Importance of self-consistency in relativistic continuum random-phase approximation calculations

A fully consistent relativistic continuum random phase approximation (RCRPA) is constructed, where the contribution of the continuum spectrum to nuclear excitations is treated exactly by the single-particle Green's function technique. The full consistency of the calculations is achieved that the same effective Lagrangian is adopted for the ground state and the excited states. The negative energy states in the Dirac sea are also included in the single-particle Green's function in the no-sea approximation. The currents from the vector meson and photon exchanges and the Coulomb interaction in RCRPA are treated exactly. The spin-orbit interaction is included naturally in the relativistic frame. Numerical results of the RCRPA are checked with the constrained relativistic mean-field theory. We study the effects of the inconsistency, particularly the currents and Coulomb interaction in various collective multipole excitations.

Can the nuclear symmetry potential at supra-saturation densities be negative?

In the framework of an isospin-dependent Boltzmann-Uehling-Uhlenbeck (IBUU) transport model, for the central Au-197 + Au-197 reaction at an incident beam energy of 400 MeV/nucleon, the effect of nuclear symmetry potential at supra-saturation densities on the preequilibrium clusters emission is studied. It is found that for the positive symmetry potential at supra-saturation densities the neutron-to-proton ratio of lighter clusters with mass number A less than or similar to 3 [(n/p)(A less than or similar to 3)] is larger than that of the heavier clusters with mass number A > 3 [(n/p)(A>3)], whereas for the negative symmetry potential at supra-saturation densities the (n/p)(A less than or similar to 3) is smaller than the (n/p)(A>3). This may be considered as a probe of the negative symmetry potential at supra-saturation densities.

Isospin-dependent pairing interaction from nuclear matter calculations

The isospin dependence of the effective pairing interaction is discussed on the basis of the Bardeen, Cooper, and Schrieffer theory of superfluid asymmetric nuclear matter. It is shown that the energy gap, calculated within the mean field approximation in the range from symmetric nuclear matter to pure neutron matter, is not linearly dependent on the symmetry parameter owing to the nonlinear structure of the gap equation. Moreover, the construction of a zero-range effective pairing interaction compatible with the neutron and proton gaps in homogeneous matter is investigated, along with some recent proposals of isospin dependence tested on the nuclear data table.

Constraints on the symmetry energy and neutron skins from pygmy resonances in Ni-68 and Sn-132

Correlations between the behavior of the nuclear symmetry energy, the neutron skins, and the percentage of energy-weighted sum rule (EWSR) exhausted by the pygmy dipole resonance (PDR) in Ni-68 and Sn-132 are investigated by using different random phase approximation (RPA) models for the dipole response, based on a representative set of Skyrme effective forces plus meson-exchange effective Lagrangians. A comparison with the experimental data has allowed us to constrain the value of the derivative of the symmetry energy at saturation. The neutron skin radius is deduced under this constraint.

Effect of information transmission on cooperative behavior

Considering the fact, in the real world, that information is transmitted with a time delay, we study an evolutionary spatial prisoner's dilemma game where agents update strategies according to certain information that they have learned. In our study, the game dynamics are classified by the modes of information learning as well as game interaction, and four different combinations, i.e. the mean-field case, case I, case II and local case, are studied comparatively. It is found that the time delay in case II smoothes the phase transition from the absorbing states of C (or D) to their mixing state, and promotes cooperation for most parameter values. Our work provides insights into the temporal behavior of information and the memory of the system, and may be helpful in understanding the cooperative behavior induced by the time delay in social and biological systems.

Concise methods for proton radioactivity

Concise methods are proposed to study proton radioactivity. The spectroscopic factor is obtained from relativistic mean field (RMF) theory combined with the BCS method (RMF+BCS). The assault frequency is estimated by a quantum mechanical method considering the structure of the parent nucleus. The penetrability is calculated by the WKB approximation. No additional parameters are introduced. The extracted experimental spectroscopic factors are compared with those from the calculations by the RMF+BCS, and the agreement is good, implying that the present methods work quite well for proton radioactivity. Predictions are provided for some most possible proton emissions, which may be useful for future experiments.

