of state is presented in a non-iterative form easily adapted for use in full hydrodynamical calculations of the supernovae process. Comparison with more detailed equations of state is made and the simplified one is found to represent well all important features.     

High density matter in the chiral bag model

We estimate the properties of dense matter in a chiral bag model, using methods previously employed for skyrmions. The bag is stabilized by the Casimir energy, and the chiral field outside the bag is described by Skyrme's model. We find that the bag radius decreases with increasing density, but that the fraction of space filled by bags increases. We also investigate the transition to quark matter.     

凝聚态物质状态方程的一个数值模型

建立了凝聚态物质的一个三项式状态方程：以Faussurier平均原子模型为基础计算电子热压和电子热能;以Cowan模型为基础计算离子热压和离子热能;用基于实验数据的半经验拟合公式计算物质的冷压和冷能。用实验数据检验了用平均原子模型计算的平均电离度。将状态方程与Hugoniot关系式相结合,计算了Be和Al的冲击绝热曲线,结果充分地展现出电子在高温、高密度条件下的壳层结构效应。     

Excluded volume effect for the nuclear matter equation of state

We present the thermodynamically consistent procedure to introduce the excluded volume effect into the equation of state of nuclear matter. Implications are discussed in the framework of a mean-field model for hadrons with eigenvolume.     

Effective nucleon-nucleon interactions and nuclear matter equation of state

Nuclear matter equations of state based on Skyrme, Myers-Swiatecki and Tondeur interactions are written as polynomials of the cubic root of density, with coefficients that are functions of the relative neutron excess δ. In the extrapolation toward states far away from the standard one, it is shown that the asymmetry dependence of the critical point ( ,) depends on the model used. However, when the equations of state are fitted to the same standard state, the value of is almost the same in Skyrme and in Myers-Swiatecki interactions, while is much lower in Tondeur interaction. Furthermore, does not depend sensitively on the choice of the parameter γ in Skyrme interaction. Received: 5 May 2000 / Accepted: 16 January 2001     

A new state of hadronic matter at high density

We propose in this article that if the chemical potential exceeds a critical value in dense hadronic medium, a first-order phase transition to a new state of matter with Lorentz symmetry spontaneously broken (in addition to the explicit breaking) takes place. As a consequence, light vector mesons get excited as “almost” Goldstone bosons. Since the light vector mesons dominantly couple to photons, the presence of these new vector mesons could lead to an enhancement in the dilepton production from dense medium at an invariant mass lower than the free-space vectormeson mass. We provide a low-energy quark model which demonstrates that the above scenario is a generic case for quark theories with a strong interaction in the vector channel. We discuss possible relevance of this phase to the phenomenon of the enhanced dilepton production at low invariant masses in relativistic heavy-ion collisions.     

Current status of equation of state of nuclear matter

The equation of state (EOS) of symmetric nuclear matter (SNM) is a very important ingredient in the study of various phenomena of interest in nuclear physics and astrophysics. Accurate assessment of the value of the SNM incompressibility coefficient, K, which is directly related to the curvature of the EOS, is needed to extend our knowledge of the EOS in the vicinity of the saturation point. We review the current status of K as determined from experimental data on compression modes in nuclei using the mean-field-based random-phase approximation. The text was submitted by the authors in English.     

Relativistic equation of state of nuclear matter for supernova and neutron star

We construct the equation of state (EOS) of nuclear matter using the relativistic mean field (RMF) theory in the wide density, temperature range with various proton fractions for the use of supernova simulation and the neutron star calculations. We first construct the EOS of homogeneous nuclear matter. We use then the Thomas-Fermi approximation to describe inhomogeneous matter, where heavy nuclei are formed together with free nucleon gas. We discuss the results on free energy, pressure and entropy in the wide range of astrophysical interest. As an example, we apply the resulting EOS on the neutron star properties by using the Oppenheimer-Volkoff equation.     

Limiting temperatures and the equation of state of nuclear matter

From experimental observations of limiting temperatures in heavy ion collisions we derive the critical temperature of infinite nuclear matter Tc=16.6+/-0.86. Theoretical model correlations between Tc, the compressibility modulus K, the effective mass m*, and the saturation density rho s are then exploited to derive the quantity (K/m*)1/2 rho -1/3 s. This quantity together with calculations employing Skyrme and Gogny interactions indicates a value of K in moderately excited nuclei that is in excellent agreement with the value determined from giant monopole resonance data.     

