Influence of the separation energy on the radius of neutron rich nuclei

The intensive studies of equilibration processes in heavy ion reactions have produced a need for information on nuclear level densities at high energies. In a recent paper, it was concluded that standard Fermi gas formulas will be incorrect by exponential factors at energies above 100 MeV. Exact calculations of the nuclear level density in bases as large as 10³⁸ have been made and are compared with Fermi gas formulas. Two possible alternative forms are considered. Both forms produce much better agreement at high energies than does the Fermi gas model. All calculations reported are for non-interacting Fermions, but the effects expected from the two-body interaction are briefly examined. These considerations have consequences not only in heavy ion physics but also in astrophysics.     

Systematics of nuclear level density parameters of nuclei deficient in one neutron

Photoneutron mean energies of 38 elements were measured as a function of peak bremsstrahlung energy for elements with 23 ≦ Z ≦ 83. Results are compared with neutron mean energies calculated from statistical theory, using for nuclear level densities modified Fermi gas formulae with and without pairing corrections and a constant temperature formula. Except near closed shells the Fermi gas formula with pairing corrections gives reasonable to good correlation between experimental and theoretical data. Derived values of the nuclear level density parameter a-except near Z = 82-are in quantitative agreement with those from recent neutron resonance data.     

Effective field theories, Landau-Migdal Fermi liquid theory, and effective chiral Lagrangians for nuclear matter

We reinterpret Landau-Migdal Fermi liquid theory of nuclear matter as an effective chiral field theory with a Fermi surface. The effective field theory is formulated in terms of a chiral Lagrangian with its mass and coupling parameters scaling à la Brown-Rho and with the Landau-Migdal parameters identified as the fixed points of the field theory. We show how this mapping works out for response functions to the EM vector current and, then using the same reasoning, make a prediction on nuclear axial current, in particular on the enhanced axial-charge transitions in heavy nuclei. We speculate on how to extrapolate the resulting theory, which appears to be sound both theoretically and empirically up to normal nuclear-matter density r₀, to hitherto unexplored higher density regime relevant to relativistic heavy-ion processes and to cold compact (neutron) stars.     

Level density of a Fermi gas: average growth and fluctuations

We compute the level density of a two-component Fermi gas as a function of the number of particles, angular momentum, and excitation energy. The result includes smooth low-energy corrections to the leading Bethe term (connected to a generalization of the partition problem and Hardy-Ramanujan formula) plus oscillatory corrections that describe shell effects. When applied to nuclear level densities, the theory provides a unified formulation valid from low-lying states up to levels entering the continuum. The comparison with experimental data from neutron resonances gives excellent results.     

Nuclear level densities below 40 MeV excitation energy in the mass regionA ≃ 50

Consistent pre-equilibrium emission and statistical model calculations of fast neutron induced reaction cross sections are used to validate nuclear level densities for excitation energies up to 40 MeV in the mass regionA ?50. A “composed” level density approach has been employed by using the back-shifted Fermi gas model for excitation energies lower than 12 MeV and a realistic analytical formula for higher excitations. In the transition region from the BSFG model range to that of full applicability of the realistic formula, an interpolation between the predictions of the two models is adopted. The interpolation rule, suggested by microscopic level density calculations, has been validated through the comparison of the calculated and experimental cross sections.     

中等质量碎片的内部激发对同位素核温度的影响

利用费米气体模型和区域密度近似分别计算单粒子能级密度,通过单粒子能级密度求得中等质量碎片(IMF)的内部配分函数. 计算表明,热核衰变过程中发射的中等质量碎片的内部激发对同位素核温度的测量结果有很大的影响.     

The strangeness of dense baryonic matter

Particle production in heavy-ion collisions is sensitive to the reaction dynamics and to the conditions inside the dense and hot fireball. In particular, experimental data on strangeness production at SIS energies, together with their theoretical interpretation based on microscopic transport theory,p permit to explore fundamental aspects of modern nuclear physics: the determination of the nuclear equation-of-state at high baryon densities and the properties of hadrons in dense nuclear matter. Experimental data and theoretical results will be reviewed.     