Effects of Pairing Correlations on Formation of Proton Halo in C-9

Properties for the ground state of C-9 are studied in the relativistic continuum Hartree-Bogoliubov theory with the NLSH, NLLN and TM2 effective interactions. Pairing correlations are taken into account by a density-dependent delta-force with the pairing strength for protons determined by fitting either to the experimental binding energy or to the odd-even mass difference from the five-point formula. The effects of pairing correlations on the formation of proton halo in the ground state of C-9 are examined. The halo structure is shown to be formed by the partially occupied valence proton levels p(3/2) and p(1/2).

Relativistic Continuum Random Phase Approximation and Applications II. Applications

The fully consistent relativistic continuum random phase approximation (RCRPA) has been constructed in the momentum representation in the first part of this paper. In this part we describe the numerical details for solving the Bethe-Salpeter equation. The numerical results are checked by the inverse energy weighted sum rules in the isoscalar giant monopole resonance, which are obtained from the constraint relativistic mean field theory and also calculated with the integration of the RCRPA strengths. Good agreement between the misachieved. We study the effects of the self-consistency violation, particularly the currents and Coulomb interaction to various collective multipole excitations. Using the fully consistent RCRPA method, we investigate the properties of isoscalar and isovector collective multipole excitations for some stable and exotic from light to heavy nuclei. The properties of the resonances, such as the centroid energies and strength distributions are compared with the experimental data as well as with results calculated in other models.

Relativistic Continuum Random Phase Approximation and Applications I. Formalism

A fully consistent relativistic continuum random phase approximation (RCRPA) is constructed in terms of the Green's function technique. In this method the contribution of the continuum spectrum to nuclear excitations is treated exactly by the single particle Green's function, which includes also the negative states in the Dirac sea in the nose aapproximation. The theoretical formalism of RCRPA and numerical details are presented. The single particle Green's function is calculated numerically by a proper product of regular and irregular solutions of the Dirac equation. The numerical details and the formalism of RCRPA in the momentum representation are presented.

重核性质的相对论平均场理论研究

本论文主要包括两部分内容，一部分是运用相对论平均场理论对超重核基态性质的研究以及Pb同位素位移微观机制的研究，第二部分是在相对论平均场框架下对BCS型对关联的改进及其在有限核性质研究中的应用。基于核子与介子自由度的量子强子动力学(QHD)， 从有效拉氏密度出发, 采取平均场近似, 已经成为当前最为成功的原子核理论之一，相对论平均理论。本文比较详细地介绍该理论模型, 并系统地探讨了新核素287115及其 衰变链上核的基态性质。结果发现所计算的结合能和四极形变符合了有限力程小液滴模型的结果，计算表明研究的 衰变链具有中等大小的长椭球形变；且计算的 衰变能 成功地与实验符合，说明相对平均场理论在原子核的超重区是有成功的。在此基础上进一步研究了新核素的单粒子能级，从而发现了超重核的一些新特点。通过分析Z=108到Z=114这四条同位素链的平均结合能，说明在这些同位素链中，对中子分离能的分析则可以看到N=162与N=184是壳效应的存在。研究了Pb同位素链的基态性质，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，由于满壳外额外中子会排布在距离满壳稍远一些的下一能级上，这自然会导致中子半径的增加．由于中子在核内的分布对质子分布的影响，将必然使原子核的电荷半径会在中子满壳后增加得更快。相对论平均场理论能够自然地给出原子核的自旋和轨道耦合，从而能给出合理的单粒子能级序列和间距，这为定量描述原子核的同位素位移提供了有力的理论基础。在论文的第二部分，通过引进密度相关的Delta力来改进传统的处理对关联的BCS方法，假定核子之间的作用为Delta力，计算得到状态相关的对能隙。相对于传统的常数对能隙是一个很重要的改进。接着我们用改进的理论研究了Sr同位素链的基态性质，得到了一些很有意义的结果。

Lattice Boltzmann study of hydrodynamic effects in lamellar ordering process of two-dimensional quenched block copolymers

By incorporating self-consistent field theory with lattice Boltzmann method, a model for polymer melts is proposed. Compared with models based on Ginzburg-Landau free energy, our model does not employ phenomenological free energies to describe systems and can consider the chain topological details of polymers. We use this model to study the effects of hydrodynamic interactions on the dynamics of microphase separation for block copolymers. In the early stage of phase separation, an exponential growth predicted by Cahn-Hilliard treatment is found. Simulation results also show that the effect of hydrodynamic interactions can be neglected in the early stage.

