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 Chin. Phys. B
 Chin. Phys. B--2008, Vol.17, No.8
GENERAL
Hou Guo-Lin, Alatancang
Chin. Phys. B, 2008, 17 (8): 2753-2758 doi: 10.1088/1674-1056/17/8/001
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The eigenvalue problem of an infinite-dimensional Hamiltonian operator appearing in the isotropic plane magnetoelectroelastic solids is studied. First, all the eigenvalues and their eigenfunctions in a rectangular domain are solved directly. Then the completeness of the eigenfunction system is proved, which offers a theoretic guarantee of the feasibility of variable separation method based on a Hamiltonian system for isotropic plane magnetoelectroelastic solids. Finally, the general solution for the equation in the rectangular domain is obtained by using the symplectic Fourier expansion method.
Yang Han-Xin, Gao Kun, Han Xiao-Pu, Wang Bing-Hong
Chin. Phys. B, 2008, 17 (8): 2759-2763 doi: 10.1088/1674-1056/17/8/002
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We study the evolutionary snowdrift game in a heterogeneous Newman--Watts small-world network. The heterogeneity of the network is controlled by the number of hubs. It is found that the moderate heterogeneity of the network can promote the cooperation best. Besides, we study how the hubs affect the evolution of cooperative behaviours of the heterogeneous Newman--Watts small-world network. Simulation results show that both the initial states of hubs and the connections between hubs can play an important role. Our work gives a further insight into the effect of hubs on the heterogeneous networks.
He Guang, Mei Feng-Xiang
Chin. Phys. B, 2008, 17 (8): 2764-2765 doi: 10.1088/1674-1056/17/8/003
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This paper studies a conformal invariance and an integration of first-order differential equations. It obtains the corresponding infinitesimal generators of conformal invariance by using the symmetry of the differential equations, and expresses the differential equations by the equations of a Birkhoff system or a generalized Birkhoff system. If the infinitesimal generators are those of a Noether symmetry, the conserved quantity can be obtained by using the Noether theory of the Birkhoff system or the generalized Birkhoff system.
Ma Song-Hua, Fang Jian-Ping, Zheng Chun-Long
Chin. Phys. B, 2008, 17 (8): 2767-2773 doi: 10.1088/1674-1056/17/8/004
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Starting from an improved mapping approach and a linear variable separation approach, a new family of exact solutions (including solitary wave solutions, periodic wave solutions and rational function solutions) with arbitrary functions for a general (2+1)-dimensional Korteweg de Vries system (GKdV) is derived. According to the derived solutions, we obtain some novel dromion-lattice solitons, complex wave excitations and chaotic patterns for the GKdV system.
Hu Jian-Lan
Chin. Phys. B, 2008, 17 (8): 2774-2782 doi: 10.1088/1674-1056/17/8/005
Show Abstract
Explicit solutions are derived for some nonlinear physical model equations by using a delicate way of two-step ansatz method.
Zhao Yun-Hui, Zhao Cheng-Lin
Chin. Phys. B, 2008, 17 (8): 2783-2789 doi: 10.1088/1674-1056/17/8/006
Show Abstract
The performance of the so-called superconvergent quantum perturbation theory (Wenhua Hai {\em et al} 2000 \emph{Phys. Rev.} A {\bf 61} 052105) is investigated for the case of the ground-state energy of the helium-like ions. The scaling transformation $r\rightarrow r/Z$ applied to the Hamiltonian of a two-electron atomic ion with a nuclear charge $Z$ (in atomic units). Using the improved Rayleigh--Schr\"{o}dinger perturbation theory based on the integral equation to helium-like ions in the ground states and treating the electron correlations as perturbations, we have performed a third-order perturbation calculation and obtained the second-order corrected wavefunctions consisting of a few terms and third-order energy corrections. We find that third-order and higher-order energy corrections are improved with decreasing nuclear charge. This result means that the former is quadratically integrable and the latter is physically meaningful. The improved quantum perturbation theory fits the higher-order perturbation case. This work shows that it is a development on the quantum perturbation problem of helium-like systems.
Wang Zhen, Wang Zhi-Xi
Chin. Phys. B, 2008, 17 (8): 2790-2794 doi: 10.1088/1674-1056/17/8/007
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This paper obtains an entangled condition for isotropic-like states by using an atomic map. It constructs a class of bound entangled states from the entangled condition and shows that the partial transposition of the state from the constructed bound entangled class is an edge bound entangled state by using range criterion.
Yu Chang-Shui, Song He-Shan, Cui Hai-Tao
Chin. Phys. B, 2008, 17 (8): 2795-2799 doi: 10.1088/1674-1056/17/8/008
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A new simplified formula is presented to characterize genuine tripartite entanglement of $(2\otimes 2\otimes n)$-dimensional quantum pure states. The formula turns out equivalent to that given in (\wx{Quant. Inf. Comp.}{7}(7) 584 (2007)), hence it also shows that the genuine tripartite entanglement can be described only on the basis of the local $(2\otimes 2)$-dimensional reduced density matrix. In particular, the two exactly solvable models of spin system studied by Yang (\wx{Phys. Rev. {\rm A}}{71} 030302(R) (2005)) are reconsidered by employing the formula. The results show that a discontinuity in the first derivative of the formula or in the formula itself of the ground state just corresponds to the existence of quantum phase transition, which is obviously different from the concurrence.
Qin Meng, Xu Sheng-Long, Tao Ying-Juan, Tian Dong-Ping
Chin. Phys. B, 2008, 17 (8): 2800-2803 doi: 10.1088/1674-1056/17/8/009
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This paper investigates thermal entanglements of a two-qubit Heisenberg $XY$ chain in the presence of the Dzyaloshinskii--Moriya anisotropic antisymmetric interaction. By the concept of concurrence, it is found that the effects of spin--orbit coupling on the entanglement are different from those of spin--spin model. The analytical expressions of concurrence are obtained for this model.
Lin Kai, Yang Shu-Zheng, Zeng Xiao-Xiong
Chin. Phys. B, 2008, 17 (8): 2804-2810 doi: 10.1088/1674-1056/17/8/010
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In this paper, Hawking radiation from the Kerr--Newman de Sitter black hole is studied via gauge anomaly and gravitational anomaly. The obtained results of Hawking radiation from the event horizon and the cosmological horizon accord with those by other methods.
