NOTE ON A MCMILLAN-LIKE Tc FORMULA

In this letter, we present an analysis to understand why the McMillan-like T_c fornula: T_c=1.134ωlog(1-1.02μ^*+0.476λ)exp{-1+1.604λ/λ-μ^*(1+0.604μ)}, proposed in a previous paper by the authcrs,applies to crystalline superconductors satisfactorily but Iess satisfactorily to non-crystalline ones.     

A Compact Exponential Operator for Generating Rotating and Squeezing Transformations

We point out that the compact exponential operator V≡exp[-i(λ₁Q²-λ₂P²)/2] (where λ₁, λ₂ are real;P and Q are momentum and coordinate operators, respectively;the units of h=m=ω=l is taken, m and ω are harmonic oscillator's mass and'frequency, respectively) is a generalized single-mode squeeze operator which can generate mixed squeezing and rotating transformations. The decomposition of V as a product of a squeeze operator and a rotating operator is derived through the technique of integration within an ordered product.The fluctuation in quadrature phases for the squeezed vacuum state generated by V is analyzed.     

THE LINEAR ELIASHBERG EQUATION

Fn the present paper, the linear Eliashberg equation is converted into a new integral equation and from it, the following T_C formula is derived analytically in the weak coupling limit:T_c=28/πωlog·(πlog/π_c)μ^*/λ^*-μ^* exp{-1+λ/λ-μ^*}, where In γ=C=0.5772 is the Eater constant.     

一个新的自由能函数对介电高弹薄膜的多组等双轴预拉伸下力电耦合实验的预测

当介电高弹聚合物薄膜被施以面内等双轴预拉伸后, 受到厚度方向的电压作用时, 薄膜在力场和电场共同作用下产生大变形. 电场采用Maxwell应力分析, 力场采用橡胶弹性模型分析. 拟合这类变形的常用橡胶弹性模型主要有Neo-Hookean, Arruda-Boyce, Gent等模型. 这些模型对实验数据的定量拟合存在不同程度的偏差. 通过对实验数据的分析, 结合数学方法, 提出了一个新的自由能函数模型. 通过该模型对VHB4905介电高弹聚合物薄膜的多组等双轴预拉伸电力耦合实验进行拟合, 并以Neo-Hookean, Gent模型作为对照, 结果与实验数据拟合很好, 比对照模型的偏差明显缩小.     

Non-Relativistic Phase Shifts for Scattering on Generalized Radial Yukawa Potentials

Non-relativistic phase shifts for a generalized Yukawa potential V(r) =-V_0( e~(-αr)/r)-V_1( e~(-2αr)/r~2) are studied by the amplitude-phase method and by a frequently used analytic method based on a Pekeris-type approximation of power-law potential terms.Small variations of V_1 seem to have marginal effects on the effective potential and on exact phase shifts.However,as pointed out in this study,a Pekeris-type approximation in scattering applications often implies serious distortions of both effective potentials and phase shifts.The Pekeris-type based analytic approximation in this study seems to give low-quality scattering results for this model potential at low energies.     

A Possible Generalization of Jaynes-Cummings Model with Degenerate Spectrum

We propose a generalized Jaynes-Cummings model (JCM) for three two-level atoms and three-mode radiation field with the interaction being H₁=λ(a₁⁺a₂⁺σ_1-σ_2-+a₂⁺a₃⁺σ_2-σ_3-+a₁⁺a₃⁺σ_1-σ_3-+H.C.). This model is characteristic of possessing partly degenerate spectrum. Some transition process of this system is calculated.     

