The Singularity of Kontsevich’s Solution for QH<Superscript>*</Superscript>(CP<Superscript>2</Superscript>)

In this paper we study the nature of the singularity of the Kontsevichs solution of the WDVV equations of associativity. We prove that it corresponds to a singularity in the change of two coordinates systems of the Frobenius manifold given by the quantum cohomology of CP². Mathematics Subject Classifications (2000) 53C99, 32D99, 14N35, 88A99.     

As-rich (2 × 2) surface reconstruction on GaAs(111)A

The atomic structures and the formation processes of the Ga- and As-rich (2×2) reconstructions on GaAs(111)A have been studied. The Ga-rich (2×2) structure is formed by heating the As-rich (2×2) phase, but the reverse change hardly occurs by cooling the Ga-rich surface under the As₂ flux. Only when the Ga-rich (2×2) surface covered with amorphous As layers was thermally annealed, the As-rich (2×2) surface is formed. The As-rich (2×2) surface consists of As trimers located at a fourfold atop site of the outermost Ga layer, in which the rest-site Ga atom is replaced by the As atom.     

Atomic and nanostructures of monolayer c(2 × 2)NiN on Cu(0 0 1)

Structures of monolayer nickel nitride (NiN) on Cu(0 0 1) surface are studied by X-ray photoelectron spectroscopy (XPS), low energy electron diffraction (LEED) and scanning tunneling microscopy (STM). Formations of Ni–N chemical bonds and NiN monolayer at the surface are confirmed by XPS on the N-adsorbed Cu(0 0 1) surfaces after Ni deposition and subsequent annealing to 670 K. A c(2 × 2) structure is always observed in the LEED patterns, which is a quite contrast to the (2 × 2)p4g structure observed usually at the N-adsorbed Ni(0 0 1) surface. Atomic images by STM indicate the mixture of Ni–N and Cu–N structures at the surface. Density of the trenches on the N-saturated surface decreases and the grid pattern on partially N-covered surfaces becomes disordered with increasing the Ni coverage. These results are attributed to the decrease of the surface compressive stress at the N-adsorbed Cu surface by mixing Ni atoms.     

类锂等电子系列(1s2p2p)~4 P~e和(1s2s2p)~4 P~0态的能量和精细结构研究

利用改进的马鞍点方法,截断变分方法,并考虑能量的相对论修正和质量极化效应,计算和研究了类理等电子系列的两个四重态（１ｓ２ｐ２ｐ）４Ｐ０和（１ｓ２ｓ２ｐ）４Ｐｅ态的精细结构和平均跃迁波长,并与实验和其它理论计算结果进行了比较。     

Calculation of refractive indices for the (NH<Subscript>2</Subscript>CH<Subscript>2</Subscript>COOH)<Subscript>2</Subscript> · HNO<Subscript>3</Subscript> crystal

The refraction R of the diglycine nitrate (DGN) crystal, (NH₂CH₂COOH)₂ · HNO₃, in the para-and ferroelectric phases has been calculated in the model of noninteracting diatomic chemical bonds of the elementary unit cell of the crystal on the basis of the longitudinal and transversal polarizabilities of these bonds. The calculated magnitudes of the principal refractive indices n _p , n _m , and n _g and the orientations of the optical indicatrix of the crystal agree satisfactorily with experimentally observed values. Introducing the coefficient of Lorenz-Lorentz interaction x into the corresponding formula permits better agreement of the calculated and experimental refractive indices of DGN crystal to be obtained. The temperature changes of these x coefficients upon the ferroelectric phase transition in the DGN crystal have been analyzed.     

Dynamic magnetic susceptibility of compounds in Gd<Subscript>5</Subscript>Si<Subscript>2−x</Subscript>Ge<Subscript>2−x</Subscript>Sn<Subscript>2x</Subscript> (2x = 0 − 0.1) system

The dynamic magnetic susceptibility (χ_ac) of magnetically ordered Gd₅Si_2?xGe_2?xSn_2x compounds with the partial substitution for silicon and germanium atoms by isovalent tin atoms (2x = 0 ? 0.1) has been investigated experimentally. From the temperature dependence of χ_ac the Curie temperatures of these alloys are determined. It is established that tin-doped alloys have higher Curie temperatures as compared to Gd₅Si₂Ge₂ (ΔT _C ≈ 15 K).     