Meng Qing-Miao, Wang Shuai, Jiang Ji-Jian, Deng De-Li
Chin. Phys. B, 2008, 17 (8): 2811-2816 doi: 10.1088/1674-1056/17/8/011
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Using the related formula of dynamic black hole, we have calculated the instantaneous radiation energy density of the slowly changing dynamic Kerr--Newman black hole. It is found that the instantaneous radiation energy density of a black hole is always proportional to the quartic of the temperature of the event horizon in the same direction. By using the Hamilton--Jacobin equation of scalar particles in the curved spacetime, the spontaneous radiation of the slowly changing dynamic Kerr--Newman black hole is studied. The energy condition for the occurrence of the spontaneous radiation is obtained.
Wang Bo-Bo
Chin. Phys. B, 2008, 17 (8): 2817-2823 doi: 10.1088/1674-1056/17/8/012
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A modified de Broglie--Bohm approach is generalized to the Schwarzschild black hole. By using this method, the quantum potential and the quantum trajectories of the black hole are investigated. And we find that the linear combination of two particular solutions of the black hole wavefunction is not physical although each of them is physical, if we think that the quantum gravity should reduce into its corresponding classical counterpart in which the gravity vanishes. It seems to confirm the argument, given by Alwis and MacIntire, that a possible resolution on the quantum gravity is to give up the superposition principle.
Li Jing-Hui
Chin. Phys. B, 2008, 17 (8): 2824-2828 doi: 10.1088/1674-1056/17/8/013
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This paper studies the mean first passage time (or exit time, or escape time) over the non-fluctuating potential barrier for a system driven only by a dichotomous noise. It finds that the dichotomous noise can make the particles escape over the potential barrier, in some circumstances; but in other circumstances, it can not. In the case that the particles escape over the potential barrier, a resonant activation phenomenon for the mean first passage time over the potential barrier is obtained.
Liu Chong-Xin, Liu Ling
Chin. Phys. B, 2008, 17 (8): 2829-2836 doi: 10.1088/1674-1056/17/8/014
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This paper introduces a new four-dimensional (4D) hyperchaotic system, which has only two quadratic nonlinearity parameters but with a complex topological structure. Some complicated dynamical properties are then investigated in detail by using bifurcations, Poincar\'{e} mapping, LE spectra. Furthermore, a simple fourth-order electronic circuit is designed for hardware implementation of the 4D hyperchaotic attractors. In particular, a remarkable fractional-order circuit diagram is designed for physically verifying the hyperchaotic attractors existing not only in the integer-order system but also in the fractional-order system with an order as low as 3.6.
Wang Sen, Cai Li, Kang Qiang, Wu Gang, Li Qin
Chin. Phys. B, 2008, 17 (8): 2837-2843 doi: 10.1088/1674-1056/17/8/015
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With the polarization of quantum-dot cell and quantum phase serving as state variables, this paper does both theoretical analysis and simulation for the complex nonlinear dynamical behaviour of a three-cell-coupled Quantum Cellular Neural Network (QCNN), including equilibrium points, bifurcation and chaotic behaviour. Different phenomena, such as quasi-periodic, chaotic and hyper-chaotic states as well as bifurcations are revealed. The system's bifurcation and chaotic behaviour under the influence of the different coupling parameters are analysed. And it finds that the unbalanced cells coupled QCNN is easy to cause chaotic oscillation and the system response enters into chaotic state from quasi-periodic state by quasi-period bifurcation; however, the balanced cells coupled QCNN also can be chaotic when coupling parameters is in some region. Additionally, both the unbalanced and balanced cells coupled QCNNs can possess hyper-chaotic behaviour. It provides valuable information about QCNNs for future application in high-parallel signal processing and novel ultra-small chaotic generators.
Ma Jun, Wang Chun-Ni, Jin Wu-Yin, Li Yan-Long, Pu Zhong-Sheng
Chin. Phys. B, 2008, 17 (8): 2844-2849 doi: 10.1088/1674-1056/17/8/016
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This paper proposes a scheme of parameter perturbation to suppress the stable rotating spiral wave, meandering spiral wave and turbulence in the excitable media, which is described by the modified Fitzhugh--Nagumo (MFHN) model. The controllable parameter in the MFHN model is perturbed with a weak pulse and the pulse period is decided by the rotating period of the spiral wave approximatively. It is confirmed that the spiral wave and spiral turbulence can be suppressed greatly. Drift and instability of spiral wave can be observed in the numerical simulation tests before the whole media become homogeneous finally.
Wang Jun-Feng, Chen Gui-Sheng, Liu Jin
Chin. Phys. B, 2008, 17 (8): 2850-2858 doi: 10.1088/1674-1056/17/8/017
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Cellular Automaton (CA) based traffic flow models have been extensively studied due to their effectiveness and simplicity in recent years. This paper develops a discrete time Markov chain (DTMC) analytical framework for a Nagel--Schreckenberg and Fukui--Ishibashi combined CA model (W$^2$H traffic flow model) from microscopic point of view to capture the macroscopic steady state speed distributions. The inter-vehicle spacing Markov chain and the steady state speed Markov chain are proved to be irreducible and ergodic. The theoretical speed probability distributions depending on the traffic density and stochastic delay probability are in good accordance with numerical simulations. The derived fundamental diagram of the average speed from theoretical speed distributions is equivalent to the results in the previous work.
Di You-Ying, Wang Da-Qi, Shi Quan, Tan Zhi-Cheng
Chin. Phys. B, 2008, 17 (8): 2859-2866 doi: 10.1088/1674-1056/17/8/018
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This paper reports that low-temperature heat capacities of N-methylnorephedrine C$_{11}$H$_{17}$NO(s) have been measured by a precision automated adiabatic calorimeter over the temperature range from $T$=78\,K to $T$=400\,K. A solid to liquid phase transition of the compound was found in the heat capacity curve in the temperature range of $T$=342--364\,K. The peak temperature, molar enthalpy and entropy of fusion of the substance were determined. The experimental values of the molar heat capacities in the temperature regions of $T$=78--342\,K and $T$=364--400\,K were fitted to two polynomial equations of heat capacities with the reduced temperatures by least squares method. The smoothed molar heat capacities and thermodynamic functions of $N$-methylnorephedrine C$_{11}$H$_{17}$NO(s) relative to the standard reference temperature 298.15\,K were calculated based on the fitted polynomials and tabulated with an interval of 5\,K. The constant-volume energy of combustion of the compound at $T$=298.15\,K was measured by means of an isoperibol precision oxygen-bomb combustion calorimeter. The standard molar enthalpy of combustion of the sample was calculated. The standard molar enthalpy of formation of the compound was determined from the combustion enthalpy and other auxiliary thermodynamic data through a Hess thermochemical cycle.
