On the isospin effects in the geometry of vanishing flow in heavy-ion collisions

We study the behavior of the geometry of vanishing flow (GVF) and its system size dependence at different incident energies. We find that the geometry of vanishing flow is sensitive to the incident energy. We also study the role of isospin degree of freedom through Coulomb potential, symmetry energy and nucleon-nucleon cross sections. Our study reveals that isospin degree of freedom through nucleon-nucleon cross section plays a dominant role compared to Coulomb potential and symmetry energy.     

Isospin effects of projectile fragmentation in a Boltzmann-Langevin approach

The iso spin effects of projectile fragmentation at intermediate energies are investigated using an iso spindependent Boltzmann-Langevin model.The collisions of mass-symmetric reactions including ~(58)Fe,~(58)Ni+~(58)Fe,and~(58)Ni at intermediate energies,in the 30 to 100 MeV/A range,are studied for different symmetry energies.Yield ratios of the isotopic,isobaric,and isotonic pairs of fragments from the intermediate-mass region using three symmetry energies are extracted as functions of the N/Z ratio of the composite systems in the entrance channel and the incident energies.It is found that the yield ratios are sensitive to symmetry energies,especially for neutron-rich systems,and the calculations using soft symmetry energy are closer to the experimental data.The iso spin effect is stronger for the soft symmetry energy,owing to the competition of the repulsive Coulomb force and the symmetry energy attractive force on the proton.For the first time,the splits are presented,revealing a transition from the iso spin equilibrium at lower energies to translucency at intermediate energies.The results show a degree of transparency in that intermediate mass fragments undergo a transition from dependence on the composite systems in the entrance channel to reliance on the projectile and target nuclei.     

Comparison of analyzing powers for the charge symmetric reactions 2H(d,n)3He and 2H(d,p)3H below 5.5 MeV

Analyzing powers for these charge symmetric reactions were measured at low energies where symmetry breaking effects due to the Coulomb interaction should be enhanced. Differences in the magnitudes exist and must be explained if charge symmetry holds; a simple energy shift, proposed earlier, is not adequate for this purpose.     

Bound Dirac states,different Lorentz-type couplings of central potentials and the non-relativistic limit

The analysis of bound radial Dirac states is shown to simplify for problems with an equal mixture of Lorentz vector and Lorentz scalar potentials, thus satisfying a so-called spin symmetry of the energy spectrum. Typical relativistic restrictions on potentials that are singular at the origin then disappear. Such potentials may even be strongly singular at the origin like the well known Lennard-Jones potentials modelling many atom-atom interactions, and they reduce to non-relativistic potentials of identical form. Bound state energies for potentials with equal vector- and scalar couplings are compared with those of a pure vector coupling of the same radial (attractive screened and unscreened Coulomb) shapes, and with non-relativistic results.     

Polarization dependence of emission spectra of multiexcitons in self-assembled quantum dots

We have investigated the polarization dependence of the emission spectra of p-shell multiexcitons of a quantum dot when the single particle level spacing is larger than the characteristic energy of the Coulomb interactions. We find that there are many degenerate multiexciton states. The emission intensities depend on the number of degenerate initial and final states of the optical transitions. However, unlike the transition energies, they are essentially independent of the strength of the Coulomb interactions. In the presence of electron-hole symmetry the independence is exact.     

The Linear Optical Polarizability Spectra of Five C78 Isomers

Effects of anisotropy, symmetry, atom arrangement and Coulomb interaction on the linear optical polarizability spectra of five C₇₈ isomers are theoretically studied by using the extended Su-Schrieffer-Heeger model with and without Coulomb interaction. The main results are as follows. 1) The spectra become anisotropic with respect to the direction of the electric field of light. The property is common in the niorlel with and without Coulomb interaction. 2) The symmetry and atom arrangement have grcat effects on the peak positions, strengths, and number. 3) The Coulomb interaction tends to shift peaks to higher energies and enhances the oscillator strengths at higher energies.     

Symmetry energies,pairing energies,and mass equations

Symmetry and pairing energies of atomic nuclei are related to the differences between the excitation energies of isobaric analog states in the same nucleus. Numerous such excitation energies are known experimentally. In addition, a comprehensive global set can be deduced from the available experimental masses by applying Coulomb energy corrections. Replacing the experimental mass data by available theoretical mass predictions as basis for this procedure to extract symmetry and pairing energies makes it possible to directly compare theoretical and experimental quantities. These comparisons reflect upon the goodness or possible shortcomings of the respective mass equation since symmetry energies are related to the curvature of the nuclear mass surface. A discussion of eleven selected mass equations or procedures for reproducing experimental masses and extrapolating into regions of unknown nuclei is presented.     

Binding energy of giant nuclear systems in an empirical density functional model

Calculations of the radial shape and the binding energy of giant nuclei are made, using an empirical density functional. The obtained binding energies are smaller than those obtained with extrapolations of the liquid drop model. The density distributions show a growing central depression (due to Coulomb and symmetry energy) which finally (forA>700) leads to bubble nuclei.     

