基于相对论平均场有效对力的中子物质BCS-BEC渡越

基于核物质的相对论Hartree-Bogoliubov（RHB）理论,采用相对论平均场单玻色子交换形式的有效对相互作用,研究了不同对力强度下双中子关联及其中的BCS-BEC渡越现象。通过引入有效衰减因子χ调节对力强度,定量分析费米面处中子对能隙和单粒子动能比值△_Fn/e_Fn及无量纲参数1/（k_Fna）随费米动量k_Fn的演化行为,发现双中子对在χ=0.51时进入BCS-BEC渡越区域,在χ=0.67时可达到幺正极限。进而分析了中子对能隙、中子对波函数及相干长度等物理量在相应临界点处的特征,并给出渡越时双中子短程关联概率的定量判据。发现当配对中子处于平均中子间距以内的概率P（d_n）?0.80时,双中子对从纯BCS耦合过渡到BCS-BEC渡越区域。Based on the relativistic Hartree-Bogoliubov theory in nuclear matter, the dineutron correlations and the crossover from Bardeen-Cooper-Schrieffer (BCS) region of neutron Cooper pairs to Bose-Einstein condensation (BEC) are investigated with the one-boson-exchange type of pairing force generated from the relativistic mean field (RMF) model. By introducing an effective factor χ in the RMF effective pairing interaction, the density dependence of the ratios between neutron pairing gap at Fermi surface and neutron Fermi kinetic energy △_Fn/e_Fn and the dimensionless parameter 1/(k_Fna) are analyzed quantitatively. Then the criteria where dineutron correlations exactly reach the threshold of BCS-BEC crossover or unitary limit are determined to be χ=0.51 or 0.67, respectively. In addition, features of neutron pairing gap, Cooper pair wave function and dineutron coherence length are illustrated, and the value of the probability for partner neutrons correlated within the average inter-neutron distance, namely P (d_n) ?0.80, is obtained as a criterion of BCS-BEC crossover.     

Resonant Continuum in Extended RMF Plus BCS Approximation

The contribution of the resonant continuum to pairing correlations is investigated in the relativistic mean field theory plus Bardeen-Cooper-Schrieffer (BCS) approximation with a constant pairing strength. The resonance states with their widths in the continuum are considered explicitly. The numerical study is performed in an effective Lagrangian with the parameter set NLSH for neutron-rich nucleus ⁸⁴Ni. The results show that the effect of the proper treatment of the resonant continuum on pairing correlations for nucleus close to neutron drip line is important. It is found that the problem of an unphysical particle gas could be overcome when the pairing correlation is performed by using the resonant states instead of the discretized states in the continuum.     

Unified fields in pentadimensional theory

The theory of Jordan-Thiry is investigated by using a five-dimensional Riemannian manifold V₅ which admits a one-parameter group of isometries. The set of trajectories is supposed to represent the space-time of Relativity.The use of the induced metric in the quotient space leads to essential difficulties. It is necessary to consider a conformal metric and to modify the energy tensor in order to obtain the classical results of relativistic celestial mechanics. Moreover, the conformal metric brings out the evident interpretation of the fifteenth potential like a massless scalar field.A mass term referring to the scalar field is introduced; then the gravitational, electromagnetic, and mesonic scalar fields are unified through the metric of V₅. Several results make the new theory very coherent; in particular, the exact relativistic equations of motion are obtained asymptotically when the matter density vanishes.Exact solutions are searched. The classical Schwarzschild solution and neighbouring solutions are valid in the interior of the matter. Special non-static solutions are also obtained; some of these may be interpreted locally as describing the “collapse” of neutron stars; others ones, analogous to Robertson's metric, can be used to build a cosmology of the unified field.     

致密天体中电子气体对原子核结构的影响

运用相对论平均场理论结合Wigner-Seitz近似,研究了致密物质中电子气体对⁵⁶Fe和¹²⁰Sr结构的影响,对关联的处理采用Bardeen-Cooper-Schrieffer方法.结果表明电子气体对单粒子能级、核子密度分布、核子分布均方根半径、原子核均方根半径等性质都有影响,并且对质子的影响大于对中子的影响. 关键词： 相对论平均场理论 Wigner-Seitz近似 单粒子能级 均方根半径     

Investigation of the Mg isotopes using the shell-model-like approach in relativistic mean field theory

Ground state properties for Mg isotopes, including binding energies, one- and two-neutron separation energies, pairing energies, nuclear matter radii and quadrupole deformation parameters, are obtained from the self-consistent relativistic mean field (RMF) model with the pairing correlations treated by a shell-mode-like approach (SLAP), in which the particle-number is conserved and the blocking effects are treated exactly. The experimental data, including the binding energies and the one- and two-neutron separation energies, which are sensitive to the treatment of pairing correlations and block effects, are well reproduced by the RMF+SLAP calculations.     

