On Evaluation of Overlap Integrals with Noninteger Principal Quantum Numbers

By use of complete orthonormal sets of ψ^α exponential-type orbitals (ψ^α-ETOs,α=1,0,-1,-2,...) the series expansion formulas for the noninteger n Slater-type orbitals (NISTOs) in terms of integer n Slater-type orbitals (ISTOs) are derived. These formulas enable us to express the overlap integrals with NISTOs through the overlap integrals over ISTOs with the same and different screening constants. By calculating concrete cases the convergence of the series for arbitrary values of noninteger principal quantum numbers and screening constants of NISTOs and internuclear distances is tested. The accuracy of the results is quite high for quantum numbers, screening constants and location of STOs.     

One-range Addition Theorems for Noninteger n Slater Functions using Complete Orthonormal Sets of Exponential Type Orbitals in Standard Convention

By the use of complete orthonormal sets of ${\psi ^{(\alpha^{\ast})}}$ -exponential type orbitals ( ${\psi ^{(\alpha^{\ast})}}$ -ETOs) with integer (for α ^* = α) and noninteger self-frictional quantum number α ^*(for α ^* ≠ α) in standard convention introduced by the author, the one-range addition theorems for ${\chi }$ -noninteger n Slater type orbitals ${(\chi}$ -NISTOs) are established. These orbitals are defined as follows $$\begin{array}{ll}\psi _{nlm}^{(\alpha^*)} (\zeta ,\vec {r}) = \frac{(2\zeta )^{3/2}}{\Gamma (p_l ^* + 1)} \left[{\frac{\Gamma (q_l ^* + )}{(2n)^{\alpha ^*}(n - l - 1)!}} \right]^{1/2}e^{-\frac{x}{2}}x^{l}_1 F_1 ({-[ {n - l - 1}]; p_l ^* + 1; x})S_{lm} (\theta ,\varphi )\\ \chi _{n^*lm} (\zeta ,\vec {r}) = (2\zeta )^{3/2}\left[ {\Gamma(2n^* + 1)}\right]^{{-1}/2}x^{n^*-1}e^{-\frac{x}{2}}S_{lm}(\theta ,\varphi ),\end{array}$$ where ${x=2\zeta r, 0<\zeta <\infty , p_l ^{\ast}=2l+2-\alpha ^{\ast}, q_l ^{\ast}=n+l+1-\alpha ^{\ast}, -\infty <\alpha ^{\ast} <3 , -\infty <\alpha \leq 2,_1 F_1 }$ is the confluent hypergeometric function and ${S_{lm} (\theta ,\varphi )}$ are the complex or real spherical harmonics. The origin of the ${\psi ^{(\alpha ^{\ast})} }$ -ETOs, therefore, of the one-range addition theorems obtained in this work for ${\chi}$ -NISTOs is the self-frictional potential of the field produced by the particle itself. The obtained formulas can be useful especially in the electronic structure calculations of atoms, molecules and solids when Hartree–Fock–Roothan approximation is employed.     

Dy2 AlFe13 Mn3 化合物的本征磁致伸缩

通过X-射线衍射及磁测量手段研究了Dy2AlFe13Mn3化合物的结构及磁性质。研究结果表明Dy2AlFe13Mn3化合物具有六角相的Th2Ni17型结构。通过X-射线热膨胀测定法发现Dy2AlFe13Mn3化合物在245到344K的温度范围内存在负热膨胀现象，其平均热膨胀系数为α＝-1.1×10-4K-1K-1。在105到360K的温度范围内，通过比较磁性状态下的晶胞参数和由高温顺磁状态外延得到的低温顺磁状态下的晶胞参数间的差别计算了Dy2AlFe13Mn3化合物的本征磁致伸缩。结果表明Dy2AlFe13Mn3化合物的本征体磁致伸缩ωS在105到245K的温度范围内随着温度的升高而增大，由105K时的7.0×10-3 增加到245K时的9.1×10-3。随着温度的进一步升高，ωS反而减小。沿c轴方向的本征线磁致伸缩λc随着温度的升高而减小。基面内的本征线磁致伸缩λa在105到270K的温度范围内随着温度的升高而增大，从105K时的0.8×10-3增大到270K时的3.4×10-3，然后随着温度的进一步升高而减小。     

