Table of contents

20 August 2008, Volume 17 Issue 8 Previous issue    Next issue

GENERAL

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On the feasibility of variable separation method based on Hamiltonian system for plane magnetoelectroelastic solids Hou Guo-Lin(侯国林) and Alatancang(阿拉坦仓) Chin. Phys. B, 2008, 17 (8):  2753-2758.  DOI: 10.1088/1674-1056/17/8/001 Abstract ( 1570 )   PDF (193KB) ( 644 )   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.

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Evolutionary snowdrift game on heterogeneous Newman--Watts small-world network Yang Han-Xin(杨涵新), Gao Kun(高坤), Han Xiao-Pu(韩筱璞), and Wang Bing-Hong(汪秉宏) Chin. Phys. B, 2008, 17 (8):  2759-2763.  DOI: 10.1088/1674-1056/17/8/002 Abstract ( 1500 )   PDF (901KB) ( 629 )   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.

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Conformal invariance and integration of first-order differential equations He Guang(何光) and Mei Feng-Xiang(梅凤翔) Chin. Phys. B, 2008, 17 (8):  2764-2765.  DOI: 10.1088/1674-1056/17/8/003 Abstract ( 1572 )   PDF (142KB) ( 671 )   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.

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Complex wave excitations and chaotic patterns for a general (2+1)-dimensional Korteweg--de Vries system Ma Song-Hua(马松华), Fang Jian-Ping(方建平), and Zheng Chun-Long(郑春龙) Chin. Phys. B, 2008, 17 (8):  2767-2773.  DOI: 10.1088/1674-1056/17/8/004 Abstract ( 1604 )   PDF (1226KB) ( 929 )   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.

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Explicit solutions to some nonlinear physical models by a two-step ansatz Hu Jian-Lan(胡建兰) Chin. Phys. B, 2008, 17 (8):  2774-2782.  DOI: 10.1088/1674-1056/17/8/005 Abstract ( 1431 )   PDF (368KB) ( 463 )   Explicit solutions are derived for some nonlinear physical model equations by using a delicate way of two-step ansatz method.

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High-order perturbed corrections with scaling transformation Zhao Yun-Hui(赵云辉) and Zhao Cheng-Lin(赵乘麟) Chin. Phys. B, 2008, 17 (8):  2783-2789.  DOI: 10.1088/1674-1056/17/8/006 Abstract ( 1063 )   PDF (178KB) ( 563 )   The performance of the so-called superconvergent quantum perturbation theory (Wenhua Hai et al 2000 Phys. Rev. A 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--Schrödinger 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.

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Bound entangled states invariant under $U_x$ Wang Zhen(王珍) and Wang Zhi-Xi(王志玺) Chin. Phys. B, 2008, 17 (8):  2790-2794.  DOI: 10.1088/1674-1056/17/8/007 Abstract ( 1360 )   PDF (162KB) ( 428 )   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.

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Genuine tripartite entanglement and quantum phase transition Yu Chang-Shui(于长水), Song He-Shan(宋鹤山), and Cui Hai-Tao(崔海涛) Chin. Phys. B, 2008, 17 (8):  2795-2799.  DOI: 10.1088/1674-1056/17/8/008 Abstract ( 1561 )   PDF (193KB) ( 560 )   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 (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 (Phys. Rev. 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.

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Thermal entanglement in a two-qubit Heisenberg XY chain with the Dzyaloshinskii--Moriya interaction Qin Meng(秦猛), Xu Sheng-Long(徐胜龙), Tao Ying-Juan(陶应娟), and Tian Dong-Ping(田东平) Chin. Phys. B, 2008, 17 (8):  2800-2803.  DOI: 10.1088/1674-1056/17/8/009 Abstract ( 1732 )   PDF (266KB) ( 547 )   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.

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Hawking radiation from Kerr--Newman de Sitter black hole via anomalies Lin Kai(林恺), Yang Shu-Zheng(杨树政), and Zeng Xiao-Xiong(曾晓雄) Chin. Phys. B, 2008, 17 (8):  2804-2810.  DOI: 10.1088/1674-1056/17/8/010 Abstract ( 1460 )   PDF (163KB) ( 525 )   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.