Hydrogen bond and exchange interaction in the (CuSO<Subscript>4</Subscript>)(en)·2H<Subscript>2</Subscript>O and (CuSO<Subscript>4</Subscript>)(en)·2D<Subscript>2</Subscript>O organometallic compounds

The influence of the replacement of hydrogen with deuterium in molecules of water of crystallization in the structure of the (CuSO₄)(en) · 2H₂O and (CuSO₄)(en)·2D₂O organometallic compound molecules on exchange interaction between copper ions was studied. The X-ray structural data and the data on angular anisotropy of the effective g-factor of Cu²⁺ ions in both compounds show that distortions of the initial structure caused by deuteration are minimum. A comparative analysis of the width of the exchange coupled EPR lines of the two compounds is indicative of a decrease in the exchange parameter in the deuterated sample, which substantiates the participation of H-bonds in exchange interactions in the systems studied.     

Temperature dependence of the quenching of N<Subscript>2</Subscript> (C <Superscript>3</Superscript>Π<Subscript>u</Subscript>) by N<Subscript>2</Subscript> (X) and O<Subscript>2</Subscript> (X)

The temperature dependences of the quenching rate constants of the states N₂ (${\rm C} \ {^{3}{ \rm \Pi }_{u}}${\rm C} \ {^{3}{ \rm \Pi }_{u}} v^′=0,1) by N₂ (X) and of the state N₂ (${\rm C} \ {^{3}{ \rm \Pi }_{u}} \ v^{\prime}=0${\rm C} \ {^{3}{ \rm \Pi }_{u}} \ v^{\prime}=0) by O₂ (X) are studied. Time-resolved light emission from the gas was analyzed in the temperature range from 300 K to 210 K keeping the gas at constant density. In case of quenching by N₂ (X), the quenching rate constant for the vibrational level v^′= 0 increases by (13 ±3)% with gas cooling whereas the quenching rate constant for v^′= 1 decreases by (5.0 ±2.5)% in this temperature range. For quenching by O₂ (X), the quenching rate constant decreases by (3 ±2)% with gas cooling. The temperature variation of the N₂ (C ³Π_u v^′=0) emission intensity for pure nitrogen and dry air are calculated using the obtained quenching rate constants and is compared with the experimental data available in the literature.     

类锂体系(Z=1120) 1s24s -1s2np(5≤n≤9)跃迁能和振子强度的理论计算

利用全实加关联的方法计算类锂体系(Z=11~20) 1s24s -1s2np(5≤n≤9)的跃迁能, 将相对论效应(电子动能的相对论修正,Darwin项,电子-电子接触项以及轨道-轨道相互作用)和质量极化效应作为微扰,计算了它们对体系能量的修正．利用得到的波函数和跃迁能计算了核电荷Z=11~20的类锂离子的1s24s -1s2np(5≤n≤9)偶极跃迁的长度、速度和加速度三种规范下的振子强度,与现有的实验数据比较,结果符合得很好.     

类铍离子磁四极M2 2s2 1S0-2s2p 3 P2(Z=10-103)禁戒跃迁

利用全相对论多组态:Dirac-Fock方法系统地计算了高离化类铍离子的磁四极M2 2s2 1S0-2s2p3P2 (Z=10-103)自旋禁戒跃迁的能级间隔、跃迁概率和振子强度,计算中考虑了重要核的有限体积效应,Breit修正和QED修正,所得结果和最近的实验数据以及理论值进行了比较,结果表明:高原子序数的高电荷离子(Z≥70)磁四极M2自旋禁戒跃迁几乎可以和中性原子的光学允许跃迁相比拟,不仅在天体等离子体中,在ICF和MCF高温激光等离子体中,磁四极自旋禁戒跃迁和其他自旋禁戒跃迁(磁偶极、电四极)一样不容忽视,在双电子复合、不透明度、自由程等理论计算中应该考虑其影响.     

Ab initio study of Yb on the Ge(111)–(3 × 2) and Si(111)–(3 × 2) surfaces

The surface reconstruction, 3 × 2, induced by Yb adsorption on a Ge (Si)(111) surface has been studied using first principles density-functional calculation within the generalized gradient approximation. The two different possible adsorption sites have been considered: (i) H₃ (this site is directly above a fourth-layer Ge (Si) atom) and (ii) T₄ (directly above a second-layer Ge (Si) atom). We have found that the total energies corresponding to these binding sites are nearly the same, indeed for the Yb/Ge (Si)(111)–(3 × 2) structure the T₄ model is slightly energetic by about 0.01 (0.08) eV/unitcell compared with the H₃ model. In particular for the Ge sublayer, the energy difference is small, and therefore it is possible that the T₄, H₃, or T₄H₃ (half of the adatoms occupy the T₄ adsorption site and the rest of the adatoms are located at the H₃ site) binding sites can coexist with REM/Ge(111)–(3 × 2). In contrast to the proposed model, we have not determined any buckling in the Ge = Ge double bond. The electronic band structures of the surfaces and the corresponding natures of their orbitals have also been calculated. Our results for both substrates are seen to be in agreement with the recent experimental data, especially that of the Yb/Si(111)–(3 × 2) surface.     

