n维氢原子的散射态

研究了n维氢原子的散射态性质．给出了精确的按“k/2π标度”归一化的散射态的精确解波函数及相移表达式，讨论了相移的解析性质，获得了束缚-连续跃迁矩阵元的解析计算公式．普通氢原子(n=3)散射态的有关结果作为特例包含在本文的一般结论之中． 关键词： n维氢原子 散射态 精确解 相移 束缚-连续跃迁矩阵元     

Intermolecular Nuclear Relaxations and Molecular Site-Site Pair Correlation Functions in Liquids

Intermolecular nuclear relaxation studies of real liquids and the results of theoretical calculations for model potential functions have provided significant information on the role of molecular interactions in the structure of liquids. The intermolecular proton-proton paircorrelation function (pcf), obtained from the reference interaction site model (RISM) is used as the equilibrium distribution and is used to obtarn an effective force for the calculation of intermolecular proton relaxation rates in liquid benzene, 1,3,5-trideuterobenzene and ethane. For liquid ethane, better agreement with experiment is observed with the pcf obtained from the Monte Carlo simulation than with the RISM result.     

Semiempirical molecular dynamics studies of C60/C70 fullerene oxides: C60O, C60O2 and C70O

The spectral analysis indicates that all isomers of C₆₀O, C₇₀O and C₆₀O₂ have an epoxide-like structure (an oxygen atom bridging across a C–C bond). According to the geometrical structure analysis, there are two isomers of fullerene monoxide C₆₀O (the 5,6 bond and the 6,6 bond), eight isomers of fullerene monoxide C₇₀O and eight isomers of fullerene dioxide C₆₀O₂. In order to simulate the real reaction conditions at 300 K, the calculation of the different isomers of C₆₀O, C₆₀O₂ and C₇₀O fullerene oxides was carried out using the semiempirical molecular dynamics method with two different approaches: (a) consideration of the geometries and thermodynamic stabilities, and (b) consideration of the ozonolysis mechanism. According to the semiempirical molecular dynamic calculation analysis, the probable product of this ozonolysis reaction is C₆₀O with oxygen bridging over the 6–6 bond (C_2v). The most probable product in this reaction contains oxygen bridging across in the upper part of C₇₀ (6–6 bond in C₇₀O-2 or C₇₀O-4) an epoxide-like structure. C₆₀O₂-1, C₆₀O₂-3 and C₆₀O₂-5 are the most probable products for the fullerene dioxides. All of these reaction products are consistent with the experimental results. It is confirmed that the calculation results with the semiempirical molecular dynamics method are close to the experimental work. The semiempirical molecular dynamics method can offer both the reaction temperature effect by molecular dynamics and electronic structure, dipole moment by quantum chemistry calculation.     

Improved Analytical Approximations to the Scattering Solutions of the Schrödinger Equation with a Hyperbolical Potential

Using an improved approximate formula to the centrifugal term, we present arbitrary l-state scattering solutions of the hyperbolic potential. The approximate analytical formula of scattering phase shifts and normalized wavefunctions are presented. All data calculated by the above approximate analytical formula are compared with those obtained by using the numerical integration method in the scattering state cases. We find that this improved approximate formula is better than previous one since the calculated results are in good agreement with those exact ones.     

Synthesis of PANI/rGO composite as a cathode material for rechargeable lithium-polymer cells

Graphene oxide (GO) was synthesized by an improved Hummers method and then reduced with NaBH₄; GO became rGO with regular layered structure. Polyaniline (PANI)/rGO composite was prepared by a adsorption double oxidant method with rGO as a template. Some physical characterization methods (Fourier transform infrared spectroscopy analysis, X-ray diffraction, scanning electron microscope, and transmission electron microscope) were used to analyze the morphology and crystallinity of the composite. The electrochemical properties were characterized by cyclic voltammetry, impedance spectroscopy, galvanostatic charge/discharge, and rate capability. The first discharge specific capacity of the rPANI/rGO and PANI/rGO was 181.2 and 147.8 mAh/g. After 100 cycles, the capacity retention rate was still 90.2 and 88.9% separately, and the coulombic efficiency of batteries is close to 100%. These results demonstrate the composite has exciting potentials for the cathode material of lithium-ion battery.     