Bose-Einstein correlations and the equation of state of nuclear matter

Within a relativistic hydrodynamic framework, we use four different equations of state of nuclear matter to compare to experimental spectra from CERN/SPS experiments NA44 and NA49. Freeze-out hypersurfaces and Bose-Einstein correlation functions for identical pion pairs are discussed. We find that two-pion Bose-Einstein interferometry measures the relationship between the temperature and the energy density in the equation of state during the late hadronic stage of the fireball expansion. Little sensitivity of the light-hadron data to a quark-gluon plasma phase-transition is seen. Received: 19 April 1999 / Published online: 15 July 1999     

重离子核反应与核物质状态方程

核物质状态方程描述核物质结合能、压强、密度和中子—质子数差异等宏观量之间的关系。核物质状态方程不仅仅与核力属性、核结构性质以及重离子核反应的动力学过程紧密相关,还与致密星体如中子星的结构、演化、辐射与并合等天体过程紧密相关。基于加速器装置的重离子核反应实验,是地面实验室模拟产生极端条件核物质的唯一手段,因而也成为研究核物质状态方程的有效途径。当核物质中的中子数远大于质子数时,例如中子星内部的情形,核物质状态方程中的主要贡献项是对称能项。迄今为止,对称能关于密度的函数是核物理和天体物理中一个未知而又非常重要的物理量。通过重离子核反应的实验和理论研究来确定对称能的密度依赖关系及其在核反应以及致密星天体事件中的物理效应,是当代核物理基础研究的重要前沿。文章介绍了中能重离子核反应和核物质状态方程的一些背景知识和研究方法,以及近年来的一些进展。     

A relativistic approach to the equation of state of asymmetric nuclear matter

The properties of asymmetric nuclear matter for a wide range of densities and asymmetric parameters are investigated within the lowest-order-constrained variational (LOCV) method by employing the relativistic Hamiltonian with a potential which has been fitted relativistically to N-N phase shifts ( [(v)\tilde]₁₄ \tilde{{v}}_{{14}}^{} and to the AV₁₄interaction. Like our previous work on symmetric nuclear matter, the boost interaction corrections as well as the relativistic one-body and two-body kinetic corrections are calculated. The various properties of asymmetric nuclear matter such as the symmetry energy, the saturation energy and the validity of the a² \alpha^{2}_{} law, etc., are examined. The symmetry energy is reduced by about 7MeV when we use [(v)\tilde]₁₄ \tilde{{v}}_{{14}}^{} instead of its non-relativistic version, i.e. the AV₁₄interaction. The results are compared with other many-body calculations.     

Probing the equation of state for cold nuclear matter in fusion reactions

To probe the nuclear equation of state, several fusion cross-sections have been analyzed using microscopic nucleus-nucleus potentials calculated in the framework of the Hamiltonian energy density approach through the well-known Skyrme nucleon-nucleon effective interaction with eighteen different parameterizations which express various equations of state. Three density-dependent M3Y-Paris effective forces are examined also within the double-folding model. The various effective forces give incompressibility modulus values which vary over a rather wide range between 188MeV and 372MeV. The extracted fusion barrier distributions are examined too with the same aim. The most successfully investigated interactions in deriving satisfactory fusion excitation functions as well as barrier distributions are those giving equations of state with nuclear incompressibility values in the range of 230-241MeV, according to the isospin asymmetry of the interacting nuclei.     

\sigma-\omega model and compressible bag model

Compressible bag model is formulated on the basis of lagrangian field theory. A specific application is done in conjunction with - model. The results are similar to Chin-Walecka model and almost reproduce our previous results. The effective nucleon mass does not become so small owing to the compressibility, in contrast to Chin-Walecka model. Received: 12 May 1998 / Revised version: 9 July 1998 / Published online: 8 September 1998     

同位旋非对称核物质状态方程

为了确定同位旋非对称核物质状态方程,利用同位旋有关的量子分子动力学理论计算和寻找实验上对于中能重离子碰撞中核子-核子碰撞截面或者对称势非常灵敏的物理观测量——探针.结果发现了几种分别对于核子-核子碰撞截面或者对称势非常灵敏的物理观测量.并对这些探针的机理进行了仔细研究,对以上研究结果进行小结和讨论,并为今后继续深入研究工作提出展望. 关键词： 对称势 核子-核子碰撞截面 同位旋依赖性 机理