Anomalous thermal expansion and spontaneous magnetostriction of Gd2Fe16Cr compound

The structural and the magnetic properties of Gd 2 Fe 16 Cr compound are investigated by x-ray diffraction and magnetization measurements.The Gd 2 Fe 16 Cr compound has a rhombohedral Th 2 Zn 17-type structure.There exist an anisotropic strong spontaneous magnetostriction and a negative thermal expansion in the magnetic state of Gd 2 Fe 16 Cr compound.The average thermal expansion coefficient ā=-7.03 × 10-6 /K in a temperature range of 294-454 K and ā=-1.31 × 10-5 /K in 454-572 K are obtained.The spontaneous magnetostrictive deformation and the Curie temperature are discussed.     

The transfer of the quantum correlation from two-mode nonclassical state field to the supercurrents in two distant SQUID rings

We have considered two distant mesoscopic superconducting quantum interference device (SQUID) rings A and B in the presence of two-mode nonclassical state fields and investigated the correlation of the supercurrents in the two rings using the normalized correlation function $C_{\rm AB}$. We show that when the parameter $\alpha$ is very small for the separable state with the density matrix $\hat {\rho } = (\left| {\alpha , - \alpha } \right\rangle \left\langle {\alpha , - \alpha } \right| + \left| { - \alpha ,\alpha } \right\rangle \left\langle { - \alpha ,\alpha } \right|) / 2$ and entangled coherent state (ECS) $\left| u \right\rangle = N_1 (\left| {\alpha , - \alpha } \right\rangle + \left| { - \alpha ,\alpha } \right\rangle )$ fields, the dynamic behaviours of the normalized correlation function $C_{\rm AB}$ are similar, but it is quite different for the entangled coherent state $\left| {u}' \right\rangle = N_2 (\left| {\alpha , - \alpha } \right\rangle - \left| { - \alpha ,\alpha } \right\rangle )$ field. When the parameter $\alpha $ is very large, the dynamic behaviours of $C_{\rm AB}$ are almost the same for the separable state, entangled coherent state $\left| u \right\rangle $ and $\left| {u}' \right\rangle $ fields. For the two-mode squeezed vacuum state field the maximum of $C_{\rm AB}$ increases monotonically with the squeezing parameter $r$, and as $r \to \infty $, $C_{\rm AB} \to 1$. This means that the supercurrents in the two rings A and B are quantum mechanically correlated perfectly. It is concluded that not all the quantum correlations in the two-mode nonclassical state field can be transferred to the supercurrents; and the transfer depends on the state of the two-mode nonclassical state field prepared.     

SF_6分子最高占据轨道对称性的判断

量化计算是理论研究分子的重要手段,对于具有高对称群的分子,采用子群计算是常用的方法.分子的电子态或分子轨道等的对称性在子群的表示中会出现重迭,从而不能从子群的结果直接给出电子态或分子轨道对称性的归属.本文以如何判断SF6基态1 A_(1g)的电子组态中最高占据轨道的对称性为例来解决这个问题.针对某些文献中的SF6基态1 A1g的电子组态中,最高占据轨道对称性是T_(1g)却写成T_(2g)的问题,采用Molpro量化计算软件,对SF6基态的平衡结构,进行了HF/6-311G*计算,得到了能量三重简并的最高占据轨道的函数表达式,进而运用O_h群的对称操作作用在三个轨道函数上,得到各操作的矩阵表示,于是得到特征标,最后确定了最高占据轨道为T_(1g)对称性.     