Mean free path of nucleons in a Fermi gas at finite temperature

The mean free path of a nucleon in a nuclear Fermi gas at finite temperature is calculated by utilizing the free nucleon-nucleon cross section modified to suppress final states excluded by the Pauli principle. The results agree with an earlier zero-temperature calculation but yield substantially smaller values than a previous finite-temperature analysis.The Fermi gas mean free paths are some two to four times shorter than those implied by phenomenological imaginary optical potentials, suggesting that the present Fermi gas model fails to adequately describe the physical processes determining the mean free path. Even so, the present results, taken as lower bounds on the mean free path, require temperatures of some 4.5 MeV before the mean free path of bound nucleons becomes as short as the nuclear diameter. It follows that very high excitation energies are prerequisite to any short mean free path assumption in nuclear heavy-ion collisions.     

Anregungsfunktionen für Compoundkernprozesse in geschlossener Form

Theoretical excitation functions in closed form for compound-nucleus reaction mechanism followed by nuclear evaporation are presented. Competition of neutron emission and charged-particle evaporation at the various stages of the evaporation chain are taken into account. The formula is derived in the framework of the nuclear evaporation model of Weisskopf using conventional Fermi gas level densities and continuum-theory reaction cross sections approximated by an empirical formula by Dostrovsky. Experimental and theoretical excitation functions are compared. The agreement of the experimental results with those calculated using our closed formula, while not entirely satisfactory, is as good as with those computed numerically with considerable effort by other authors.     

密度分布对原子核阻止同位旋效应的影响

利用同位旋相关的量子分子动力学（IQMD）模型,分析了中能重离子碰撞过程中相对论平均场和SkyrmeHartrere－Fork等核结构模型给出的核密度分布对原子核阻止的影响。研究表明,从费米能到的较大能量范围内,无论小质量体系还是大质量体系,原子核阻止对同位旋相关的核子－核子碰撞截面都非常灵敏,而不同模型给出的核密度分布对原子核阻止影响不大,说明原子核阻止作为提取同位旋相关核子－核子碰撞截面的灵敏探针是与原子核结构模型无关的。 Influence of densitydistributionwhichisgivenbyRMFandSkyrme－Hartrere－Fork etalnuclearstructuremodelonnuclearstoppinginheavy－ioncollisionsatintermediateenergiesarestudiedbyusingisospin－dependentquantummoleculardynamics(IQMD)model.ResearchshowsthatrangeformtheFermienergytothelargerenergyof 100 Mev/u, for bothsmallandlargemasssystem,nuclearstoppingisfoundtobestronglydependentonthenucleon－nucleoncrosssections,andweaklyondifferentdensitydistribution.ThisshowsthatnuclearstoppingcanbeusedasaprobetoextracttheinformationontheisospindependenceN－Ncrosssectionsandhasnorelationshipwithnuclearstructuremodels.     

Modified Glauber model for the total reaction cross-section of 12C + 12C collisions

Glauber's theory has been adopted to calculate the total heavy-ion reaction cross-sections at high energies. At relatively low energies, Glauber's total reaction cross-section has been modified in order to take into account the Coulomb field effect and is called modified Glauber model I. In addition to the Coulomb field effect, the nuclear effect has also been taken into account in the Glauber model and is called modified Glauber model II. An analytical expression for the transparency function for heavy-ion reactions, involving the nuclear densities of the colliding ions and the nucleon-nucleon cross- section, has been obtained within the framework of the modified Glauber models I and II. The transparency and the total reaction cross-sections of the ¹²C + ¹²C collisions are calculated at different bombarding energies. The obtained results are in good agreement with the experimental data and with previous theoretical calculations. Received: 26 January 2001 / Accepted: 15 October 2001     

Recent progress and new challenges in isospin physics with heavy-ion reactions

The ultimate goal of studying isospin physics via heavy-ion reactions with neutron-rich, stable and/or radioactive nuclei is to explore the isospin dependence of in-medium nuclear effective interactions and the equation of state of neutron-rich nuclear matter, particularly the isospin-dependent term in the equation of state, i.e., the density dependence of the symmetry energy. Because of its great importance for understanding many phenomena in both nuclear physics and astrophysics, the study of the density dependence of the nuclear symmetry energy has been the main focus of the intermediate-energy heavy-ion physics community during the last decade, and significant progress has been achieved both experimentally and theoretically. In particular, a number of phenomena or observables have been identified as sensitive probes to the density dependence of nuclear symmetry energy. Experimental studies have confirmed some of these interesting isospin-dependent effects and allowed us to constrain relatively stringently the symmetry energy at sub-saturation densities. The impact of this constrained density dependence of the symmetry energy on the properties of neutron stars have also been studied, and they were found to be very useful for the astrophysical community. With new opportunities provided by the various radioactive beam facilities being constructed around the world, the study of isospin physics is expected to remain one of the forefront research areas in nuclear physics. In this report, we review the major progress achieved during the last decade in isospin physics with heavy ion reactions and discuss future challenges to the most important issues in this field.     