Wang Li-Guo, Sun Jiu-Xun, Yang Wei
Chin. Phys. B, 2008, 17 (8): 2867-2873 doi: 10.1088/1674-1056/17/8/019
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The thermodynamic properties of the $\varepsilon$ phase of solid oxygen are studied by using the analytic mean field approach (AMFP). Analytic expressions for the Helmholtz free energy, internal energy and equation of state of solid oxygen have been derived based on the multi-exponential potential. The formulism for the case of double-exponential (DE) model is applied to the $\varepsilon$ phase of solid oxygen. Its four potential parameters are determined through fitting the experimental compression data of the $\varepsilon$ phase of solid oxygen. Numerical results of the pressure dependence of the volume calculated by using the AMFP are in good agreement with the original experimental data. This suggests that the AMFP is a useful approach to study the thermodynamic properties of the $\varepsilon$ phase of solid oxygen. Furthermore, we predict the variation of the volume, lattice parameters and intermolecular distances with pressure, and some thermodynamic quantities versus volume, at several higher temperatures.
Zhu Zhen-Tao, Zhou Jing, Li Ping, Chen Xing-Guang
Chin. Phys. B, 2008, 17 (8): 2874-2880 doi: 10.1088/1674-1056/17/8/020
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In this paper, an evolutionary model of bus transport network in B-space is developed. It includes the effect of the overlapping ratio of new route on network performance and overcomes the disadvantage, i.e. lack of economic consideration, in the evolutionary bus transport network model in P-space proposed by Chen {\it et al} (2007). The degree distribution functions are derived by using the mean-field method and the master equation method, separately. The relationship between the new stop ratio of a route, $\lambda$, and the error in exponential of degree distribution function from the mean-field method is developed as ${\Delta}$Slope$=\lambda/(1 - \lambda ) + \ln (1 - \lambda)$. Finally, the bus transport networks of Hangzhou and Nanjing are simulated by using this model, and the results show that some characteristic index values of the simulated networks are closer to the empirical data than those from Chen's model.
Cheng Jin-Xing, Ouyang Xiao-Ping, Zheng Yi, Zhang An-Hui, Ouyang Mao-Jie
Chin. Phys. B, 2008, 17 (8): 2881-2884 doi: 10.1088/1674-1056/17/8/021
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It is a very complex and time-consuming process to simulate the nuclear reactor neutron spectrum from the reactor core to the export channel by applying a Monte Carlo program. This paper presents a new method to calculate the neutron spectrum by using the convolution technique which considers the channel transportation as a linear system and the transportation scattering as the response function. It also applies Monte Carlo Neutron and Photon Transport Code (MCNP) to simulate the response function numerically. With the application of convolution technique to calculate the spectrum distribution from the core to the channel, the process is then much more convenient only with the simple numerical integral numeration. This saves computer time and reduces some trouble in re-writing of the MCNP program.
Li Yuan-Yuan, Hou Xun, Bai Jin-Tao, Yan Jun-Feng, Gan Chen-Li, Zhang Yan-Peng
Chin. Phys. B, 2008, 17 (8): 2885-2889 doi: 10.1088/1674-1056/17/8/022
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This paper investigates the absorptive reduction and the width narrowing of electromagnetically induced transparency (EIT) in a thin vapour film of $\Lambda$-type atoms confined between two dielectric walls whose thickness is comparable with the wavelength of the probe field. The absorptive lines of the weak probe field exhibit strong reductions and very narrow EIT dips, which mainly results from the velocity slow-down effects and transient behaviour of atoms in a confined system. It is also shown that the lines are modified by the strength of the coupling field and the ratio of $L / \lambda$, with $L$ the film thickness and $\lambda$ the wavelength of the probe field. A simple robust recipe for EIT in a thin medium is achievable in experiment.
NUCLEAR PHYSICS
Chi Bao-Qian, Liu Ling, Wang Jian-Guo
Chin. Phys. B, 2008, 17 (8): 2890-2896 doi: 10.1088/1674-1056/17/8/023
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The non-dissociative charge-transfer processes in collisions between O$^{3 + }$ and H$_{2}$ are investigated by using the quantum-mechanical molecular-orbital coupled-channel (QMOCC) method. The adiabatic potentials and radial coupling matrix elements utilized in the QMOCC calculations are obtained with the spin-coupled valence-bond approach. Electronic and vibrational state-selective differential cross sections are presented for projectile energies of 0.1, 1.0 and 10.0\,eV/u in the H$_{2}$ orientation angles of 45$^\circ$ and 89$^{\circ}$. The electronic and the vibrational state-selective differential cross sections show similar behaviours: they decrease as the scattering angle increases, and beyond a specific angle the oscillating structures appear. Moreover, it is also found that the vibrational state-selective differential cross sections are strongly orientation-dependent, which provides a possibility to determine the orientations of molecule H$_{2}$ by identifying the vibrational state-selective differential scattering processes.
CLASSICAL AREAS OF PHENOMENOLOGY
Ren Xin-Cheng, Guo Li-Xin
Chin. Phys. B, 2008, 17 (8): 2956-2962 doi: 10.1088/1674-1056/17/8/032
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A normalized two-dimensional band-limited Weierstrass fractal function is used for modelling the dielectric rough surface. An analytic solution of the scattered field is derived based on the Kirchhoff approximation. The variance of scattering intensity is presented to study the fractal characteristics through theoretical analysis and numerical calculations. The important conclusion is obtained that the diffracted envelope slopes of scattering pattern can be approximated as a slope of linear equation. This conclusion will be applicable for solving the inverse problem of reconstructing rough surface and remote sensing.