Correlation between α-decay energies of superheavy nuclei involving the effects of symmetry energy

A formula for the relationship between the α-decay energies (Q values) of superheavy nuclei (SHN) is presented, which is composed of the effects of Coulomb energy and symmetry energy. It can be employed not only to validate the experimental observations and measurements to a large extent, but also to predict the Q values of heaviest SHN with a high accuracy generally which will be very useful for future experiments. Furthermore, the shell closures in superheavy region and the effect of the symmetry energy on the stability of SHN against α decay are discussed with the help of this formula.     

Electron correlations in a C20 fullerene cluster

The ground-state properties of C₂₀ fullerene clusters are determined in the framework of the Hubbard model by using lattice density-functional theory (LDFT) and scaling approximations to the interaction-energy functional. Results are given for the ground-state energy, kinetic and Coulomb energies, local magnetic moments, and charge-excitation gap, as a function of the Coulomb repulsion U/t and for electron or hole doping δ close to half-band filling (|δ| ≤1). The role of electron correlations is analyzed by comparing the LDFT results with fully unrestricted Hartree-Fock (UHF) calculations which take into account possible noncollinear arrangements of the local spin-polarizations. The consequences of the spin-density-wave symmetry breaking, often found in UHF, and the implications of this study for more complex fullerene structures are discussed.     

Chiral symmetry breaking in Hamiltonian QCD in Coulomb gauge

Spontaneous breaking of chiral symmetry is investigated in the Hamiltonian approach to QCD in Coulomb gauge. The quark wave functional is determined by the variational principle using an ansatz which goes beyond the commonly used BCS-type of wave functionals and includes the coupling of the quarks to the transversal spatial gluons. Using the lattice gluon propagator as input it is shown that the low energy chiral properties of the quarks, like the quark condensate and the constituent quark mass, are substantially increased by the coupling of the quarks to the spatial gluons. Our results compare favorably with the phenomenological values.     

A computational investigation of topological insulator Bi2Se3 film

Topological insulators have a bulk band gap like an ordinary insulator and conducting states on their edge or surface which are formed by spin–orbit coupling and protected by time-reversal symmetry. We report theoretical analyses of the electronic properties of three-dimensional topological insulator Bi₂Se₃ film on different energies. We choose five different energies (–123, –75, 0, 180, 350 meV) around the Dirac cone (–113 meV). When energy is close to the Dirac cone, the properties of wave function match the topological insulator’s hallmark perfectly. When energy is far way from the Dirac cone, the hallmark of topological insulator is broken and the helical states disappear. The electronic properties of helical states are dug out from the calculation results. The spin-momentum locking of the helical states are confirmed. A 3-fold symmetry of the helical states in Brillouin zone is also revealed. The penetration depth of the helical states is two quintuple layers which can be identified from layer projection. The charge contribution on each quintuple layer depends on the energy, and has completely different behavior along K and M direction in Brillouin zone. From orbital projection, we can find that the maximum charge contribution of the helical states is p_z orbit and the charge contribution on p_yand p_x orbits have 2-fold symmetry.     

Physical properties of hot,dense matter: The general case

The thermodynamic properties of hot, dense matter are examined in the density range 10^?5 fm^?3 ? n ? 0.35 fm^?3 and the temperature range 0 ? T ? 21 MeV, for fixed lepton fractions Y_? = 0.4, 0.3 and 0.2 and for matter in β-equilibrium with no neutrinos. Three phases of the matter are considered: the nuclei phase is assumed to consist of Wigner-Seitz cells with central nuclei surrounded by a nucleon vapor containing also α-particles; in the bubbles phase the cell contains a central spherical bubble of nucleon vapor surrounded by dense nuclear matter; the third phase is that of uniform nuclear matter. All are immersed in a sea of leptons (electrons and neutrinos) and photons. The nuclei and bubbles are described by a compressible liquid drop model which is self-consistent in the sense that all of the constituent properties — bulk, surface, Coulomb energies and other minor contributions — are calculated from the same nuclear effective hamiltonian, in this case the Skyrme 1' interaction. The temperature dependence of all of these energies is included, for bulk and surface energies by direct calculation, for the Coulomb energy by combining in a plausible way the usual electrostatic energy and the numerical results pertaining to a hot Coulomb plasma. Lattice contributions to the Coulomb energy are an essential ingredient, and lattice modifications to the nuclear translational energy are included. A term is constructed to allow also for the reduced density of excited states of light nuclei. All of these modifications incorporate necessary physical effects which modify significantly the matter properties in some regions.     