Positivity of energy in five dimensional classical unified field theories, II

Five dimensional classical unified field theories as well as Yang-Mills theory with gauge group U(1), are described in terms of a Lorentzian five dimensional space V₅ with metric tensor γβ which admits a space-like Killing vector ζ. It is assumed that: (1) V₅ has the topology of V₄ x S¹, S¹ is a circle and V₄ is a four dimensional Lorentzian space that is asymptotically flat and (2) the Einstein tensor Γ_β of V₅ satisfies Γ_β Uυ^{β 0} where U and υ are future oriented time-like vectors with γ_βυζ^β = 0. The spinor approach of Witten [4], Nester [3] and Moreschi and Sparling [5] is used to show that the conserved five dimensional energymomentum vector P = ifΓ_β = 0 then V₅ must admit a time-like Killing vector. Lichnerowicz's results [1] then imply that V₅ must be flat. A lower bound for P⁴ (the mass) similar to that found by Gibbons and Hull [6] is obtained.     

Exact Solutions of the Morse-like Potential,Step-Up and Step-Down Operators via Laplace Transform Approach

We intend to realize the step-up and step-down operators of the potential V (x) = V₁ e ^2βx + V₂ e ^βx. It is found that these operators satisfy the commutation relations for the SU(2) group. We find the eigenfunctions and the eigenvalues of the potential by using the Laplace transform approach to study the Lie algebra satisfied the ladder operators of the potential under consideration. Our results are similar to the ones obtained for the Morse potential (β → -β).     

Exact Solutions of Schrödinger Equation with Improved Ring-Shaped Non-Spherical Harmonic Oscillator and Coulomb Potential

We propose improved ring shaped like potential of the form, V(r,θ)=V(r)+(?²/2Mr²) [(βsin²θ +γcos²θ +λ)/sin θcosθ]² and its exact solutions are presented via the Nikiforov-Uvarov method. The angle dependent part V(θ)=(?²/2Mr²) [(βsin²θ +γcos²θ +λ)/sin θcosθ]², which is reported for the first time embodied the novel angle dependent (NAD) potential and harmonic novel angle dependent potential (HNAD) as special cases. We discuss in detail the effects of the improved ring shaped like potential on the radial parts of the spherical harmonic and Coulomb potentials.     

AlH~+离子5个Λ-S态和10个?态的光谱性质以及激光冷却的理论研究

利用考虑Davidson修正的内收缩多参考组态相互作用(icMRCI+Q)方法结合相关一致基组aug-ccpV6Z计算了AlH~+离子前两个离解极限对应的5个Λ-S态和10个?态的势能曲线.为了提高势能曲线的可靠性和精确性,计算中考虑了自旋轨道耦合效应、芯电子价电子相关和标量相对论修正以及将势能外推至完全基组极限.基于得到的势能曲线,获得了束缚和准束缚的4个Λ-S态和8个?态的光谱常数和振动能级,与已有的实验结果符合.计算了2(1/2)→X~2Σ_(1/2)~+和A~2Π_(3/2)→X~2Σ_(1/2)~+跃迁的跃迁偶极距.利用计算的精确的势能曲线和跃迁偶极矩,获得了2(1/2)~(第一势阱)(υ′=0, 1)→X~2Σ_(1/2)~+(υ′′)和A~2Π_(3/2)(υ′=0, 1)→X~2Σ_(1/2)~+(υ′′)跃迁的高度对角化分布的Franck-Condon因子(f_(00)和f_(11))和大的振动分支比;预测了2(1/2)~(第一势阱)(υ′=0, 1)和A~2Π_(3/2)(υ′=0, 1)态短的自发辐射寿命和窄的辐射宽度,这适合于AlH~+离子的快速激光致冷.所需的3束激光冷却波长都在紫外区域.这些结果表明了激光冷却AlH~+离子的可行性.此外,评估了自旋轨道耦合效应对光谱常数、振动能级和激光冷却AlH~+离子的影响.     