STUDY OF COARSENING OF MICRODOMAINS IN BLOCK COPOLYMERS BY LATTICE BOLTZMANN METHODS

In order to understand the coarsening of microdomains in symmetric diblock copolymers at the late stage, a model for block copolymers is proposed. By incorporating the self consistent field theory with the free energy approach Lattice Boltzmann model, hydrodynamic interactions can be considered. Compared with models based on Ginzburg-Landau free energy, this model does not employ phenomenological free energies to describe systems. The model is verified by comparing the simulation results obtained using this method with those of a dynamical version of the self consistent mean field theory. After that,the growth exponents of the characteristic domain size for symmetric block copolymers at late stage are studied. It is found that the viscosity of the system affects the growth exponents greatly, although the growth exponents are all less than 1/3 Furthermore, the relations between the growth exponent, the interaction parameter and the chain length are studied.

Microphase Separation of Mixed Polymer Brushes: Dependence of the Morphology on Grafting Density, Composition, Chain-Length Asymmetry, Solvent Quality, and Selectivity

Microphase separation of binary mixed A/B polymer brushes exposed to different solvents is studied using Single-Chain-in-Mean-Field simulations. Effects of solvent quality and selectivity, grafting density, composition, and chain-length asymmetry are systematically investigated, and diagrams of morphologies in various solvents are constructed as a function of grafting density and composition or chain-length asymmetry. The structure of the microphase segregated morphologies lacks long-range periodic order, and it is analyzed quantitatively Using Minkowski measures.

Inverted to normal phase transition in solution-cast polystyrene-poly(methyl methacrylate) block copolymer thin films

We have investigated the inverted phase formation and the transition from inverted to normal phase for a cylinder-forming polystyrene-block-poly(methyl methacrylate) (PS-b-PMMA) diblock copolymer in solution-cast films with thickness about 300 nm during the process of the solution concentrating by slow solvent evaporation. The cast solvent is 1, 1,2,2-tetrachloroethane (Tetra-CE), a good solvent for both blocks but having preferential affinity for the minority PMMA block. During such solution concentrating process, the phase behavior was examined by freeze-drying the samples at different evaporation time, corresponding to at different block copolymer concentrations, phi. As phi increases from similar to 0.1 % (nu/nu), the phase structure evolved from the disordered sphere phase (DS), consisting of random arranged spheres with the majority PS block as I core and the minority PMMA block as a corona, to ordered inverted phases including inverted spheres (IS), inverted cylinders (IC), and inverted hexagonally perforated lamellae (IHPL) with the minority PMMA block comprising the continuum phase, and then to the lamellar (LAM) phase with alternate layers of the two blocks, and finally to the normal cylinder (NC) phase with the majority PS block comprising the continuum phase. The solvent nature and the copolymer solution concentration are shown to be mainly responsible for the inverted phase formation and the phase transition process.

Self-assembly of star block copolymers by dynamic density functional theory

The dynamic mean-field density functional method, driven from the generalized time-dependent Ginzburg-Landau equation, was applied to the mesoscopic dynamics of the multi-arms star block copolymer melts in two-dimensional lattice model. The implicit Gaussian density functional expression of a multi-arms star block copolymer chain for the intrinsic chemical potentials was constructed for the first time. Extension of this calculation strategy to more complex systems, such as hyperbranched copolymer or dendrimer, should be straightforward. The original application of this method to 3-arms block copolymer melts in our present works led to some novel ordered microphase patterns, such as hexagonal (HEX) honeycomb lattice, core-shell HEX lattice, knitting pattern, etc. The observed core-shell HEX lattice ordered structure is qualitatively in agreement with the experiment of Thomas [Macromolecules 31, 5272 (1998)].