Constraining symmetry energy at subnormal density by isovector giant dipole resonances of spherical nuclei

In our previous study, the deduced Langevin equation has been applied to investigate the isoscalar giant monopole resonance. In the current study, the framework is extended to study the isovector giant dipole resonance(IVGDR). The potential well in the IVGDR is calculated by separating the neutron and proton densities based on the Hartree-Fock ground state. Subsequently, the Langevin equation is solved self-consistently, resulting in the centroid energy of the IVGDR without width. The symmetry energy around the density of 0.02 fm~(-3) contributes the most to the potential well in the IVGDR. By comparison with the updated experimental data of IVGDR energies in spherical nuclei, the calculations within 37 sets of Skyrme functionals suggest the symmetry energy to be in the range of 8.13-9.54 MeV at a density of 0.02 fm~(-3).     

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。     

Description of cross sections for photonuclear reactions in the energy range between 7 and 140 MeV

A combination of the exciton and evaporation models is used to describe photonuclear reactions induced in light, medium-mass, and heavy nuclei by photons of energy in the range 7 ≤ E _γ ≤ 140 MeV. Two mechanisms of the photoexcitation of nuclei are considered. These are the formation of a giant dipole resonance at energies in the range E _γ ? 30 MeV and quasideuteron photoabsorption, which is dominant at energies in the region E _γ ? 40 MeV. The density of particle-hole states, which appears in the exciton model, is calculated on the basis of the Fermi gas model. The emission of two preequilibrium particles is taken into account in describing the quasideuteron reaction channel. The effect of isospin conservation on giant-dipole-resonance decay accompanied by photonucleon emission is examined. The model in question is used to describe cross sections for photon-induced reactions on ²⁶Mg, ⁵⁴Fe, ^{112,118,119,124}Sn, and ¹⁸¹Ta nuclei.     

质子椭圆流与对称能的密度依赖性

基于同位旋和动量依赖的强子输运IBUU04模型, 研究了¹³²Sn+¹²⁴Sn碰撞系统中的质子椭圆流对对称能的敏感关系. 研究发现入射能量从每核子400MeV到800MeV时质子椭圆流在低横动量端对对称能的敏感性高于高横动量端, 同时发现随着入射能量的增大, 质子椭圆流对对称能的敏感性在降低. 在研究入射能量范围内, 当入射能量为每核子400MeV左右时质子椭圆流对对称能最为敏感.     

Crust-core properties of neutron stars in the Nambu–Jona-Lasinio model

We adopt the Nambu–Jona-Lasinio(NJL) model to study the crust-core transition properties in neutron stars(NSs). For a given momentum cutoff and symmetry energy of saturation density in the NJL model, decreasing the slope of the symmetry energy gives rise to an increase in the crust-core transition density and transition pressure.Given the slope of the symmetry energy at saturation density, the transition density and corresponding transition pressure increase with increasing symmetry energy. The increasing trend between the fraction of the crustal moment of inertia and the slope of symmetry energy at saturation density indicates that a relatively large momentum cutoff of the NJL model is preferred. For a momentum cutoff of 500 Me V, the fraction of the crustal moment of inertia clearly increases with the slope of symmetry energy at saturation density. Thus, at the required fraction(7%) of the crustal moment of inertia, the NJL model with momentum cutoff of 500 Me V and a large slope of the symmetry energy of saturation density can give the upper limit of the mass of the Vela pulsar to be above 1.40 M_⊙.     

MULTIPOLE GLANT RESONANCES IN HIGHLY EXCITED NUCLEI

The isoscalar giant surface resonance and giant dipole resonance in highly excited nuclei are discussed.Excitation energies of the giant modes in ²⁰⁸Pb are calculated in a simplified model,using the concept of energy weighted sum rule (EWSR),and the extended Thomas-Fermi approximation at the finite temperature is employed to describe the finite temperature equilibrium state.It is shown that EWSR and the enrgy of the resonance depend only weakly on temperature in the system.This weak dependence is analysed.     

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.     

Effects of the symmetry energy slope on the axial oscillations of neutron stars

The impact of symmetry energy slope L on the axial w-mode oscillations is explored, where the range of the con- strained slope L of symmetry energy at saturation density is adopted from 25 MeV to 115 MeV while keeping the equation of state （EOS） of symmetric nuclear matter fixed. Based on the range of the symmetry energy slope, a constraint on the frequency and damping time of the wi-mode of the neutron star is given. It is found that there is a perfect linear relation between the frequency and the stellar mass for a fixed slope L, and the softer symmetry energy corresponds to a higher frequency. Moreover, it is confirmed that both the frequencies and damping times have a perfect universal scaling behavior for the EOSs with different symmetry energy slopes at saturation density.     