水热合成ZnO:Cd纳米棒的微结构及光致发光特性

采用水热法制备了ZnO和不同掺杂浓度的ZnO:Cd纳米棒,通过SEM,XRD、拉曼光谱等的分析,研究了ZnO和ZnO:Cd的微结构并测试分析了其光致发光特性.结果表明,ZnO和ZnO:Cd纳米棒呈六角纤锌矿结构,Cd掺杂使得纳米棒体积更小.由于内部张应力的影响,Cd掺杂使得材料光学带隙减少.当掺杂浓度为2%时,合成的材料光致发光谱中出现了位于2.67 eV处,由导带底和Zn空位(VZn)缺陷能级跃迁造成的蓝光发射峰,并且Cd的掺入使得位于2.90 eV附近的紫光发射峰强度增强,对于研究ZnO蓝紫发光器件具有重要的意义.     

The saturated hydrides of C<Subscript>60</Subscript>:F<Subscript>5</Subscript>F<Subscript>6</Subscript> PK F<Subscript>5</Subscript>F<Subscript>7</Subscript> isomers

The carbon cages composed of pentagons and heptagons (F₅F₇ isomers) are the analogs of fullerenes composed of pentagons and hexagons (F₅F₆ isomers). To provide insight into the structures and stability of the hydrides of F₅F₆ and F₅F₇ isomers, systematical density functional theory calculations are performed on all the 1,812 F₅F₆–C₆₀H₆₀ and 56 F₅F₇–C₆₀H₆₀. The calculated results demonstrate that the isomer with lowest/highest energy has most/fewest fused pentagons for both F₅F₆ and F₅F₇ hydrides and the stability of these hydrides increase with the number of fused pentagons roughly. The lowest energy F₅F₆–C₆₀H₆₀ and F₅F₇–C₆₀H₆₀ are 237.1 and 152.5 kcal/mol lower in energy than the isolated pentagon rule (IPR) C₆₀H₆₀, respectively; however, these two parent cages are 529.6 and 660.0 kcal/mol higher in energy than the IPR C₆₀. The calculations suggest that heptagon-containing cages, not only those violating the IPR can be the candidate cages for fullerene derivatives and the possible repulsion between the added atoms may play an important role in determining the structures and stability of the hydrides of carbon cages.     

Relativistic Scattering States of Coulomb Potential Plus a New Ring-Shaped Potential

In this paper, exact solutions of scattering states of the Klein-Gordon equation with Coulomb potential plus a new ring-shaped potential are studied under the condition that the scalar potential is equal to the vector potential. The normalized wave functions of scattering states on the “k/2π scale” and the calculation formula of phase shifts are presented. Analytical properties of the scattering amplitude are discussed.     

环形非球谐振子势Klein-Gordon方程的束缚态

用分离变量方法讨论了在环形非球谐振子标量势和矢量势相等条件下的Klein-Gordon方程的束缚态解.给出了用广义连带勒让得多项式表示的归一化角向波函数和用合流超几何函数表示的归一化径向波函数，获得了精确的束缚态能谱方程. 关键词： 环形非球谐振子势 Klein-Gordon方程 束缚态     

Scattering states of modified PSschl-Teller potential in D-dimension

We present a new approximation scheme for the centrifugal term,and apply this new approach to the Schrdinger equation with the modified Pschl-Teller potential in the D-dimension for arbitrary angular momentum states.The approximate analytical solutions of the scattering states are derived.The normalized wave functions expressed in terms of the hypergeometric functions of the scattering states on the k/2π scale and the calculation formula of the phase shifts are given.The numerical results show that our results are in good agreement with those obtained by using the amplitude-phase method(APM).