Wu Qin, Fang Mao-Fa, Feng Yong-Zhen, Hu Yao-Hua
Chin. Phys. B, 2008, 17 (8): 2963-2968 doi: 10.1088/1674-1056/17/8/033
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Considering a two-level atom interacting with the competing two-mode field, this paper investigates the entanglement between the two-level atom and the two-mode field by using the quantum reduced entropy, and that between the two-mode field by using the quantum relative entropy of entanglement. It shows that the two kinds of entanglement are dependent on the relative coupling strength of atom-field and the atomic distribution, and exhibit the periodical evolution. The maximal atom--field entanglement state can be prepared via the appropriate selection of system parameters and interaction time.
Zheng Shi-Biao
Chin. Phys. B, 2008, 17 (8): 2969-2972 doi: 10.1088/1674-1056/17/8/034
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In this paper a scheme is proposed for the purification of entangled states for two atoms trapped in two distant cavities via cavity decay. In the scheme, the atoms have no probability of being populated in the excited state and thus the atomic spontaneous emission is suppressed. This scheme is valid no matter when the cavity decay rate is larger or smaller than the effective atom-cavity coupling strength. The fidelity of the final state is not affected by the imperfection of the photodetectors.
Meng Xiang-Guo, Wang Ji-Suo, Li Hong-Qi
Chin. Phys. B, 2008, 17 (8): 2973-2978 doi: 10.1088/1674-1056/17/8/035
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The $q$-analogues of two-mode squeezed states are introduced by virtue of deformation quantization methods and the technique of integration within an ordered product (IWOP) of operators. Some new completeness relations about these squeezed states composed of the bra and ket which are not mutually Hermitian conjugates are obtained. Furthermore, the antibunching effects of the two-mode squeezed vacuum state $S_2' (r)\left| {00} \right\rangle$ are investigated. It is found that, in different ranges of the squeezed parameter $r$, both modes of the state exhibit the antibunching effects and the two modes of the state are always nonclassical correlation.
Zhu Jun, Zhao Yan, Jin Guo-Fan
Chin. Phys. B, 2008, 17 (8): 2979-2983 doi: 10.1088/1674-1056/17/8/036
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Fibre sensors exhibit a number of advantages over other sensors such as high sensitivity, electric insulation, corrosion resistance, interference rejection and so on. And laser self-mixing interference can accurately detect the phase difference of feedback light. In this paper, a novel laser self-mixing interference fibre sensor that combines the advantages of fibre sensors with those of laser self-mixing interference is presented. Experimental configurations are set up to study the relationship between laser power output and phase of laser feedback light when the fibre trembles or when the fibre is stretched or pressed. The theoretical analysis of pressure sensors based on laser self-mixing interference is indicated to accord with the experimental results.
An Yu
Chin. Phys. B, 2008, 17 (8): 2984-2988 doi: 10.1088/1674-1056/17/8/037
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Using the equations of fluid mechanics with proper boundary conditions and taking account of the gas properties, we can numerically simulate the process of single bubble sonoluminescence, in which electron--neutral atom bremsstrahlung, electron--ion bremsstrahlung and recombination radiation, and the radiative attachment of electrons to atoms and molecules contribute to the light emission. The calculation can quantitatively or qualitatively interpret the experimental results. We find that the accumulated heat energy inside the compressed gas bubble is mostly consumed by the chemical reaction, therefore, the maximum degree of ionization inside Xe bubble in water is much lower than that in sulfuric acid, of which the vapour pressure is very low. In addition, in sulfuric acid much larger $p_{\rm a}$ and $R_{0}$ are allowed which makes the bubbles in it much brighter than that in water.
Yang Xiao-Xia, Duan Wen-Shan, Li Sheng-Chang, Han Jiu-Ning
Chin. Phys. B, 2008, 17 (8): 2989-2993 doi: 10.1088/1674-1056/17/8/038
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This paper investigates the collision between two nonlinear waves with arbitrary angle in two-dimensional nonlinear lattice. By using the extended Poincar\'{e}--Lighthill--Kuo perturbation method, it obtains two Korteweg--de Vries equations for nonlinear waves in both the $\xi$ and $\eta$ directions, respectively, and derives the analytical phase shifts after the collision of two nonlinear waves. Finally, the solution of $u(v)$ up to $O(\epsilon^{3})$ order is given.
ATOMIC AND MOLECULAR PHYSICS
Lee Teck-Ghee, Wong Cheuk-Yin, Wang Lee-Shien
Chin. Phys. B, 2008, 17 (8): 2897-2908 doi: 10.1088/1674-1056/17/8/024
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This paper evaluates the interaction potential between a hydrogen and an antihydrogen using the second-order perturbation theory within the framework of the four-body system in a separable two-body basis. It finds that the H--$\bar{\rm H}$ interaction potential possesses the peculiar features of a shallow local minimum located around interatomic separations of $r\sim 6$\,a.u. and a barrier rising at $r\lesssim5$\,a.u.
Wang Zhi-Wen, Liu Ying, Hu Mu-Hong, Li Xin-Ru, Wang Ya-Nan
Chin. Phys. B, 2008, 17 (8): 2909-2913 doi: 10.1088/1674-1056/17/8/025
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The transition energies, wavelengths and dipole oscillator strengths of 1s$^{2}$2p-1s$^{2}n$d ($3 \le n \le 9$) for Cr$^{21 +}$ ion are calculated. The fine structure splittings of 1s$^{2}n$d ($n \le 9$) states for this ion are also calculated. In calculating energy, we have estimated the higher-order relativistic contribution under a hydrogenic approximation. The quantum defect of Rydberg series 1s$^{2}n$d is determined according to the quantum defect theory. The results obtained in this paper excellently agree with the experimental data available in the literature. Combining the quantum defect theory with the discrete oscillator strengths, the discrete oscillator strengths for the transitions from initial state 1s$^{2}$2p to highly excited 1s$^{2}n$d states ($n \ge 10$) and the oscillator strength density corresponding to the bound--free transitions are obtained.