Spontaneous magnetostriction of Y2Fe16Al compound

The structure and magnetic properties of Y₂Fe₁₆Al compound have been investigated by means of x-ray diffraction and magnetization measurements. The Y₂Fe Fe₁₆Al compound has a hexagonal Th$_{2}$Ni$_{17}$-type structure. Negative thermal expansion was found in Y₂Fe₁₆Al compound in the temperature range from 332 to 438K by x-ray dilatometry. The coefficient of the average thermal expansion is \alpha =-3.4\times 10^-5K^-1. The spontaneous magnetostrictive deformations from 293 to 427K have been calculated based on the differences between the experimental values of the lattice parameters and the corresponding values extrapolated from the paramagnetic range. The result shows that the spontaneous volume magnetostrictive deformation \textit{$\omega $}$_{\rm S}$ decreases from 5.4$\times $10^-3to near zero with temperature increasing from 293 to 427K, the spontaneous linear magnetostrictive deformation \textit{$\lambda $}$_{\rm c}$ along the $c$ axis is much larger than the spontaneous linear magnetostrictive deformation \textit{$\lambda $}$_{\rm a}$ in basal-plane in the same temperature range except near 427K.     

Chirality-asymmetry force between ɑ-quartz and copper block

The chirality-asymmetry macroscopic force mediated by light pseudoscalar particles between α -quartz and some achiral matter is studied. If this force between achiral source mass and α -quartz with some chirality is attractive, it will become repulsive when the chirality of the α -quartz crystal is changed. According to the tested limits of the coupling constant g_s g_p /\hbar c< 1.5× 10^-24 at the Compton wavelength λ = 10^-3 m, the force (F) between a 0.08× 0.08× 0.002 m³ block of α -quartz and a 0.08× 0.08× 0.01 m³ copper block with a separation being 0.5× 10^-3 \mbox{m} in between, is estimated from the published data at less than 4.64× 10^-24 N, i.e. F < 4.64× 10^-24 N.     

Invariant Algebraic Surfaces for Generalized Raychaudhuri Equations

We consider a generalized Raychaudhuri equation, $$\begin{array}{llll} \dot x = -\frac 1 2 x^2 -\alpha x -2(y^2 +z^2 -w^2)-2 \beta,\\ \dot y = -(\alpha +x) y -\gamma,\\ \dot z = -(\alpha +x) z -\delta,\\ \dot w = -(\alpha +x) w, \end{array}$$ where ??, ??, ??, ?? are real parameters. This model has appeared in modern string cosmology. We study the algebraic invariants of this model for all values of the parameters ${\alpha,\beta,\gamma,\delta\in \mathbb{R}}$ . We prove that when ???=????=?0 the system is integrable and for any other values of the parameters ??, ??, ??, ?? we characterize all the invariant surfaces of this system. In particular we characterize all the polynomial and proper rational first integrals.     

Shock-induced phase transition and spalling characteristic in pure iron and FeMnNi alloy

This paper provides an investigation of the phase transition and spalling characteristic induced during shock loading and unloading in the pure iron and the FeMnNi alloy. The impact for the pure iron is symmetric and with same-thickness for both the flyer and the target plate. It is found that an abnormal multiple spalling happens in the pure iron sample as the pressure exceeds the $\alpha -\varepsilon $ transition threshold of 13 GPa. In the symmetric and same-thickness impact and reverse impact experiments of the FeMnNi alloy, two abnormal tension regions occur when the pressure exceeds the $\alpha -\varepsilon $ transition threshold of 6.3~GPa, and the reverse phase transition $\varepsilon -\alpha $ begins below 4.2~GP. The experimental process is simulated successfully from the non-equilibrium mixture phase and Boettger's model. Such abnormal spalling phenomena are believed to relate to the shocked $\alpha -\varepsilon $ phase transition. The possible reasons for the abnormal multiple spalling, which occurs during the symmetric and same-thickness impact experiments of pure iron and FeMnNi alloy, are discussed.     

X-ray diffraction study of effect of deposition conditions on α--β phase transition and stress evolution in sputter-deposited W coatings

Pure W and W-Cu-W trilayer coatings were deposited on an Fe substrate by d.c. magnetron sputtering. The α-β phase evolution, intragranular stress evolution in sputter-deposited W layer were investigated by x-ray diffraction. They are directly related to the film microstructure, density and adhesion. Therefore, control of the film stress and phase component transition is essential for its applications. The phase component transition from β-W to α-W and intragranular stress evolution from tensile to compressive strongly depend on the deposition parameters and can be induced by lowering Ar pressure and rising target power. The compressively stressed films with α-W phase have a dense microstructure and high adhesion to Fe substrate.     