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Thermal radiation and nonthermal radiation of the slowly changing dynamic Kerr--Newman black hole Meng Qing-Miao(孟庆苗), Wang Shuai(王帅), Jiang Ji-Jian(蒋继建), and Deng De-Li(邓德力) Chin. Phys. B, 2008, 17 (8):  2811-2816.  DOI: 10.1088/1674-1056/17/8/011 Abstract ( 1601 )   PDF (114KB) ( 670 )   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.

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Modified de Broglie--Bohm approach to the Schwarzschild black hole Wang Bo-Bo(王波波) Chin. Phys. B, 2008, 17 (8):  2817-2823.  DOI: 10.1088/1674-1056/17/8/012 Abstract ( 1477 )   PDF (325KB) ( 650 )   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.

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Could one single dichotomous noise cause resonant activation for exit time over potential barrier? Li Jing-Hui(李静辉) Chin. Phys. B, 2008, 17 (8):  2824-2828.  DOI: 10.1088/1674-1056/17/8/013 Abstract ( 1305 )   PDF (242KB) ( 407 )   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.

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Circuit implementation of a new hyperchaos in fractional-order system .. Liu Chong-Xin(刘崇新) and Liu Ling(刘凌) Chin. Phys. B, 2008, 17 (8):  2829-2836.  DOI: 10.1088/1674-1056/17/8/014 Abstract ( 1523 )   PDF (3413KB) ( 1082 )   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, Poincaré 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.

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The characteristics of nonlinear chaotic dynamics in quantum cellular neural networks Wang Sen(王森), Cai Li(蔡理), Kang Qiang(康强), Wu Gang(吴刚), and Li Qin(李芹) Chin. Phys. B, 2008, 17 (8):  2837-2843.  DOI: 10.1088/1674-1056/17/8/015 Abstract ( 1413 )   PDF (350KB) ( 679 )   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.

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Stabilization of spiral wave and turbulence in the excitable media using parameter perturbation scheme Ma Jun(马军), Wang Chun-Ni(王春妮), Jin Wu-Yin(靳伍银), Li Yan-Long(李延龙), and Pu Zhong-Sheng(蒲忠胜) Chin. Phys. B, 2008, 17 (8):  2844-2849.  DOI: 10.1088/1674-1056/17/8/016 Abstract ( 1482 )   PDF (6626KB) ( 899 )   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.

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Steady state speed distribution analysis for a combined cellular automaton traffic model Wang Jun-Feng(王俊峰), Chen Gui-Sheng(陈桂生), and Liu Jin(刘进) Chin. Phys. B, 2008, 17 (8):  2850-2858.  DOI: 10.1088/1674-1056/17/8/017 Abstract ( 1481 )   PDF (1427KB) ( 613 )   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.

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Low-temperature heat capacities and standard molar enthalpy of formation of N-methylnorephedrine C11H17NO(s) Di You-Ying(邸友莹), Wang Da-Qi(王大奇), Shi Quan(史全), and Tan Zhi-Cheng(谭志诚) Chin. Phys. B, 2008, 17 (8):  2859-2866.  DOI: 10.1088/1674-1056/17/8/018 Abstract ( 1195 )   PDF (198KB) ( 709 )   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.

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Analytic equation of state for solids with multi-exponential potential based on analytic mean field potential approach and applied to the epsilon phase of solid oxygen Wang Li-Guo(王立国), Sun Jiu-Xun(孙久勋), and Yang Wei(杨维) Chin. Phys. B, 2008, 17 (8):  2867-2873.  DOI: 10.1088/1674-1056/17/8/019 Abstract ( 1195 )   PDF (1042KB) ( 464 )   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.

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An evolutionary model of urban bus transport network based on B-space Zhu Zhen-Tao(朱振涛), Zhou Jing(周晶), Li Ping(李平), and Chen Xing-Guang(陈星光) Chin. Phys. B, 2008, 17 (8):  2874-2880.  DOI: 10.1088/1674-1056/17/8/020 Abstract ( 1365 )   PDF (683KB) ( 954 )   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 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.

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Calculation of the reactor neutron time of flight spectrum by convolution technique Cheng Jin-Xing(程金星), Ouyang Xiao-Ping(欧阳晓平), Zheng Yi(郑毅), Zhang An-Hui(张安慧), and Ouyang Mao-Jie (欧阳茂解) Chin. Phys. B, 2008, 17 (8):  2881-2884.  DOI: 10.1088/1674-1056/17/8/021 Abstract ( 1327 )   PDF (377KB) ( 455 )   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.