Zhang Shi-An, Wang Zu-Geng, Sun Zhen-Rong
Chin. Phys. B, 2008, 17 (8): 2914-2918 doi: 10.1088/1674-1056/17/8/026
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A femtosecond laser pulse can be tailored to control the two-photon transitions using the ultra-fast pulse-shaping technique. This paper theoretically and experimentally demonstrates that two-photon transitions in molecular system with broad absorption line can be effectively controlled by square phase-modulation in frequency domain, and the influence of all parameters characterizing the square phase-modulation on two-photon transitions is systemically investigated and discussed. The obtained results have potential application in nonlinear spectroscopy and molecular physics.
Wang Jian-Kun, Wu Zhen-Sen
Chin. Phys. B, 2008, 17 (8): 2919-2924 doi: 10.1088/1674-1056/17/8/027
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This paper calculates the equilibrium structure and the potential energy functions of the ground state ($X^2\Si ^{ + })$ and the low lying excited electronic state ($A^2{\it \Pi}$) of CN radical are calculated by using CASSCF method. The potential energy curves are obtained by a least square fitting to the modified Murrell--Sorbie function. On the basis of physical theory of potential energy function, harmonic frequency ($\omega _{\rm e}$) and other spectroscopic constants ($\omega _{\rm e}\chi _{\rm e}$, $\beta _{\rm e}$ and $\alpha _{\rm e})$ are calculated by employing the Rydberg--Klein--Rees method. The theoretical calculation results are in excellent agreement with the experimental and other complicated theoretical calculation data. In addition, the eigenvalues of vibrational levels have been calculated by solving the radial one-dimensional Schr\"{o}dinger equation of nuclear motion using the algebraic method based on the analytical potential energy function.
Yan Shi-Ying
Chin. Phys. B, 2008, 17 (8): 2925-2931 doi: 10.1088/1674-1056/17/8/028
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Density functional theory (DFT) (B3P86) of Gaussian 03 has been used to optimize the structure of the Cr$_{2}$ molecule, a transition metal element molecule. The result shows that the ground state for the Cr$_{2}$ molecule is a 13-multiple state, indicating that there exists a spin polarization effect in the Cr$_{2}$ molecule. Meanwhile, we have not found any spin pollution because the wave function of the ground state does not mingle with wave functions of higher-energy states. So the ground state for Cr$_{2}$ molecule being a 13-multiple state is indicative of spin polarization effect of the Cr$_{2}$ molecule among transition metal elements, that is, there are 12 parallel spin electrons in the Cr$_{2}$ molecule. The number of non-conjugated electrons is greatest. These electrons occupy different spatial orbitals so that the energy of the Cr$_{2}$ molecule is minimized. It can be concluded that the effect of parallel spin in the Cr$_{2}$ molecule is larger than the effect of the conjugated molecule, which is obviously related to the effect of electron d delocalization. In addition, the Murrell--Sorbie potential functions with the parameters for the ground state and other states of the Cr$_{2}$ molecule are derived. The dissociation energy {\it D}e for the ground state of the Cr$_{2}$ molecule is 0.1034\,eV, equilibrium bond length {\it R}e is 0.3396\,nm, and vibration frequency $\omega_{\rm e}$ is 73.81\,cm$^{-1}$. Its force constants $f_2$, $f_3$ and $f_4$ are 0.0835, $-$0.2831 and 0.3535\,aJ\,$\cdot$\,nm$^{- 4}$ respectively. The other spectroscopic data for the ground state of the Cr$_{2}$ molecule $\omega_{\rm e}\chi _{\rm e}$, $B_{\rm e}$ and $\alpha_{\rm e}$ are 1.2105, 0.0562 and 7.2938\,$\times10^{-4}$cm$^{-1}$ respectively.
Li Hong-Yun, Gao Song, Zhou Hui, Zhang Yan-Hui, Lin Sheng-Lu
Chin. Phys. B, 2008, 17 (8): 2932-2937 doi: 10.1088/1674-1056/17/8/029
The chaotic behaviours of the Rydberg hydrogen atom near a metal surface are presented. A numerical comparison of Poincar\'{e} surfaces of section with recurrence spectra for a few selected scaled energies indicates the correspondence between classical motion and quantum properties of an excited electron. Both results demonstrate that the scaled energy dominates sensitively the dynamical properties of system. There exists a critical scaled energy $\varepsilon _{\rm c}$, for $\varepsilon < \varepsilon _{\rm c}$, the system is near-integrable, and as the decrease of $\varepsilon$ the spectrum is gradually rendered regular and finally turns into a pure Coulomb field situation. On the contrary, if $\varepsilon>\varepsilon_{\rm c}$, with the increase of $\varepsilon$, the system tends to be non-integrable, the ergodic motion in phase space presages that chaotic motion appears, and more and more electrons are adsorbed on the metal surface, thus the spectrum becomes gradually simple.