Translocation of closed polymers through a nanopore under an applied external field

The dynamic behaviours of the translocations of closed circular polymers and closed knotted polymers through a nanopore, under the driving of an applied field, are studied by three-dimensional Langevin dynamics simulations. The power-law scaling of the translocation time τ with the chain length N and the distribution of translocation time are investigated separately. For closed circular polymers, a crossover scaling of translocation time with chain length is found to be τ～ N α , with the exponent α varying from α = 0.71 for relatively short chains to α = 1.29 for longer chains under driving force F = 5. The scaling behaviour for longer chains is in good agreement with experimental results, in which the exponent α = 1.27 for the translocation of double-strand DNA. The distribution of translocation time D(τ) is close to a Gaussian function for duration time τ < τ p and follows a falling exponential function for duration time τ > τ p . For closed knotted polymers, the scaling exponent α is 1.27 for small field force (F = 5) and 1.38 for large field force (F = 10). The distribution of translocation time D(τ) remarkably features two peaks appearing in the case of large driving force. The interesting result of multiple peaks can conduce to the understanding of the influence of the number of strands of polymers in the pore at the same time on translocation dynamic process and scaling property.     

Corrections of order O(\bar \alpha \bar \alpha _s ) and O(\overline \alpha ^2 ) to the \bar bb-decay width of the neutral Higgs boson

Analytical expressions are presented for contributions of order $O(\overline \alpha \overline \alpha _s )$ and $O(\overline \alpha ^2 )$ to the $\bar bb$ -decay width of the neutral Higgs boson of the standard model of electroweak interactions. The numerical value of the mixed QED and QCD correction of order $O(\overline \alpha \overline \alpha _s )$ is comparable to other computed terms in the perturbation series.     

Plasma characterization on carbon fiber cathode by spectroscopic diagnostics

This paper mainly investigates plasma characterization on carbon fiber cathodes with and without cesium iodide (CsI) coating powered by a ～300~ns, ～ 200~kV accelerating pulse. It was found that the CsI layers can not only improve the diode voltage, but also maintain a stable perveance. This indicates a slowly changed diode gap or a low cathode plasma expansion velocity. By spectroscopic diagnostics, in the vicinity of the cathode surface the average plasma density and temperature were found to be ～ 3× 10¹⁴~cm^-3 and ～ 5~eV, respectively, for an electron current density of ～ 40~A/cm². Furthermore, there exists a multicomponent plasma expansion toward the anode. The plasma expansion velocity, corresponding to the carbon and hydrogen ions, is estimated to be ～ 1.5~cm/μ s. Most notably, Cs spectroscopic line was obtained only at the distance ≤ 0.5~mm from the cathode surface. Carbon and hydrogen ions are obtained up to the distance of 2.5~mm from the cathode surface. Cs ions almost remain at the vicinity of the cathode surface. These results show that the addition of CsI enables a slow cathode plasma expansion toward the anode, providing a positive prospect for developing long-pulse electron beam sources.     

Calculation of Electric Mult ipole Moment Integrals Using Translation Formulas for Slater-Type Orbitals

Using translation formulas for Slater-type orbitals the infinite series through the overlap integrals are derived for the electric multipole moment integrals. By the use of the derived expressions the electric multipole moment integrals, and therefore, the electric properties of molecules can be evaluated most efficiently and accurately. The convergence of the series is tested by calculating concrete cases. An accuracy of for 10^-5 the computer results is obtained for 1 ≤ v ≤ 5, and for the arbitrary values of internuclear distances and screening constants of atomic orbitals.     