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Absorptive reduction and width narrowing in $\Lambda$-type atoms confined between two dielectric walls Li Yuan-Yuan(李院院), Hou Xun(侯洵), Bai Jin-Tao(白晋涛), Yan Jun-Feng(闫军锋), Gan Chen-Li(甘琛利), and Zhang Yan-Peng(张彦鹏) Chin. Phys. B, 2008, 17 (8):  2885-2889.  DOI: 10.1088/1674-1056/17/8/022 Abstract ( 1513 )   PDF (864KB) ( 492 )   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

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Calculations of state-selective differential cross sections for charge transfer in collisions between O3+ and H2 Chi Bao-Qian(迟宝倩), Liu Ling(刘玲), and Wang Jian-Guo(王建国) Chin. Phys. B, 2008, 17 (8):  2890-2896.  DOI: 10.1088/1674-1056/17/8/023 Abstract ( 1300 )   PDF (683KB) ( 595 )   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.

ATOMIC AND MOLECULAR PHYSICS

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Peculiar features of the interaction potential between hydrogen and antihydrogen at intermediate separations Lee Teck-Ghee(李德义), Wong Cheuk-Yin(黄卓然), and Wang Lee-Shien(王礼贤) Chin. Phys. B, 2008, 17 (8):  2897-2908.  DOI: 10.1088/1674-1056/17/8/024 Abstract ( 1259 )   PDF (775KB) ( 430 )   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.

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Transition energy and dipole oscillator strength for 1s22p-1s2nd of Cr2l+ ion Wang Zhi-Wen(王治文), Liu Ying(刘影), Hu Mu-Hong(胡木宏), Li Xin-Ru(李新汝), and Wang Ya-Nan(王亚男) Chin. Phys. B, 2008, 17 (8):  2909-2913.  DOI: 10.1088/1674-1056/17/8/025 Abstract ( 1289 )   PDF (185KB) ( 505 )   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.

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Quantum coherent control of two-photon transitions by square phase-modulation Zhang Shi-An(张诗按), Wang Zu-Geng(王祖赓), and Sun Zhen-Rong(孙真荣) Chin. Phys. B, 2008, 17 (8):  2914-2918.  DOI: 10.1088/1674-1056/17/8/026 Abstract ( 1276 )   PDF (193KB) ( 491 )   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.

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Investigation of analytical potential energy function, harmonic frequency and vibrational levels for the $X^2\varSigma^+$ and $A^2\varPi$ states of CN radical Wang Jian-Kun(王建坤) and Wu Zhen-Sen(吴振森) Chin. Phys. B, 2008, 17 (8):  2919-2924.  DOI: 10.1088/1674-1056/17/8/027 Abstract ( 1534 )   PDF (197KB) ( 444 )   This paper calculates the equilibrium structure and the potential energy functions of the ground state ($X^2\varSigma^{ + })$ 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.

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Spin polarization effect for Cr2 molecule Yan Shi-Ying(阎世英) Chin. Phys. B, 2008, 17 (8):  2925-2931.  DOI: 10.1088/1674-1056/17/8/028 Abstract ( 1099 )   PDF (568KB) ( 673 )   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 De for the ground state of the Cr$_{2}$ molecule is 0.1034 eV, equilibrium bond length Re 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.

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Correspondence between classical dynamics and recurrence spectra of Rydberg hydrogen atom near a metal surface Li Hong-Yun(李洪云), Gao Song(高嵩), Zhou Hui(周慧), Zhang Yan-Hui(张延惠), and Lin Sheng-Lu(林圣路) Chin. Phys. B, 2008, 17 (8):  2932-2937.  DOI: 10.1088/1674-1056/17/8/029 Abstract ( 1250 )   PDF (839KB) ( 497 )   The chaotic behaviours of the Rydberg hydrogen atom near a metal surface are presented. A numerical comparison of Poincaré 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.