用原子轨道强耦合方法研究H(1s) + H(2s)碰撞的反应截面

采用单电子的双中心原子轨道强耦合方法,研究了1-100 碰撞体系的激发、俘获和失去电子总截面,并分别与前人的理论结果和实验结果进行了比较。研究表明,采用双中心原子轨道强耦合方法得到的 体系激发到 过程和失去电子过程的截面与实验符合很好。     

Superconductivity at normal pressure in κ-(BEDT-TTF)<Subscript>2</Subscript>Cu[N(CN)<Subscript>2</Subscript>]Cl crystals

Single crystals of the κ-(BEDT-TTF)₂Cu[N(CN)₂]Cl cation-radical salt are obtained. These crystals exhibit metallic properties and pass to a superconducting state with T_c = 11.5 K at ambient pressure.     

钪原子的自电离里德伯能级3d4s(~1D_2)nf~2D_(3/2),3d4s(~1D_2)nf~2F_(5/2)和3d4s(~1D_2)np~2D_(3/2)的理论研究

在多通道量子亏损理论框架下,利用相对论多通道理论,分别在冻结实近似和考虑偶极极化下计算钪原子的Jπ=(3/2)-,(5/2)-的三个收敛于[Ar]3d4s(1D2)的自电离里德伯系列的能级.对3d4s(1D2)np2D3/2和3d4s(1D2)nf2F5/2这两个系列,计算结果表明,考虑偶极极化效应后,理论计算和实验测量的量子数亏损之差普遍小于0.01.而对3d4s(1D2)nf2D3/2系列,考虑偶极极化效应后的结果和仅考虑冻结实的结果比较接近,理论计算和实验测量的量子数亏损之差普遍在0.04左右.     

Green’s function approach to the low temperature properties of Cs<Subscript>2</Subscript>CuCl<Subscript>4</Subscript>: anisotropy effects

We have studied the effect of both axial and transverse anisotropy on the critical field and thermodynamic properties of the field induced three dimensional antiferromagnetic Heisenberg model on the frustrated hexagonal lattice for Cs₂CuCl₄ compound. The spin model is mapped to a bosonic one with the hard core repulsion constraint and the Green’s function approach has been implemented to get the low energy spectrum and the corresponding thermodynamic properties. To find the critical field (B _c ) we have looked for the Bose-Einstein condensation of quasi-particles (magnons) which takes place when the magnon spectrum vanishes at the ordering spiral wave vector. We have also obtained the dispersion of magnon spectrum in the critical magnetic field for each anisotropy parameter to find the spiral wave vector where the spectrum gets its minimum. The magnon energies show a linear dispersion relation close to the quantum critical point. The effect of hard core boson interaction on the single particle excitation energies leads to a temperature dependence of the magnon spectrum versus magnetic field. We have also studied the behavior of specific heat and static structure factor versus temperature and magnetic field.     

Optical solitons and periodic solutions of the (2 + 1)-dimensional nonlinear Schrödinger's equation

In this Letter, we consider the $(2+1)$-dimensional nonlinear Schrödinger's equation. With the aid of the Jacobian elliptic equation, we derive the exact bright soliton, dark soliton, singular soliton and periodic solutions of this equation expressed in terms of trigonometric functions, hyperbolic functions and Jacobian elliptic functions, respectively. Finally, for certain parametric values, we plot three dimensional graphics of modulus, real and imaginary parts of some solutions, which can help one better understand their dynamical behavior via their graphics analysis.     

Intense 2.7 µm emission and structural origin in Er³⁺-doped bismuthate (Bi₂O₃-GeO₂-Ga₂O₃-Na₂O) glass

The 2.7 μm emission properties in Er³⁺-doped bismuthate (Bi₂O₃-GeO₂-Ga₂O₃-Na₂O) glass were investigated in the present Letter. An intense 2.7 μm emission in Er³⁺-doped bismuthate glass was observed. It is found that Er³⁺-doped bismuthate glass possesses high spontaneous transition probability A (65.26 s^-1) and large 2.7 μm emission cross section σ_em (9.53×10^-21?cm²) corresponding to the stimulated emission of Er³⁺:⁴I_11/2→⁴I_13/2 transition. The emission characteristic and energy transfer process upon excitation of a conventional 980 nm laser diode in bismuthate glass were analyzed. Additionally, the structure of bismuthate glass was analyzed by the Raman spectrum. The advantageous spectroscopic characteristics of Er³⁺ single-doped bismuthate glass together with the prominent thermal property indicate that bismuthate glass might become an attractive host for developing solid-state lasers around 2.7 μm.