On the validity of pre-equilibrium model assumptions

The Hartree-Fock calculation is performed for nuclear matter using the Skyrme interaction. It is shown that a stable density wave periodic in only one direction exists at densities below about one-third of the normal nuclear density. The critical densityρ _c below which the energy of the density wave is lower than that of the Fermi gas is determined for Skyrme interactions SKI to SKVI. It is further shown that even at densities slightly higher thanρ _c the density wave still exists as ametastable state in the sense that its energy is a local minimum in the variation parameter space. The density wave solution suddenly disappears at a higher density, since there the local minimum changes to an inflection point.     

The nuclear self-energy and related quantities in the semiclassical approximation

By using our recently developed semiclassical model for the imaginary part of the optical potential, we calculate here the polarization and correlation contributions to the real part via the dispersion relation. As underlying nonlocal mean-field potential, the semiclassical Hartree-Fock potential evaluated with the Gogny D1 effective interaction or the Perey-Buck potential is employed. With this full self-energy or second-order mass operator we calculate consistently depths, radial dependence and volume integrals of the single-particle potential, rearrangement energies and effective masses, the momentum distribution, mean free paths of a nucleon in a nucleus, and single-particle level densities. We obtain depths which are in excellent agreement with experiment including the Fermi anomaly: the effective mass exhibits a strong bump at the Fermi and the nuclear surface and the single-particle level density at the Fermi energy is enhanced by 65% yielding almost the correct average experimental value.     

Inferences concerning the real part of the heavy-ion optical potential through folding techniques

Analytic solutions are given for the real part of the heavy-ion optical potential through the use of single and double folding models. The effective potential between the nucleons is in the form of a sum of Yukawa terms and the distributions of the densities and the nucleon optical potential are taken to be of Woods-Saxon form. Consideration is given to the influence of the tails of the density distribution as well as that of the effective potential. Calculations suggest there is little need to delineate effective interactions with momentum components much beyond the Fermi level. This provides a rationale for realistic treatments of the effective interaction. A crucial parameter specifying the density distribution is found to be the rms radius.     

非晶碳结构建模和电子结构的第一性原理研究

基于密度泛函理论,采用了一种更为精确的交换相关泛函OLYP(OPTX+LYP),对密度范围从2.0到3.2 g/cm³的非晶碳进行结构建模. 模拟得到的5个碳网络结构无论从径向分布函数还是sp³含量都与实验符合得很好. 对非晶碳电子结构的研究表明费米能级附近的电子态密度主要是sp²碳原子的贡献. 随着密度的增加,sp³碳原子增加,费米能级附近的态密度越来越小. 小环结构增加了费米能级附近的电子态密度,缺陷态在费米能级形 关键词： 非晶碳 密度泛函理论 电子结构     

非晶碳结构建模和电子结构的第一性原理研究

基于密度泛函理论，采用了一种更为精确的交换相关泛函OLYP(OPTX+LYP)，对密度范围从2.0到3.2 g/cm³的非晶碳进行结构建模. 模拟得到的5个碳网络结构无论从径向分布函数还是sp³含量都与实验符合得很好. 对非晶碳电子结构的研究表明费米能级附近的电子态密度主要是sp²碳原子的贡献. 随着密度的增加，sp³碳原子增加，费米能级附近的态密度越来越小. 小环结构增加了费米能级附近的电子态密度，缺陷态在费米能级形     

Level density in large spectroscopic spaces

Statistical spectroscopy methods are used to calculate level densities for one-body Hamiltonians in the space of 440 single particle states. Comparisons are made with combinatorial counting and Fermi gas model. Possibilities to arrive at a more realistic level density formula including two-body effects are discussed.