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Structures and electronic properties of SimN8-m(0<m<8) clusters: a density functional theory study Zhang Cai-Rong(张材荣), Chen Yu-Hong(陈玉红), Wang Dao-Bin(王道斌), Wu You-Zhi(吴有智), and Chen Hong-Shan(陈宏善) Chin. Phys. B, 2008, 17 (8):  2938-2950.  DOI: 10.1088/1674-1056/17/8/030 Abstract ( 1416 )   PDF (4284KB) ( 1113 )   The geometries, electronic structures and related properties of Si$_{m}$N$_{8 - m}(0<m<8)$ clusters are studied using density functional theory (DFT) with hybrid functional B3LYP. The calculated results reveal several trends. For any stoichiometric clusters, the lowest energy isomers with an alteration of N and Si atoms are favourable in energy if the numbers of Si and N atoms are large enough to form $\ldots$ Si--N--Si--N$\ldots$ alternative chains. The bond lengths of single Si--N bonds are very close to the corresponding values of the bulk and other Si--N clusters. The geometries for N-rich and Si$_{4}$N$_{4}$ clusters are planar structures, but three-dimensional structures are favourable in energy for Si-rich clusters. With the increase of $m$, the isotropic polarizability and average polarizability increase, the total binding energies generally decrease, the HOMO-LUMO gap and vertical ionization potential oscillate with increasing number of valence electrons, and their values with even valence electrons are larger than those with odd valence electrons. The atomic charges, IR and Raman properties are also reported.

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Density functional investigations for geometric and electronic properties of In4M and In12M (M = C, Si, In) clusters Li Zhi-Jian(李志坚) and Li Jin-Hui(李锦茴) Chin. Phys. B, 2008, 17 (8):  2951-2955.  DOI: 10.1088/1674-1056/17/8/031 Abstract ( 1444 )   PDF (3995KB) ( 560 )   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.

CLASSICAL AREAS OF PHENOMENOLOGY

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Fractal characteristics investigation on electromagnetic scattering from 2-D Weierstrass fractal dielectric rough surface Ren Xin-Cheng(任新成) and Guo Li-Xin(郭立新) Chin. Phys. B, 2008, 17 (8):  2956-2962.  DOI: 10.1088/1674-1056/17/8/032 Abstract ( 1483 )   PDF (245KB) ( 559 )   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.

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Quantum entanglement in the mode-mode competition system Wu Qin(吴琴), Fang Mao-Fa(方卯发), Feng Yong-Zhen(冯永振), and Hu Yao-Hua(胡要花) Chin. Phys. B, 2008, 17 (8):  2963-2968.  DOI: 10.1088/1674-1056/17/8/033 Abstract ( 1421 )   PDF (376KB) ( 477 )   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.

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Purification of entangled states for two atoms via cavity decay Zheng Shi-Biao(郑仕标) Chin. Phys. B, 2008, 17 (8):  2969-2972.  DOI: 10.1088/1674-1056/17/8/034 Abstract ( 1353 )   PDF (139KB) ( 446 )   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.

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The q-analogues of two-mode squeezed states constructed by virtue of the IWOP technique Meng Xiang-Guo(孟祥国), Wang Ji-Suo(王继锁), and Li Hong-Qi(李洪奇) Chin. Phys. B, 2008, 17 (8):  2973-2978.  DOI: 10.1088/1674-1056/17/8/035 Abstract ( 1273 )   PDF (178KB) ( 494 )   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.

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Laser self-mixing interference fibre sensor Zhu Jun(朱钧), Zhao Yan(赵燕), and Jin Guo-fan(金国藩) Chin. Phys. B, 2008, 17 (8):  2979-2983.  DOI: 10.1088/1674-1056/17/8/036 Abstract ( 1095 )   PDF (582KB) ( 462 )   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.

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Comparison of Xe single bubble sonoluminescence in water and sulfuric acid An Yu(安宇) Chin. Phys. B, 2008, 17 (8):  2984-2988.  DOI: 10.1088/1674-1056/17/8/037 Abstract ( 1429 )   PDF (598KB) ( 482 )   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.

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The interaction of nonlinear waves in two-dimensional lattice Yang Xiao-Xia(杨晓霞), Duan Wen-Shan(段文山), Li Sheng-Chang(栗生长), and Han Jiu-Ning(韩久宁) Chin. Phys. B, 2008, 17 (8):  2989-2993.  DOI: 10.1088/1674-1056/17/8/038 Abstract ( 1194 )   PDF (433KB) ( 536 )   This paper investigates the collision between two nonlinear waves with arbitrary angle in two-dimensional nonlinear lattice. By using the extended Poincaré--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.