Shell-model-like Approach (SLAP) for the Nuclear Properties in Relativistic Mean field Theory

A Shell-model-like approach suggested to treat the pairing correlations in relativistic mean field theory is introduced, in which the occupancies thus obtained have been iterated back into the densities. The formalism and numerical techniques are given in detail. As examples, the ground state properties and low-lying excited states for Ne isotopes are studied. The results thus obtained are compared with the data available. The binding energies, the odd–even staggering, as well as the tendency for the change of the shapes in Ne isotopes are correctly reproduced.     

Nonrelativistic mean-field description of the deformation of Λ hypernuclei

The deformations of light Λ hypernuclei are studied in an extended nonrelativistic deformed Skyrme-Hartree-Fock approach with realistic modern nucleonic Skyrme forces,pairing correlations,and a microscopical lambda-nucleon interaction derived from Brueckner-Hartree-Fock calculations.Compared to the large effect of an additional Λ particle on nuclear deformation in the light soft nuclei within relativistic mean field method,this effect is much smaller in the nonrelativistic mean-field approximation.     

相对论平均场理论对Pb同位素位移的研究

运用变形的相对论平均场理论研究了Pb同位素链的基态性质. 对关联的处理采用了BCS方法, 不成对核子的处理运用了“阻塞”法. 计算的结果很好地符合了实验上Pb的平均结合能, 中子分离能, 同位素位移. 接着从原子核的微观结构出发, 比较详细地研究了Pb链同位素位移出现反常扭折这一重要性质的物理机制.     

Relativistic Hartree-Bogoliubov description of the lithium isotopes

Here we report the development of the relativistic Hartree-Bogoliubov theory in coordinate space. Pairing correlations are taken into account by both density dependent force of zero range and finite range Gogny force. As a primary application the relativistic HB theory is used to describe the chain of Lithium isotopes reaching from ⁶Li to ¹¹Li. In contrast to earlier investigations within a relativistic mean field theory and a density dependent Hartree Fock theory, where the halo in ¹¹Li could only be reproduced by an artificial shift of the 1p _1/2 level close to the continuum limit, the halo is now reproduced in a self-consistent way without further modifications using the scattering of Cooper pairs to the 2s _1/2 level in the continuum. Excellent agreement with recent experimental data is observed.     

The surface diffuseness and the spin-orbital splitting in relativistic continuum Hartree-Bogoliubov theory

The relativistic continuum Hartree-Bogoliubov (RCHB) theory, which is the extension of the relativistic mean field and the Bogoliubov transformation in the coordinate representation, has been used to study tin isotopes. The pairing correlation is taken into account by a density-dependent force of zero range. The RCHB theory is used to describe the even-even tin isotopes all the way from the proton drip line to the neutron drip line. The contribution of the continuum which is important for nuclei near the drip-line has been taken into account. The theoretical S_2n as well as the neutron, proton, and matter rms radii are presented and compared with the experimental values where they exist. The change of the potential surface with the neutron number has been investigated. The diffuseness of the potentials in tin isotopes is analyzed through the spin-orbital splitting in order to provide new way to understand the halo phenomena in exotic nuclei. The systematic of the isospin and energy dependence of these results are extracted and analyzed.     

Effect of resonant continuum on pairing correlations in the relativistic approach

A proper treatment of the resonant continuum is to take account of not only the energy of the resonant state, but also its width. The effect of resonant states on pairing correlations is presented in the framework of the relativistic mean-field theory plus Bardeen-Cooper-Schrieffer (BCS) approximation with a constant pairing strength. The study is performed in an effective Lagrangian with the parameter set NL3 for neutron-rich even-even Ni isotopes. Results show that the contribution of the proper treatment of the resonant continuum to pairing correlations for those nuclei close to the neutron drip line is important. The pairing gaps, Fermi energies, pairing correlation energies, and binding energies are considerably affected by a proper consideration of the width of resonant states. The problem of unphysical particle gas, which may appear in the calculation of the traditional mean field plus BCS method for nuclei in the vicinity of the drip line could be well overcome when the pairing correlation is performed by using the resonant states instead of the discretized states in the continuum.PACS: 21.60.-n Nuclear-structure models and methods - 24.10.Jv Relativistic modelsZhong-Yu Ma: Also at Center of Theoretical Nuclear Physics, National Laboratory of Heavy Ion Accelerator of Lanzhou, Lanzhou 730000, PRC and Institute of Theoretical Physics, Beijing 100080, PRC.     