Formation of Li2O in a chemically Li-intercalated V2O5 xerogel

We studied the electronic structure of a chemically Li-intercalated V₂O₅ xerogel. The technique used in the study was V 2p and O 1s X-ray absorption spectroscopy (XAS). The V ions in the as-prepared V₂O₅ xerogel are mostly in a pentavalent V⁵⁺ state. The spectra show that the V ions are partially reduced to V⁴⁺ and V³⁺ states upon Li intercalation. The results also show that low Li intercalation (x<1) affects mostly O 2p–V 3d mixed states, whereas for higher Li intercalation (x>1), this mechanism saturates and leads to Li₂O formation.     

Semi-Relativistic Reflection and Transmission Coefficients for Two Spinless Particles Separated by a Rectangular-Shaped Potential Barrier

A generalized Schrödinger approximation, due to Ikhdair & Sever, of the semi-relativistic two-body problem with a rectangular barrier in (1+1) dimensions is compared with exact computations. Exact and approximate transmission and reflection coefficients are obtained in terms of local wave numbers. The approximate transmission and reflection coefficients turn out to be surprisingly accurate in an energy range |ε-V₀|<2μ c², where μ is the reduced mass, ε the scattering energy, and V₀ the barrier top energy. The approximate wave numbers are less accurate.     

白光LED用蓝绿色荧光粉Sr1-xBax Al2O4:Eu2+的发光性质

采用高温固相法在还原气氛中合成Sr1-xBaxAl2 O4:Eu2+荧光材料.XRD显示,当钡掺杂量x＜0.4时,对应样品主要为单斜SrAl2 O4晶体结构;当x≥0.4时,对应样品主要为简单六方BaAl2 O4晶体结构.在360nn激发下,样品的发射光谱随x的增加由单一的绿光发射(λmax=516nm)逐渐转变为蓝绿...     

Solutions to Buoyancy-Drag Equation for Dynamical Evolution of Rayleigh-Taylor and Richtmyer-Meshkov Mixing Zone

With a self-similar parameter b( A_t ) = H_i /λa_i, where A_t is the Atwood number, H_i andλ_i are the amplitude and wavelength of bubble (i = 1) and spike (i =
2) respectively, we derive analytically the solutionsto the Buoyancy-Drag equation recently proposed for dynamical evolution of Rayleigh-Taylor and Richtmyer-Meshkov mixing zone.Numerical solutions are obtained with a simple form of b(A_t ) = 1/(1 + A_t ) and comparisons with recent LEM (linear electric motor) experiments are made, and an agreement is found with properly chosen initial conditions.     

Energy Spectrum,g Factors,Strain-Induced Level-Splittingsand R-Line Thermal Shift of MgO:V2+

Traditional ligand-field theory has to be improved by taking into account both pure electronic contribution and electron-phonon interaction one (including lattice-vibrational relaxation energy). By means of improved ligand-field theory, the R line, t₂^{3 2}T₁ and t₂^{3 2}T₂ lines, t₂² (³T₁)e⁴T₂, t₂² (³T₁)e⁴T₁ and t₂ e²(⁴A₂)⁴T₁ bands, g factors of t₂^{3 4}A₂ and t₂^{3 2}E, four strain-induced level-splittings and R-line thermal shift of MgO:V₂₊ have been calculated. The results are in very good agreement with the experimental data. It is found that for MgO:V₂₊, the contributions due to electron-phonon interaction (EPI) come from the first-order term; the contributions from the second-order and higher terms are insignificant. In thermal shift of R line of MgO:V₂₊, the temperature-dependent contribution due to EPI is dominant. The results obtained in this work may be used in theoretical calculations of other effects of EPI.     

