热核表面能的Thomas－Fermi统计模型理论

用Ｓｅｙｌｅｒ－Ｂｌａｎｃｈａｒｄ动量相关非定域相互作用的含温Ｔｈｏｍａｓ－Ｆｅｒｍｉ统计理论，对半无穷大核物质模型计算了核物质表面能系数σ（Ｔ，δ）随温度Ｔ和不对称度δ的变化，发现在低温Ｔ≤５ＭｅＶ和不对称度δ≤０．２时，可以近似写成σ（Ｔ，δ）＝σ０（Ｔ）［１＋Ｋ（Ｔ）δ２］，其中σ０（Ｔ）和Ｋ（Ｔ）可以拟合成温度Ｔ的二次函数．     

Analytic continuation of Taylor series and the boundary value problems of some nonlinear ordinary differential equations

We compare and discuss the respective efficiency of three methods (with two variants for each of them), based respectively on Taylor (Maclaurin) series, Padé approximants and conformal mappings, for solving quasi-analytically a two-point boundary value problem of a nonlinear ordinary differential equation (ODE). Six configurations of ODE and boundary conditions are successively considered according to the increasing difficulties that they present. After having indicated that the Taylor series method almost always requires the recourse to analytical continuation procedures to be efficient, we use the complementarity of the two remaining methods (Padé and conformal mapping) to illustrate their respective advantages and limitations. We emphasize the importance of the existence of solutions with movable singularities for the efficiency of the methods, particularly for the so-called Padé-Hankel method. (We show that this latter method is equivalent to pushing a movable pole to infinity.) For each configuration, we determine the singularity distribution (in the complex plane of the independent variable) of the solution sought and show how this distribution controls the efficiency of the two methods. In general the method based on Padé approximants is easy to use and robust but may be awkward in some circumstances whereas the conformal mapping method is a very fine method which should be used when high accuracy is required.     

A new analytical and numerical treatment for singular two-point boundary value problems via the Adomian decomposition method

Based on the Adomian decomposition method, a new analytical and numerical treatment is introduced in this research to investigate linear and non-linear singular two-point BVPs. The effectiveness of the proposed approach is verified by several linear and non-linear examples.     

雪茄形铷原子玻色-爱因斯坦凝聚中单极子模的朗道阻尼和频移

采用含时哈特里-福克-博戈留波夫近似研究雪茄形铷原子玻色-爱因斯坦凝聚中单极子模的朗道阻尼和频移. 通过考虑元激发的实际弛豫及其各弛豫间的正交关系改进原有方法, 并由此给出计算朗道阻尼和频移的新公式. 此外, 令凝聚体边界处动能密度为零代替令基态能量极小以改进原消除三模耦合矩阵元的方法. 通过这些改进, 同时计算阻尼和频移, 并讨论它们的温度依赖, 所得理论结果都与实验符合. 关键词： 玻色-爱因斯坦凝聚 朗道阻尼和频移 哈特里-福克-博戈留波夫近似 托马斯-费米近似     

Variation and series approach to the Thomas-Fermi equation

The Thomas-Fermi equation describing the screening of the Coulomb potential inside heavy neutral atoms is reconsidered. An accurate representation for its numerical solution was obtained by means of the variational principle. The proposed new solution has more precise asymptotic behaviour at large distances from the origin and allows us to obtain the exact value of the initial slope. The obtained new variational solution can also be developed in power series similar to the Baker’s ones but more precise even than some series solutions that have been recently obtained within the homotopy analysis method and a modified variational method.     

Efficient Implementation of a Spectral-Tau Method for a Class of Two-Point Boundary-Value and Initial-Boundary-Value Problems

A simple and efficient spectral method for solving the second, third order and fourth order elliptic equations with variable coefficients and nonlinear differential equations is presented. It is different from spectral-collocation method which leads to dense, ill-conditioned matrices. The spectral method in this paper solves for the coefficients of the solution in a Chebyshev series, leads to discrete systems with special structured matrices which can be factorized and solved efficiently. We also extend the method to boundary value problems in two space dimensions and solve 2-D separable equation with variable coefficients. As an application, we solve Cahn-Hilliard equation iteratively via first-order implicit time discretization scheme. Ample numerical results indicate that the proposed method is extremely accurate and efficient.     

Solution of the Thomas-Fermi problem for continuous,spherical, positive charge distribution

A method to make anab initio calculation of the free energy of small drops of liquid metal is presented. The model chosen involves the replacing of the positive ion cores by an equivalent continuous spherical distribution of charge. The Thomas-Fermi potential is calculated as a starting point for a Hartree-Fock self-consistent field calculation. The results of the Thomas-Fermi calculation are reported as an example of the preliminary calculations.Research supported under NSF Grant #20884.     

Coulomb effect in rotating nuclei in the Thomas-Fermi approach

The effect of nuclear Coulomb potential in rotating nuclei has been studied in the Thomas-Fermi approach. The numerical calculations of typical rotating nuclei show that Coulomb potential plays an important role in the rotational mass regions 150–190 and >224.     

Quantum dot with N interacting electrons confined in a power-law external potential

The ground-state physical properties, such as electron density, chemical potential, and total energy, of a two-dimensional quantum dot with N interacting electrons confined in a power-law external potential are numerically determined by the Thomas-Fermi approximation. The effect of the confining potential on properties such as electron density and chemical potential is examined for both interacting and non-interacting systems. It is shown that the results of the calculations are in excellent agreement with those given in the literature. The results indicate that interactions and the shape of the confinement affect the density and thus the ground-state properties of the electrons significantly.     

球对称铷原子玻色-爱因斯坦凝聚中单极子模的朗道阻尼和频移

采用含时哈特里-福克-博戈留波夫近似研究球对称铷原子玻色-爱因斯坦凝聚中单极子模的朗道阻尼和频移,并用现有实验和数值模拟研究的粒子数和囚禁频率参量,解析计算了阻尼系数和频移大小及其它们的温度依赖.计算中,考虑元激发的实际弛豫及其各弛豫间的正交关系以获得阻尼和频移计算公式,把基态波函数取为高斯分布函数的一级近似以消除三模耦合矩阵元的发散.我们的计算结果与数值模拟结果和实验结果分别进行直接和间接地对比,讨论和说明了我们理论方法的合理性.