稀土区对关联经验参数公式的研究

在相对论平均场理论框架下， 采用不同对关联的参数公式对Ce, Gd和Yb稀土区同位素链进行了计算和研究。 理论计算表明: 尽管采用能隙经验参数公式和对力强度经验参数公式在能否表现出原子核的壳结构上有所区别， 但具体计算的其它物理量（如结合能、 双中子分离能等）趋向一致， 都能很好地反映原子核的基态性质。 In the framework of relativistic mean field (RMF)theory， we use BCS approximation to calculate Ce， Gd and Yb isotopic chains with different pairing parameters. And found whether they can show shell structure are different， but other physical quantities are similar by using different kinds of pairing parameters， both can correctly reproduce the experimental binding energies， two neutron separation energy and potential curves.     

RMF理论框架下用粒子数守恒方法处理对关联

在相对论平均场理论框架下,利用粒子数守恒方法处理对关联,给出了具体的理论公式和数值细节;并以24Ne为例,用该方法研究了它的基态和低激发态性质. Particle-number conserving method is adopted to treat the pairing correlations in the relativistic mean-field theory. The formalism and numerical techniques are presented. As an example, the ground state properties and low-lying excited states in~(24)Ne are studied.     

The Coulomb sum for electron scattering in the relativistic random phase approximation

The Coulomb sum value for electron scattering is estimated using the relativistic random phase approximation (RPA) in the field theory for nuclear matter. RPA correlations due to σ-, ω- and ϱ-meson exchanges reduce the sum value of the relativistic Hartree approximation by about 15–20%.     

Quark dynamics and strong meson decays

The strong decays of meson resonances are treated in a dynamical quark model. The model is formulated in the framework of general field theory and therefore all calculations are fully relativistic covariant. Spectrum and wave functions are derived from a Bethe-Salpeter equation describing the binding of heavy quarks by a smooth, very strong interaction. The mesonic vertices are calculated with help of these BS amplitudes in triangle graph approximation, thereby guaranteeing a symmetric treatment of all mesons involved in the process. A particular spin dependence of the interaction has the consequence that the super-strong quark binding forces lead to mesonic forces of moderate strength only (saturation of quark forces!).The applications refer to the decays of vector mesons, tensor mesons, scalar mesons into pseudoscalars and vectors and are extended to resonances in the R region. In particular, we include the decays into two pions of the radial excited ?′(1600). The helicity structure of the decays of the axial vector meson is discussed.     

Conventional BCS,unconventional BCS,and non-BCS hidden dineutron phases in neutron matter

The nature of pairing correlations in neutron matter is re-examined. Working within the conventional approximation in which the nn pairing interaction is provided by a realistic bare nn potential fitted to scattering data, it is demonstrated that the standard BCS theory fails in regions of neutron number density, where the pairing constant λ, depending crucially on density, has a non-BCS negative sign. We are led to propose a non-BCS scenario for pairing phenomena in neutron matter that involves the formation of a hidden dineutron state. In low-density neutron matter, where the pairing constant has the standard BCS sign, two phases organized by pairing correlations are possible and compete energetically: a conventional BCS phase and a dineutron phase. In dense neutron matter, where λ changes sign, only the dineutron phase survives and exists until the critical density for termination of pairing correlations is reached at approximately twice the neutron density in heavy atomic nuclei.     

Non-static plane symmetric cosmological models in bimetric theory

The problems of non-static plane symmetric meson field and mesonic perfect fluid in Rosen’s [Gen. Rel. Grav., Vol. 4 (1973) 435] bimetric theory of gravitation are considered. It is observed that plane symmetric non-static cosmological model exists in case of scalar meson field where the scalar field becomes constant. Further it is found that in case of mesonic perfect fluid, the bimetric theory does not admit perfect fluid but allows only mesonic scalar field with constant scalar field. In both the cases a cosmological model with constant scalar field is obtained.     

Ground State Structure of Hs Super-heavy Isotopes

The ground state properties of Hs nuclei studied in the framework of the relativistic mean field theory revealed that more stable isotopes are located on the proton abundant side of the chain.The last stable nucleus to the proton drip line is ~(256)Hs.The most stable unknown Hs nucleus may be ~(268)Hs.The density dependent delta interaction pairing is used to improve the BCS pairing correction,which results in more reasonable single-particle energy level distributions and nucleon occupation,and it is shown to be available to describe the properties of nuclei in the superheavy region.