Theoretical Calculation of Drag Component of Tensor M in Quantizing Magnetic Field

All the previous homogeneous theories result in M_ΧΧ = 0 which are at variance with the experimental data. It is for this reason, previous theories have consistently used experimental value of M_ΧΧ in calculating thermopower tensor S. The inhomogeneous and non-equilibrium formalism proposed by Dyakin et al. was generalized to including both transverse and longitudinal modes of electron-phonon interaction and considering the broadening of the Landau level. The resulting formula gives theoretical values of M_ΧΧ for GaAs/AlGaAs heterojunctions which are in accord with experimental ,data at oscillation phases but (λ_p/)^l/2 times smaller than experimental data for T = 1.275 K, 2.937 K, 5.005 K and C = 0.20 where λ_p and are the phonon mean free path and effective thickness of the heterojunctions. By means of the semi-empirical formula of MzZ with extra factor (λ_p/)^l/2 in, phonon drag magnetothermopower can be calculated from theoretical values of M_yΧ and M_ΧΧ.     

Lithium ion batteries cathode material: V2O5

Among all the known electrode materials, vanadium pentoxide (V₂O₅) has high reversible capacity. It is a very valuable material for research of the complexity, rich structure and morphology. However, it also has some disadvantages, such as poor cycle stability, low discharge voltage, low conductivity and Li⁺ diffusion coefficient. In this regard, researchers have carried out a lot of research, such as using various methods to improve the nanostructures, introducing heterostructures, introducing point defects or cation doping in the crystal structure, etc. The electrochemical performance of V₂O₅ has been significantly improved in reversible capacity, high-rate capacity and long-term cycle stability. In this paper, V₂O₅ based nanostructure with different chemical composition are briefly introduced, and it covers V₂O₅ nanomaterials with different morphology, including 1D nanorods, nanobelts, nanotubes, 2D leaf like nanosheets and other nanosheets, and 3D hollow structures, porous nanostructures, porous eggshell microsphere structures. The composite nanomaterials of V₂O₅ and different carbonaceous supports are also introduced. Finally, the V₂O₅ composite materials doped with cations are discussed. The electrochemical performance of V₂O₅ based electrode can be improved effectively by obtaining appropriate nanostructure and optimized chemical composition.     

Lithium insertion into V6O13 studied by deformation electron density refinement of single-crystal X-ray data

Deformation electron density refinement of single-crystal X-ray data has been performed for V₆O₁₃ and for one of its electrochemically lithiated phases Li₂V₆O₁₃. The electron rearrangement associated with lithium insertion is extracted by subtracting the two derived electron deformation models from one another. The reduction (from nominally V⁵⁺ to V⁴⁺) of one of the three independent vanadium atoms (V2) in the asymmetric unit can be identified, along with significant changes in the effective charges on certain of the oxygens.     

Strain-induced magnetism in ReS_2 monolayer with defects

We investigate the effects of strain on the electronic and magnetic properties of ReS_2 monolayer with sulfur vacancies using density functional theory.Unstrained ReS_2 monolayer with monosulfur vacancy(V_s) and disulfur vacancy(V_(2S))both are nonmagnetic.However,as strain increases to 8%,V_S-doped ReS_2 monolayer appears a magnetic half-metal behavior with zero total magnetic moment.In particular,for V_(2S)-doped ReS_2 monolayer,the system becomes a magnetic semiconductor under 6%strain,in which Re atoms at vicinity of vacancy couple anti-ferromagnetically with each other,and continues to show a ferromagnetic metal characteristic with total magnetic moment of 1.60μb under 7%strain.Our results imply that the strain-manipulated ReS_2 monolayer with V_S and V_(2S) can be a possible candidate for new spintronic applications.     

Lattice Model with Traveling Compactons

We introduce a purely anharmonic lattice model with specific double-well on-site potential, which admits traveling compacton-like solitary wave solutions by the inverse method with the help of Mathematica. By properly choosing the shape of the solitary wave solution of the system, we can calculate the parameters of the specific on-site potential. We also found that the localization of the compacton is related to the nonlinear coupling parameter Cn1 and the potential parameter Vo of the on-site potential, and the velocity of the propagation of the compacton is determined by the localization parameter q and the potential parameter Vo. Numerical calculation results demonstrate that the narrow compacton is unstable while the wide compacton is stable when they move along the lattice chain.