PHYSICS OF GASES, PLASMAS, AND ELECTRIC DISCHARGES

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Stability analysis of viscous Z-pinch plasma with a sheared axial flow Zhang Yang(张扬) and Ding Ning(丁宁) Chin. Phys. B, 2008, 17 (8):  2994-3002.  DOI: 10.1088/1674-1056/17/8/039 Abstract ( 1350 )   PDF (225KB) ( 577 )   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

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Compositional and structural evolution of the titanium dioxide formation by thermal oxidation Su Wei-Feng(苏卫锋), Gnaser Hubert , Fan Yong-Liang(樊永良), Jiang Zui-Min(蒋最敏), and Le Yong-Kang(乐永康) Chin. Phys. B, 2008, 17 (8):  3003-3007.  DOI: 10.1088/1674-1056/17/8/040 Abstract ( 1342 )   PDF (966KB) ( 891 )   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.

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Morphologies of epitaxial islands on a lattice-misfitted substrate Wang Jian-Ping(汪建平), Zhou Wang-Min(周旺民), Wang Chong-Yu(王崇愚), and Yin Shu-Yuan(尹姝媛) Chin. Phys. B, 2008, 17 (8):  3008-3013.  DOI: 10.1088/1674-1056/17/8/041 Abstract ( 1335 )   PDF (185KB) ( 513 )   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.

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Phase transition on speed limit traffic with slope Li Xing-Li(李兴莉), Song Tao(宋涛), Kuang Hua(邝华), and Dai Shi-Qiang(戴世强) Chin. Phys. B, 2008, 17 (8):  3014-3020.  DOI: 10.1088/1674-1056/17/8/042 Abstract ( 1324 )   PDF (1399KB) ( 985 )   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.

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Influence of HF catalyst on the microstructure properties of ultra low-k thin films prepared by sol-gel method He Zhi-Wei(何志巍), Xu Da-Yin(徐大印), Jiang Xiang-Hua(江祥华), and Wang Yin-Yue(王印月) Chin. Phys. B, 2008, 17 (8):  3021-3025.  DOI: 10.1088/1674-1056/17/8/043 Abstract ( 1449 )   PDF (1128KB) ( 559 )   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

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Effect of electric field on the spectrum and the persistent current of a quantum ring with two electrons (II)---additional effect of a charged impurity Wu Hong(吴洪) Chin. Phys. B, 2008, 17 (8):  3026-3034.  DOI: 10.1088/1674-1056/17/8/044 Abstract ( 1534 )   PDF (1226KB) ( 536 )   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 Rp 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.

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Modelling of spreading process: effect from hydrogen bonds Li Xin(李欣), Hu Yuan-Zhong(胡元中), and Jiang Lan(姜澜) Chin. Phys. B, 2008, 17 (8):  3035-3039.  DOI: 10.1088/1674-1056/17/8/045 Abstract ( 1270 )   PDF (1324KB) ( 517 )   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.

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Electronic structure and physical properties of ScN in pressure: density-functional theory calculations Guan Peng-Fei(管鹏飞), Wang Chong-Yu(王崇愚), and Yu Tao(于涛) Chin. Phys. B, 2008, 17 (8):  3040-3053.  DOI: 10.1088/1674-1056/17/8/046 Abstract ( 1351 )   PDF (7051KB) ( 506 )   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).

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Electronic states of InAs/GaAs tyre-shape quantum ring Wang Chuan-Dao(王传道), Yang Fu-Hua(杨富华), and Feng Song-Lin(封松林) Chin. Phys. B, 2008, 17 (8):  3054-3057.  DOI: 10.1088/1674-1056/17/8/047 Abstract ( 1287 )   PDF (477KB) ( 513 )   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.

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Spin-dependent quantum transport through an Aharonov--Bohm structure spin splitter Li Yu-Xian(李玉现) Chin. Phys. B, 2008, 17 (8):  3058-3061.  DOI: 10.1088/1674-1056/17/8/048 Abstract ( 1421 )   PDF (189KB) ( 471 )   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.