The geometries, electronic structures and related properties of Si$_{m}$N$_{8 - m}(0 Li Zhi-Jian, Li Jin-Hui Chin. Phys. B, 2008, 17 (8): 2951-2955 doi: 10.1088/1674-1056/17/8/031 Full Text: [PDF 3995 KB] (Downloads:461) Show Abstract First-principle calculations are performed to study geometric and electronic properties of both neutral and anionic In$_{4}M$and In$_{12}M$($M$= C, Si, In) clusters. In$_{4}$C and In$_{4}$Si are found to be tetrahedral molecules. The icosahedral structure is found to be unfavourable for In$_{12}M$. The most stable structure for In$_{12}$C is a distorted buckled biplanar structure while for In$_{12}$Si it is of an In-cage with the Si located in the centre. Charge effect on the structure of In$_{12}M$is discussed. In$_{4}$C has a significantly large binding energy and an energy gap between the highest-occupied molecular-orbital level and the lowest unoccupied molecular-orbital level, a low electron affinity, and a high ionization potential, which are the characters of a magic cluster, enriching the family of doped-group-IIIA metal clusters for cluster-assembled materials. PHYSICS OF GASES, PLASMAS, AND ELECTRIC DISCHARGES Zhang Yang, Ding Ning Chin. Phys. B, 2008, 17 (8): 2994-3002 doi: 10.1088/1674-1056/17/8/039 Full Text: [PDF 225 KB] (Downloads:490) Show Abstract Within the magnetohydrodynamics (MHD) frame, we analyse the effect of viscosity on magneto-Rayleigh--Taylor (MRT) instability in a Z-pinch configuration by using an exact method and an approximate method separately. It is demonstrated that the plasma viscosity indeed has a stabilization effect on the MRT mode in the whole wavenumber region, and its influence increases with the perturbation wavenumber increasing. After the characteristics and feasibility of the approximate method have been investigated, we apply it to the stability analysis of viscous plasma where a sheared axial flow (SAF) is involved, and we attain an analytical dispersion relation. It is suggested that the viscosity and the SAF are complemental with each other, and a wide wavenumber range of perturbation is possible to be restrained if the SAF and the viscosity are large enough. Finally, we calculate the possible value of viscosity parameter according to the current experimental conditions, and the results show that since the value of viscosity is much less than the threshold value, its mitigation effect is small enough to be neglected. The role of the viscosity in the stabilization becomes considerable only if special techniques are so developed that the Z-pinch plasma viscosity can be increased greatly. CONDENSED MATTER: STRUCTURAL, MECHANICAL, AND THERMAL PROPERTIES Su Wei-Feng, Gnaser Hubert, Fan Yong-Liang, Jiang Zui-Min, Le Yong-Kang Chin. Phys. B, 2008, 17 (8): 3003-3007 doi: 10.1088/1674-1056/17/8/040 Full Text: [PDF 966 KB] (Downloads:775) Show Abstract Titanium oxide films were prepared by annealing DC magnetron sputtered titanium films in an oxygen ambient. X-ray diffraction (XRD), Auger electron spectroscopy (AES) sputter profiling, MCs$^{ + }$-mode secondary ion mass spectrometry (MCs$^{ + }$-SIMS) and atomic force microscopy (AFM) were employed, respectively, for the structural, compositional and morphological characterization of the obtained films. For temperatures below 875\,K, titanium films could not be fully oxidized within one hour. Above that temperature, the completely oxidized films were found to be rutile in structure. Detailed studies on the oxidation process at 925\,K were carried out for the understanding of the underlying mechanism of titanium dioxide (TiO$_{2})$formation by thermal oxidation. It was demonstrated that the formation of crystalline TiO$_{2}$could be divided into a short oxidation stage, followed by crystal forming stage. Relevance of this recognition was further discussed. Wang Jian-Ping, Zhou Wang-Min, Wang Chong-Yu, Yin Shu-Yuan Chin. Phys. B, 2008, 17 (8): 3008-3013 doi: 10.1088/1674-1056/17/8/041 Full Text: [PDF 185 KB] (Downloads:433) Show Abstract Under certain growth conditions for systems with a film/substrate lattice misfit, the deposited material is known to aggregate into island-like shapes. We have obtained an analytical expression of the total free energy, which consists of strain energy, surface energy and interfacial energy of a coherent island/substrate system, and the change of equilibrium aspect ratio versus the volume of the island and the misfit of lattices in the system, which provides a broad perspective on island behaviour. These then were used to study the equilibrium shapes of the system. The results show that in order to minimize the total free energy, a coherent island will have a particular height-to-width aspect ratio, called equilibrium aspect ratio, that is a function of the island volume and misfit. The aspect ratio is increased with increasing island volume at a fixed misfit, and with increasing misfit strain between the island and substrate at a fixed island volume. Moreover, the effect of misfit dislocation on the equilibrium shape of the island is also examined. The results obtained are in good agreement with experiment of observations and thus can serve as a basis for interpreting the experiments. Li Xing-Li, Song Tao, Kuang Hua, Dai Shi-Qiang Chin. Phys. B, 2008, 17 (8): 3014-3020 doi: 10.1088/1674-1056/17/8/042 Full Text: [PDF 1399 KB] (Downloads:832) Show Abstract Through introducing a generalized optimal speed function to consider spatial position, slope grade and variable safe headway, the effect of slope in a single-lane highway on the traffic flow is investigated with the extended optimal speed model. The theoretical analysis and simulation results show that the flux of the whole road with the upgrade (or downgrade) increases linearly with density, saturates at a critical density, then maintains this saturated value in a certain density range and finally decreases with density. The value of saturated flux is equal to the maximum flux of the upgrade (or downgrade) without considering the slight influence of the driver's sensitivity. And the fundamental diagrams also depend on sensitivity, slope grade and slope length. The spatiotemporal pattern gives the segregation of different traffic phases caused by the rarefaction wave and the shock wave under a certain initial vehicle number. A comparison between the upgrade and the downgrade indicates that the value of saturated flux of the downgrade is larger than that of the upgrade under the same condition. This result is in accordance with the real traffic. He Zhi-Wei, Xu Da-Yin, Jiang Xiang-Hua, Wang Yin-Yue Chin. Phys. B, 2008, 17 (8): 3021-3025 doi: 10.1088/1674-1056/17/8/043 Full