On the energy of Yang-Mills fields in the presence of an external source

An expression is derived for the energy of a non-Abelian solution of the Yang-Mills equations in the presence of an external source, which permits an immediate comparison with the energy of the corresponding Coulomb-type solution, For any semisimple gauge group, a number of different field configurations are exhibited which always lead to solutions of lower energy than the Coulomb solution independent of the strength and symmetry properties of the source. The various implications of these results in view of the known instability of the Coulomb-type solution of a spherically symmetric source are discussed.     

磁场对量子阱中弱耦合束缚极化子性质的影响

采用线性组合算符及幺正变换方法研究了磁场对量子阱中弱耦合束缚极化子的性质的影响。导出了量子阱中束缚极化子的基态能量与振动频率、库仑束缚势、磁场和阱宽之间的变化关系。同时也讨论了振动频率与库仑束缚势、磁场之间的变化关系。通过数值计算结果表明:量子阱中束缚极化子的基态能量因振动频率、库仑束缚势、磁场和阱宽的不同而不同,它随振动频率和磁场的增加而增大,随库仑束缚势和阱宽的增大而减小。量子阱中束缚磁极化子的基态能量与振动频率无关,随库仑束缚势和阱宽的增大而减小,随磁场的增大而增大。     

Extraction of Nuclear Matter Properties from Nuclear Masses by a Model of Equation of State

The extraction of nuclear matter properties from measured nuclear masses is investigated in the energy density functional formalism of nuclei.It is shown that the volume energy a1 and the nuclear incompressibility Ko depend essentially on μ_nN + μ_pZ - 2E_N,whereas the symmetry energy J and the density symmetry coefficient L as well as symmetry incompressibility Ks depend essentially on μ_n - μ_p,where μ_p ＝μp - ∂E_c/∂Z,μ_n and μ_p are the neutron and proton chemical potentials respectively,E_N the nuclear energy,and E_c the Coulomb energy.The obtained symmetry energy is J ＝ 28.5 MeV,while other coefficients are uncertain within ranges depending on the model of nuclear equation of state.     

张量力在16O+16O熔合动力学中的效应（英文）

利用时间相关Hartree-Fock 理论和完整Skyrme 有效相互作用研究了16O+16O 碰撞在库仑位垒附近的熔合动力学。数值计算是在没有任何对称性约束的三维笛卡尔基下完成。将时间相关Hartree-Fock 理论和冻结密度近似下的能量密度泛函方法给出的库仑位垒与实验结果进行了比较,发现同位旋标量的张量项能降低自旋饱和体系16O+16O的库仑位垒,而库仑位垒高度随着同位旋矢量的张量项的耦合常数减小而降低。并计算了包含和不包含张量力的16O+16O熔合截面,发现张量力对16O+16O碰撞在库仑位垒附近的熔合动力学影响较小。The fusion dynamics of 16O+16O around Coulomb barrier has been studied in the timedependent Hartree-Fock (TDHF) theory with the full Skyrme effective interaction. The calculations have been carried out in three-dimensional Cartesian basis without any symmetry restrictions. We have included the full tensor force and all the time-odd terms in Skyrme energy density functional (EDF). The Coulomb barrier obtained from the dynamical TDHF calculations and EDF with frozen density approximation has been compared with the available experimental data. The isoscalar tensor terms and the rearrangement of other terms are found to decrease the barrier height in the spin-saturated system 16O+16O, while the energy of Coulomb barrier tends to decrease as the isovector coupling constant decreases. The fusion cross section for 16O+16O collision has been calculated with and without the tensor force. We found that the tensor force has minor effect on the fusion dynamics of 16O+16O at the energies around Coulomb barrier.     

Coulomb displacement energies of the T = 1, J = 0 states of A = 42 nuclei

Coulomb displacement energies of the T = 1, J = 0⁺ and 6₁⁺ states of A = 42 nuclei are analyzed with previously known charge dependent forces and effects, and with the available HartreeFock single-particle wave functions. From the study of the Coulomb displacement energies of the 6₁⁺ states, it is found that the present knowledge on the charge dependence, including a phenomenological charge symmetry breaking force previously introduced so as to help explain the Nolen-Schiffer anomaly, gives a sufficient and consistent explanation for both single-particle and twoparticle systems. From the study of the 0⁺ states, we found that the Coulomb displacement energies of the second 0₂⁺ states can be explained with a compensation between the smaller Coulomb energies of the second lowest two-particle state and larger ones of the deformed 4p-2h state.     

Exponential wave functions for atomic-molecular systems

Geometric properties of correlated exponential basis functions for n-particle Coulomb systems are studied. Using a system of model Schrödinger equations, the relations between the average values of Coulomb interaction energies of pairs of the particles and average values of cosines of the angles of mutual tilt of interparticle bonds are derived. The use of these relations significantly simplifies calculations of the energy operator matrix of many-particle systems by reducing them to evaluation of the Coulomb and normalization integrals. Geometric inequalities are established that allow one to estimate the many-particle Coulomb interaction integrals that are hard to evaluate. The results obtained can be used in calculations of atomic-molecular systems.