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First-principles investigation of BAs and BxGa1-xAs alloys Xiong De-Ping(熊德平), Zhou Shou-Li(周守利), Wang Qi(王琦), and Ren Xiao-Min(任晓敏) Chin. Phys. B, 2008, 17 (8):  3062-3066.  DOI: 10.1088/1674-1056/17/8/049 Abstract ( 1358 )   PDF (200KB) ( 600 )   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 $\varGamma_{\rm 15c}$ state rather than s-like $\varGamma_{\rm 1c}$ state, and the conduction band minimum (CBM) is along the $\varDelta$ line between the $\varGamma$ 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.

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Dynamical study on charge injection and transport in a metal/polythiophene/metal structure Li Dong-Mei(李冬梅), Liu Xiao-Jing(刘晓静), Li Yuan(李元), Li Hai-Hong(李海宏), Hu Gui-chao(胡贵超), Gao Kun(高琨), Liu De-Sheng(刘德胜), and Xie Shi-Jie(解士杰) Chin. Phys. B, 2008, 17 (8):  3067-3076.  DOI: 10.1088/1674-1056/17/8/050 Abstract ( 1304 )   PDF (1389KB) ( 460 )   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.

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Quantum compact model for thin-body double-gate Schottky barrier MOSFETs Luan Su-Zhen(栾苏珍) and Liu Hong-Xia(刘红侠) Chin. Phys. B, 2008, 17 (8):  3077-3082.  DOI: 10.1088/1674-1056/17/8/051 Abstract ( 1479 )   PDF (782KB) ( 469 )   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.

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Fabrication of high-quality submicron Nb/Al--AlOx/Nb tunnel junctions Yu Hai-Feng(于海峰), Cao Wen-Hui(曹文会), Zhu Xiao-Bo(朱晓波), Yang Hai-Fang(杨海方), Yu Hong-Wei(于洪伟), Ren Yu-Feng (任育峰), Gu Chang-Zhi(顾长志), Chen Geng-Hua(陈赓华), and Zhao Shi-Ping(赵士平) Chin. Phys. B, 2008, 17 (8):  3083-3086.  DOI: 10.1088/1674-1056/17/8/052 Abstract ( 1325 )   PDF (437KB) ( 771 )   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.

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Magnetic properties and magnetocaloric effect in NdxLa1-xFe11.5Al1.5 compounds Wang Fang(王芳), Wang Guang-Jun(王光军), Sun Ji-Rong(孙继荣), and Shen Bao-Gen(沈保根) Chin. Phys. B, 2008, 17 (8):  3087-3092.  DOI: 10.1088/1674-1056/17/8/053 Abstract ( 1700 )   PDF (267KB) ( 455 )   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.

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Effects of exchange interaction and spin-fluctuation on the magnetic and magneto-optic properties of NdF3 Zhang Guo-Ying(张国营), Xia Tian(夏天), Zhang Xue-Long(张学龙), and Xue Liu-Ping(薛刘萍) Chin. Phys. B, 2008, 17 (8):  3093-3096.  DOI: 10.1088/1674-1056/17/8/054 Abstract ( 1090 )   PDF (270KB) ( 502 )   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 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 H$_{\rm in} = - (0.75 + 0.22{\rm T})$ $\times 10^{^{ - 5}}$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 H$_{\rm in} $ and the applied field H$_e$. The calculated results are in agreement with the measured ones.

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White organic light-emitting device with both phosphorescent and fluorescent emissive layers .. Zhang Li-Juan(张丽娟), Hua Yu-Lin(华玉林), Wu Xiao-Ming(吴小明), Wang Yu(王宇), and Yin Shou-Geng(印寿根) Chin. Phys. B, 2008, 17 (8):  3097-3102.  DOI: 10.1088/1674-1056/17/8/055 Abstract ( 1374 )   PDF (276KB) ( 890 )   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.

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Trap induced slow photoresponse of single CdS nanoribbons Wang Fei-Fei(王菲菲), Wang Chong(王翀), Cheng Ke(程轲), and Zou Bing-Suo(邹炳锁) Chin. Phys. B, 2008, 17 (8):  3103-3107.  DOI: 10.1088/1674-1056/17/8/056 Abstract ( 1212 )   PDF (1243KB) ( 503 )   Wurtzite CdS nanoribbons are prepared by using a simple thermal evaporation method. Electron microscopy shows that the ribbons are smooth in surface and uniform in size. Besides the intrinsic emission, the photoluminescence spectrum of a CdS nanoribbon shows a peak at about 580 nm, which may arise from the defect- and the trap- related transitions. The photoresponse of single CdS nanoribbons is researched. When these nanoribbons are exposed to a laser with a wavelength of 400 nm, their conductivity is enhanced greatly. The conductivity of CdS nanoribbons cannot be restored to a value without any illumination even at 5 minutes after the illumination. A model is proposed to explain this phenomenon, which may be due to a slow photoresponse induced by the trap.