Structural, thermodynamic and electronic properties of zinc-blende AlN from first-principles calculations

Structural, thermodynamic and electronic properties of zinc-blende AlN under pressure are investigated by first-principles calculations based on the plane-wave basis set. Through the analysis of enthalpy variation of AlN in the zinc-blende (ZB) and the rock-salt (RS) structures with pressure, we find the phase transition of AlN from ZB to RS structure occurs at 6.7 GPa. By using the quasi-harmonic Debye model, we obtain the heat capacity C_V, Debye temperature Θ_D, Grüneisen parameter γ and thermal expansion coefficient α. The electronic properties including fundamental energy gaps and hydrostatic deformation potentials are investigated and the dependence of energy gaps on pressure is analysed.     

The rehybridization of electronic orbitals in carbon nanotubes

Rehybridization of electronic orbitals in carbon nanotubes contains tilting angles of π orbital, electrons wavefunctions of π orbital and a orbital, degrees of hybridization, etc. In this paper, we have obtained analytical formulas of tilting angle of π orbital relative to tube surface, electrons wavefunctions of π orbital and a orbital, degrees of hybridization, separately, as well as the numerical results.     

Electronic structure and thermodynamic properties of LiBC under high pressure

This paper investigates the electronic structure and thermodynamic properties of LiBC in the hexagonal structure by using the generalized gradient approximation （GGA） and local density approximation correction scheme in the frame of density functional theory. The geometric structure of LiBC under zero pressure, and the dependences of the normalized lattice parameters a/ao and c/co, the ratio e/a, the normalized primitive volume V/Vo on pressure are given. The thermodynamic quantity （including the heat capacity Cv, Debye temperature 6~D, thermal expansion a and Grfineisen parameter -y） dependences on temperature and pressure are obtained through the GGA method and the quasi-harmonic Debye model. The band structures and density of state of LiBC under different pressures have also been analysed.     

Structural,electronic, and optical properties of beryllium monochalcogenides

The results of first-principles theoretical study of the structural, electronic and optical properties of beryllium monochalcogenides BeTe, BeSe and BeS, performed using the full potential linearized augmented plane wave (FP-LAPW) method are presented. The calculated structural parameters and band gaps compare very well with previous theoretical results. The trends of the band gap pressure coefficients and volume deformation potentials for these II-VI compounds are investigated. The linear pressure coefficients for the X and band gaps increase with decrease in anion atomic weight. The dependence of the direct and indirect band gaps on the relative change of lattice constant are found to follow almost the same type of trends in each of these compounds. The volume deformation potential ( ) for the direct ( ) and indirect ( ) gaps are positive, but negative for the indirect ( ) gap. Furthermore, , for transitions decreases with increase in anion atomic number whereas , increases. The optical properties have also been calculated. From the reflectivity spectra, the compounds will be useful for optical applications. The variation of the band gaps with respect to the application of pressure and the origin of some of the peaks in the optical spectra are discussed in terms the calculated electronic structure.Received: 26 September 2003, Published online: 18 June 2004PACS: 71.15.Ap Basis sets (LCAO, plane-wave, APW, etc.) and related methodology (scattering methods, ASA, linearized methods, etc.) - 71.15.Mb Density functional theory, local density approximation, gradient and other corrections - 71.20.Nr Semiconductor compounds     

A new transition metal diphosphide α-MoP2 synthesized by a high-temperature and high-pressure technique

Monoclinic $\alpha $-MoP$_{2}$, with the OsGe$_{2}$-type structure (space group $C2/m$, $Z = 4$) and lattice parameters $a = 8.7248(11) $ Å, $b = 3.2322(4) $ Å, $c = 7.4724(9) $ Å, and $\beta =119.263^\circ $, was synthesized under a pressure of 4 GPa at a temperature between 1100 ${^\circ}$C and 1200 ${^\circ}$C. The structure of $\alpha $-MoP$_{2}$ and its relationship to other transition metal diphosphides are discussed. Surprisingly, the ambient pressure phase orthorhombic $\beta $-MoP$_{2}$ (space group Cmc2$_{1}$) is denser in structure than $\alpha $-MoP$_{2}$. Room-temperature high-pressure x-ray diffraction studies exclude the possibility of phase transition from $\beta $-MoP$_{2}$ to $\alpha $-MoP$_{2}$, suggesting that $\alpha $-MoP$_{2}$ is a stable phase at ambient conditions; this is also supported by the total energy and phonon calculations.