Text: [PDF 1128 KB] (Downloads:472) Show Abstract This paper reports that by using the hydrofluoric acid (HF) as the acid catalyst, F doped nanoporous low-k SiO$_{2}$thin films have been prepared by means of sol-gel method. The characterization of atomic force microscopy and Fourier transform infrared spectroscopy demonstrates that the HF catalyzed films are more hydrophobic. The N$_{2}$adsorption/desorption experiments show that the suited introduction of HF increases the porosity and decreases the pore size distribution (about 10\,nm) in the films. The above results indicate that the hydrofluoric acid is the more suitable acid catalyst than the hydrochloric one for preparing nanoporous ultra low-k SiO$_{2}$thin films. CONDENSED MATTER: ELECTRONIC STRUCTURE, ELECTRICAL, MAGNETIC, AND OPTICAL PROPERTIES Wu Hong Chin. Phys. B, 2008, 17 (8): 3026-3034 doi: 10.1088/1674-1056/17/8/044 Full Text: [PDF 1226 KB] (Downloads:453) Show Abstract This paper studies the effect of a~charged~impurity together with or without an external homogeneous~electric field~on a~quantum~ring threaded by a magnetic field$B$and containing two electrons. The potential caused by the impurity has been plotted which is helpful to the understanding of the electronic structures inside the ring. The deep valley appearing in the potential curve is the source of localization, which affects seriously the Aharonov--Bohm oscillation (ABO) of the energy and persistent current. It also causes the fluctuation of the total orbital angular momentum$L$of the pair of electrons. It is found that the appearance of the impurity reduces the domain of the fractional ABO. During the increase of$B$, the domain of the integral ABO may appear earlier when$B$is even quite small. The transition from the localized states to extended states has also been studied. Furthermore, it has deduced a set of related formulae for a transformation, by which an impurity with a charge$e_p$placed at an arbitrary point${\bm R}_p$is equivalent to an impurity with a revised charge$\tilde {e}_p$placed at the$X$-axis with a revised radial distance$\tilde {R}_p$. This transformation facilitates the calculation and make the analysis of the physical result clearer. Li Xin, Hu Yuan-Zhong, Jiang Lan Chin. Phys. B, 2008, 17 (8): 3035-3039 doi: 10.1088/1674-1056/17/8/045 Full Text: [PDF 1324 KB] (Downloads:411) Show Abstract Lubricant spreading on solid substrates has drawn considerable attention not only for the microscopic wetting theory but also for the dramatic application in head-disk interface of magnetic storage drive systems. Molecular dynamic simulation based on a coarse-grained bead-spring model has been used to study such a spreading process. The spreading profiles indicate that the hydrogen bonds among lubricant molecules and the hydrogen bonds between lubricant molecules and polar atoms of solid substrates will complicate the spreading process in a tremendous degree. The hydrogen bonds among lubricant molecules will strengthen the lubricant combination intensity, which may hinder most molecules from flowing down to the substrates and diffusing along the substrates. And the hydrogen bonds between lubricant molecules and polar atoms of solid substrates will confine the lubricant molecules around polar atoms, which may hinder the molecules from diffusing along the substrates and cause precursor film to vanish. Guan Peng-Fei, Wang Chong-Yu, Yu Tao Chin. Phys. B, 2008, 17 (8): 3040-3053 doi: 10.1088/1674-1056/17/8/046 Full Text: [PDF 7051 KB] (Downloads:403) Show Abstract Local density functional is investigated by using the full-potential linearized augmented plane wave (FP-LAPW) method for ScN in the hexagonal structure and the rocksalt structure and for hexagonal structures linking a layered hexagonal phase with wurtzite structure along a homogeneous strain transition path. It is found that the wurtzite ScN is unstable and the layered hexagonal phase, labelled as$h_{\rm o}$, in which atoms are approximately fivefold coordinated, is metastable, and the rocksalt ScN is stable. The electronic structure, the physical properties of the intermediate structures and the energy band structure along the transition are presented. It is found that the band gaps change from 4.0 to 1.0\,eV continuously when$c/a$value varies from 1.68 to 1.26. It is noticeable that the study of ScN provides an opportunity to apply this kind of material (in wurtzite[$h$]-derived phase). Wang Chuan-Dao, Yang Fu-Hua, Feng Song-Lin Chin. Phys. B, 2008, 17 (8): 3054-3057 doi: 10.1088/1674-1056/17/8/047 Full Text: [PDF 477 KB] (Downloads:448) Show Abstract In the framework of the effective mass theory, this paper calculates the electron energy levels of an InAs/GaAs tyre-shape quantum ring (TSQR) by using the plane wave basis. The results show that the electron energy levels are sensitively dependent on the TSQR's section thickness$d$, and insensitively dependent on TSQR's section inner radius$R_1$and TSQR's inner radius$R_2$. The model and results provide useful information for the design and fabrication of InAs/GaAs TSQRs. Li Yu-Xian Chin. Phys. B, 2008, 17 (8): 3058-3061 doi: 10.1088/1674-1056/17/8/048 Full Text: [PDF 189 KB] (Downloads:389) Show Abstract Using the tight-binding model approximation, this paper investigates theoretically spin-dependent quantum transport through an Aharonov--Bohm (AB) interferometer. An external magnetic field is applied to produce the spin-polarization and spin current. The AB interferometer, acting as a spin splitter, separates the opposite spin polarization current. By adjusting the energy and the direction of the magnetic field, large spin-polarized current can be obtained. Xiong De-Ping, Zhou Shou-Li, Wang Qi, Ren Xiao-Min Chin. Phys. B, 2008, 17 (8): 3062-3066 doi: 10.1088/1674-1056/17/8/049 Full Text: [PDF 200 KB] (Downloads:503) Show Abstract Using first-principles calculations in the generalized gradient approximation, the electronic properties of BAs and B$_{x}$Ga$_{1 - x}$As alloys are studied. At the Brillouin-zone centre, the lowest conduction band is the three-degenerate p-like$\Ga _{\rm 15c}$state rather than s-like$\Ga_{\rm 1c}$state, and the conduction band minimum (CBM) is along the \textit{$\De$} line between the$\Ga$and$X$points-at approximately 11/14(1,0,0)2$\pi /a$. With boron content at 0{\%}--18.75{\%}, B$_{x}$Ga$_{1 - x}$As alloys have a small (2.6\,eV) and relatively composition-independent band-gap bowing parameter, the band-gap increases monotonically by$\sim$18\,meV/B{\%} with increasing boron content. In addition, the formation enthalpies of mixing for B$_{x}$Ga$_{1 - x}$As alloys with boron content at 6.25{\%} and 