Evolution of the giant dipole resonance in excited 120Sn and 208Pb nuclei populated by inelastic alpha scattering

The evolution of the giant dipole resonance (GDR) in ¹²⁰Sn and ²⁰⁸Pb nuclei at excitation energies in the range of 30–130 MeV and 40–110 MeV, respectively, were studied by measuring high energy γ rays from the decay of the resonance. The excited states were populated by inelastic scattering of α particles at beam energies of 40 and 50 MeV/nucleon for ¹²⁰Sn and 40 MeV/nucleon for ²⁰⁸Pb. A systematic increase of the resonance width with increasing excitation energy was observed for both nuclei. The observed width evolution was compared to calculations employing a model that adiabatically couples the collective excitation to the nuclear shape, and to a model based on the collisional damping of nucleons. The adiabatic coupling model described the width evolution in both nuclei well, whereas the collisional damping calculation could describe the width evolution only in ²⁰⁸Pb. Light-particle inelastic scattering populates low angular momentum states in the target nucleus. The observed width increase is therefore interpreted to be predominantly due to fluctuations in the nuclear shape induced by temperature. This interpretation is consistent with the adiabatic model calculations and with recent angular momentum-gated measurements of the GDR in excited Sn isotopes.     

利用中-质微分流探测对称能的高密行为

基于同位旋和动量依赖的强子输运模型IBUU04，研究了¹³²Sn+¹²⁴Sn在三种不同碰撞能量、两种不同对称能作用下，中-质微分流随快度的变化关系. 发现中-质微分流的强度随碰撞能量的增大而增强. 在碰撞能量为400 MeV每核子时，中-质微分流对对称能最为敏感. 关键词： 重离子碰撞 中-质微分流 对称能     

Electric dipole strength distribution below the <Emphasis Type="Italic">E</Emphasis>1 giant resonance in <Emphasis Type="Italic">N</Emphasis> = 82 nuclei

In this study quasiparticle random-phase approximation with the translational invariant Hamiltonian using deformed mean field potential has been conducted to describe electric dipole excitations in ¹³⁶Xe, ¹³⁸Ba, ¹⁴⁰Ce, ¹⁴²Nd, ¹⁴⁴Sm and ¹⁴⁶Gd isotones. The distribution of the calculated E1 strength shows a resonance like structure at energies between 6–8 MeV exhausting up to 1% of the isovector electric dipole Energy Weighted Sum Rule and in some aspects nicely confirms the experimental data. It has been shown that the main part of E1 strength, observed below the threshold in these nuclei may be interpreted as main fragments of the Pygmy Dipole resonance. The agreement between calculated mean excitation energies as well as summed B(E1) value of the 1⁻ excitations and the available experimental data is quite good. The calculations indicate the presence of a few prominent positive parity 1⁺ States in heavy N = 82 isotones in the energy interval 6–8 MeV which shows not all dipole excitations were of electric character in this energy range.     

Soft Giant Dipole Modes in Ca Isotopes in the Relativistic RPA

The isovector giant dipole resonance in Ca isotopes is investigated in the framework of the fully consistent relativistic random phase approximation.The calculations are performed in an effective Lagrangian with a parameter set NL3,which was proposed for satisfactorily describing nuclear ground state properties.It is found that a soft isovector dipole mode for Ca isotopes near drip lines exists at energy around 6-7MeV.The soft dipole states are mainly due to the excitation of the weakly bound and pure neutron (proton)states near Fermi surface as well as the correlation of isoscalar and isovector operators.For nuclei with the extreme value of N/Z,the contributions of isoscalar mesons in the isovector mode play a non-negligible role.     

Fine Structure and Collectivity of the Levels of the Pygmy Dipole Resonance in <Superscript>208</Superscript>Pb in a Self-Consistent Model

A novel fully self-consistent microscopic approach based on the energy density functional method is employed to calculate the fine structure of the pygmy dipole resonance in ²⁰⁸Pb, i.e., the energies and reduced probabilities of E1 transitions for the states with energies below 10 MeV. The approach includes the random-phase approximation, quasiparticle–phonon interaction and the single-particle continuum. The theoretical results are compared to the available high-resolution data and found to agree with measured integral characteristics of the pygmy dipole resonance at energies above 5.7 MeV. Residual spin–spin forces are quantified, and their contribution is found to be significant at both low and high energies. A recently proposed criterion is employed to analyze the collectivity of the 1^–states in ²⁰⁸Pb.     

质量数A≈125的热核GDR特性的研究

简单介绍了利用LNS的回旋加速器产生的^116。Sn束轰击^12C和^24Mg靶的实验装置以及实验过程．该实验通过MEDEA探测器测量了由全熔合与非全熔合反应产生的较低激发能区(160-300MeV)质量数A≈125的热核的巨偶极共振特性，比较了不同靶子、不同束流能量时巨偶极共振的7产额的变化．The experiment was carried out at the National Laboratory of South in Italy using~(116)Sn beam of 17 and 23 MeV/u delivered from the Superconducting Cyclotron impinging on~(12)C and~(24)Mg targets. The hot nuclei have been formed by complete and incomplete fusion reactions. The characteristics of the giant dipole resonance(GDR) in hot nuclei of mass A≈125 at lower excitation energies between 160 and 300 MeV have been measured with the multi element detector array (MEDEA) detector. A comparison of GDR ...     