12.5{\%} are calculated, and the large formation enthalpies may explain the difficulty in alloying boron to GaAs. Li Dong-Mei, Liu Xiao-Jing, Li Yuan, Li Hai-Hong, Hu Gui-chao, Gao Kun, Liu De-Sheng, Xie Shi-Jie Chin. Phys. B, 2008, 17 (8): 3067-3076 doi: 10.1088/1674-1056/17/8/050 Full Text: [PDF 1389 KB] (Downloads:375) Show Abstract The dynamical process of charge injection from metal electrode to a nondegenerate polymer in a metal/polythiophene (PT)/metal structure has been investigated by using a nonadiabatic dynamic approach. It is found that the injected charges form wave packets due to the strong electron-lattice interaction in PT. We demonstrate that the dynamical formation of the wave packet sensitively depends on the strength of applied voltage, the electric field, and the contact between PT and electrode. At a strength of the electric field more than$3.0\times 10^{4}$\,V/cm, the carriers can be ejected from the PT into the right electrode. At an electric field more than$3.0\times 10^{5}$\,V/cm, the wave packet cannot form while it moves rapidly to the right PT/metal interface. It is shown that the ejected quantity of charge is noninteger. Luan Su-Zhen, Liu Hong-Xia Chin. Phys. B, 2008, 17 (8): 3077-3082 doi: 10.1088/1674-1056/17/8/051 Full Text: [PDF 782 KB] (Downloads:359) Show Abstract Nanoscale Schottky barrier metal oxide semiconductor field-effect transistors (MOSFETs) are explored by using quantum mechanism effects for thin-body devices. The results suggest that for small nonnegative Schottky barrier heights, even for zero barrier height, the tunnelling current also plays a role in the total on-state current. Owing to the thin body of device, quantum confinement raises the electron energy levels in the silicon, and the tradeoff takes place between the quantum confinement energy and Schottky barrier lowering (SBL). It is concluded that the inclusion of the quantum mechanism effect in this model, which considers an infinite rectangular well with a first-order perturbation in the channel, can lead to the good agreement with numerical result for thin silicon film. The error increases with silicon thickness increasing. Yu Hai-Feng, Cao Wen-Hui, Zhu Xiao-Bo, Yang Hai-Fang, Yu Hong-Wei, Ren Yu-Feng, Gu Chang-Zhi, Chen Geng-Hua, Zhao Shi-Ping Chin. Phys. B, 2008, 17 (8): 3083-3086 doi: 10.1088/1674-1056/17/8/052 Full Text: [PDF 437 KB] (Downloads:666) Show Abstract Nb/Al--AlO$_x$/Nb tunnel junctions are often used in the studies of macroscopic quantum phenomena and superconducting qubit applications of the Josephson devices. In this work, we describe a convenient and reliable process using electron beam lithography for the fabrication of high-quality，submicron-sized Nb/Al--AlO$_x$/Nb Josephson junctions. The technique follows the well-known selective Nb etching process and produces high-quality junctions with$V_m$=100\,mV at 2.3 K for the typical critical current density of 2.2\,kA/cm$^2$, which can be adjusted by controlling the oxygen pressure and oxidation time during the formation of the tunnelling barrier. We present the results of the temperature dependence of the sub-gap current and in-plane magnetic-field dependence of the critical current, and compare them with the theoretical predictions. Wang Fang, Wang Guang-Jun, Sun Ji-Rong, Shen Bao-Gen Chin. Phys. B, 2008, 17 (8): 3087-3092 doi: 10.1088/1674-1056/17/8/053 Full Text: [PDF 267 KB] (Downloads:374) Show Abstract Effects of Nd-doping on the magnetic properties and magnetocaloric effects (MCEs) of Nd$_{x}$La$_{1 - x}$Fe$_{11.5}$Al$_{1.5}$have been investigated. Substitution of Nd leads to a weakening of the antiferromagnetic (AFM) coupling and an enhancement of the ferromagnetic (FM) coupling. This in turn results in a complex magnetic behaviour for Nd$_{0.2}$La$_{0.8}$Fe$_{11.5}$Al$_{1.5}$characterized by the occurrence of two phase transitions at$\sim$188\,K (PM--AFM) and$\sim $159\,K (AFM--FM). As a result, a table-like MCE (9\,J/kg$\cdot$K) is found in a wide temperature range (160--185\,K) for a field change of 0--5\,T around the transition temperature, as evidenced by both the magnetic and calorimetric measurements. Based on the analysis of low-temperature heat capacity, it is found that the AFM--FM phase transition modifies the electron density significantly, and the major contribution to the entropy change comes from the electronic entropy change. Zhang Guo-Ying, Xia Tian, Zhang Xue-Long, Xue Liu-Ping Chin. Phys. B, 2008, 17 (8): 3093-3096 doi: 10.1088/1674-1056/17/8/054 Full Text: [PDF 270 KB] (Downloads:391) Show Abstract The exchange interaction between the electrons in the different magnetic ions and the spin-fluctuation of the magnetic ions exist in the paramagnetic media NdF$_{3}$. The exchange interaction between the electrons in the different magnetic ions may be equivalent to an effective field$H_{in}$that is in direct proportion to the magnetization$\bm M$. The spin-fluctuation of the magnetic ions leads the coefficient of the effective field to vary with temperature. The effective field is given as$\bm H_{\rm in} = - (0.75 + 0.22{\rm T})\times 10^{^{ - 5}}\bm M$in NdF$_{3}$. When the secondary crystal field effect is taken into account, the magnetic susceptibility and Verdet constant are calculated for NdF$_{3}$by means of the effective field$\bm H_{\rm in} $and the applied field$\bm H_e$. The calculated results are in agreement with the measured ones. Zhang Li-Juan, Hua Yu-Lin, Wu Xiao-Ming, Wang Yu, Yin Shou-Geng Chin. Phys. B, 2008, 17 (8): 3097-3102 doi: 10.1088/1674-1056/17/8/055 Full Text: [PDF 276 KB] (Downloads:767) Show Abstract This paper reports the fabrication of novel white organic light-emitting device(WOLED) by using a high efficiency blue fluorescent dye$N$-(4-((E)-2-(6-((E)-4-(diphenylamino)styryl)naphthalen-2-yl)vinyl)phenyl)-$N$-phenylbenzenamine ($N$-BDAVBi) and a red phosphoresecent dye bis (1-(phenyl) isoquinoline) iridium (III) acetylanetonate (Ir(piq)$_{2}$(acac)). The configuration of the device was ITO/PVK:TPD/CBP:$N$-BDAVBi /CBP/ BALq: Ir(piq)$_{2}$(acac)/BCP/Alq$_{3}$/LiF:AL. By adjusting the proportion of the dopants ($N$-BDAVBi, Ir(piq)$_{2}$(acac)) in the light-emitting layer, white light with Commission Internationale de l'Eclairage (CIE) coordinates of (0.35, 0.35) and a maximum luminance of 25350cd/m$^{2}\$ were obtained at an applied voltage of 22V. The WOLED exhibits maximum external quantum and current efficiency of 6.78{\%} and 12cd/A respectively. By placing an undoped spacer CBP layer between the two light-emitting layers and using BCP as hole blocking layer, the colour stabilization slightly changed when the driving voltage increased from 6 to 22\,V.