具有Gogny等效核力的有限核物质的饱和性质与液气相变

在核物质的Ｈａｒｔｒｅｅ－Ｆｏｃｋ理论框架下，通过动量空间状态数的修正Ｈｉｌｌ－Ｗｈｅｅｌｅｒ公式来顾及核的有限尺度效应，应用Ｇｏｇｎｙ等效核力和唯象Ｃｏｕｌｏｍｂ能公式得到了合理的有限核零温饱和性质，得到有限核的液－气相变临界温度Ｔ_c约为１２ＭｅＶ，与由重离子碰撞实验提取到的一致。而且发现，目前广泛使用的有限核表面能唯象公式对于非正常核密度区是不适用的，本文给出了它的一个新的表达式。 关键词：     

On the charge and shape polarization of fission fragments,fusioning nuclei,or scattering heavy ions near contact

The polarization of the fragments from binary fission or of scattering or fusioning heavy nuclei is investigated in the liquid drop model. Due to the mutual Coulomb repulsion near contact the fragments may be polarized with respect to their charges (electric dipole moments from inhomogeneous charge distributions) as well as with respect to their shapes (quadrupole and octupole deformations). The lowering of the minimum energy near contact due to charge polarization is in the order of 1 MeV if one takes into account the energy from the giant dipole restoring force derived from the volume symmetry energy in addition to the liquid drop energies. The question whether one obtains prolate or oblate shapes is entirely due to the restriction in deformation space (fixed distance between centers-of mass or between the tips of the fragments).     

Photonuclear data and modern physics of giant resonances

The results of the development (“renaissance”) of giant-resonance physics are briefly discussed from the point of view of their application to creating a photonuclear database. It is indicated that part of the recommendations from corresponding libraries of data are not at the level of the present-day status of giant-resonance physics. A Lorentzian parametrization of the most reliable experimental data on isovector M1 resonances is constructed for seven spherical nuclei, and it is shown that the widths of M1 resonances are severalfold, sometimes an order of magnitude, smaller than the value of Γ₀ = 4 MeV, which was recommended for all nuclei. The need for microscopically taking into account configurations more complex than those that are included within the standard random-phase approximation or within the quasiparticle random-phase approximation is emphasized. To be more precise, it is necessary to take into account coupling to phonons, since this changes the temperature dependence of the resonance width in relation to that which was used earlier and since, without this, one cannot explain the properties of pygmy dipole resonances in the region of the nucleon binding energy. Our calculations of the average energies of the pygmy dipole resonances in the Ca and Sn isotopes within the microscopic extended theory of finite Fermi systems reveal that the inclusion of coupling to phonons reduces these energies considerably toward the improvement of agreement with experimental data. The idea of creating a library of photonuclear data for unstable nuclei, including fission fragments, on the basis of the extended theory of finite Fermi systems is discussed in connection with the fact that information necessary for fitting the parameters of phenomenological theories is absent or insufficient for such nuclei.     

Pygmy dipole resonance in nuclei

A brief survey of the state of the modern microscopic theory of the so-called pygmy dipole resonance in nuclei is given—in particular, some unresolved problems are listed. It is emphasized that, in order to explain the pygmy dipole resonance, it is necessary but not sufficient to take into account the coupling of single-particle degrees of freedom to photon degrees of freedom. The results of the calculations performed for the first time for the isovector pygmy dipole resonance and the isovector electric giant dipole resonance in ¹²⁴Sn within a self-consistent approach involving, in addition to the standard quasiparticle random-phase approximation, a single-particle continuum and quasiparticle-phonon coupling of single-particle degrees of freedom to phonon degrees of freedom are presented. The results are found to be in satisfactory agreement with experimental data. The calculation of the isoscalar strength function in the energy region of the pygmy dipole resonance revealed that the nuclear-structure mechanism does not provide the isoscalar-strength suppression observed at energies in excess of 7 MeV in (α, α′γ) reactions; therefore, this suppression may stem from the reaction mechanism.     

The symmetry energy in nuclei and in nuclear matter

We discuss to what extent information on ground-state properties of finite nuclei (energies and radii) can be used to obtain constraints on the symmetry energy in nuclear matter and its dependence on the density. The starting point is a generalized Weizs?cker formula for ground-state energies. In particular, effects from the Wigner energy and shell structure on the symmetry energy are investigated. Strong correlations in the parameter space prevent a clear isolation of the surface contribution. Use of neutron skin information improves the situation. The result of the analysis appears consistent with a rather soft density dependence of the symmetry energy in nuclear matter.