CROSS DISCIPLINARY PHYSICS AND RELATED AREAS OF SCIENCE AND TECHNOLOGY

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Studies of diamond-like carbon (DLC) films deposited on stainless steel substrate with Si/SiC intermediate layers Wang Jing(王静), Liu Gui-Chang(刘贵昌), Wang Li-Da(王立达), Deng Xin-Lü(邓新绿), and Xu Jun(徐军) Chin. Phys. B, 2008, 17 (8):  3108-3114.  DOI: 10.1088/1674-1056/17/8/057 Abstract ( 997 )   PDF (751KB) ( 726 )   In this work, diamond-like carbon (DLC) films were deposited on stainless steel substrates with Si/SiC intermediate layers by combining plasma enhanced sputtering physical vapour deposition (PEUMS-PVD) and microwave electron cyclotron resonance plasma enhanced chemical vapour deposition (MW-ECRPECVD) techniques. The influence of substrate negative self-bias voltage and Si target power on the structure and nano-mechanical behaviour of the DLC films were investigated by Raman spectroscopy, nano-indentation, and the film structural morphology by atomic force microscopy (AFM). With the increase of deposition bias voltage, the G band shifted to higher wave-number and the integrated intensity ratio $I_{D}$/$I_{G}$ increased. We considered these as evidences for the development of graphitization in the films. As the substrate negative self-bias voltage increased, particle bombardment function was enhanced and the sp$^{3}$-bond carbon density reducing, resulted in the peak values of hardness ($H$) and elastic modulus ($E$). Silicon addition promoted the formation of sp$^{3}$ bonding and reduced the hardness. The incorporated Si atoms substituted sp$^{2}$- bond carbon atoms in ring structures, which promoted the formation of sp$^{3}$-bond. The structural transition from C--C to C--Si bonds resulted in relaxation of the residual stress which led to the decrease of internal stress and hardness. The results of AFM indicated that the films was dense and homogeneous, the roughness of the films was decreased due to the increase of substrate negative self-bias voltage and the Si target power.

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The phase behaviour of single polyethylene chains with and without fixing one end Su Jia-Ye(苏加叶) and Zhang Lin-Xi(章林溪) Chin. Phys. B, 2008, 17 (8):  3115-3122.  DOI: 10.1088/1674-1056/17/8/058 Abstract ( 1105 )   PDF (980KB) ( 469 )   The phase behaviour of a single polyethylene chain is studied by using molecular dynamics simulations. A free chain and a chain with fixing one end are considered here, since the atomic force microscope (AFM) tip can play a significant role in polymer crystallization in experiment. For a free chain, it is confirmed in our calculation that the polymer chain exhibits an extended coil state at high temperatures, collapses into a condensed state at low temperatures, i.e. the coil-to-globule transition that is determined by a high temperature shoulder of the heat capacity curve, and an additional liquid-to-solid transition that is described by a low temperature peak of the same heat curve. These results accord with previous studies of square-well chains and Lennard-Jones homopolymers. However, when one of the end monomers of the same chain is fixed the results become very different, and the chain cannot reach an extended coil-like state as a free chain does at high temperatures, i.e. there exists no coil-to-globule-like transition. These results may provide some insights into the influence of AFM tip when it is used to study the phase behaviour of polymer chains. If the interaction force between AFM tip and polymer monomers is strong, some monomers or one of them can be seen as being fixed by the tip, which is similar to our simulation model, and it is also found that AFM tip could induce polymer crystallization.

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The rehybridization of electronic orbitals in carbon nanotubes Ouyang Yu(欧阳玉), Peng Jing-Cui(彭景翠), Wang Hui(王慧), and Peng Zhi-Hua(彭志华) Chin. Phys. B, 2008, 17 (8):  3123-3129.  DOI: 10.1088/1674-1056/17/8/059 Abstract ( 1154 )   PDF (187KB) ( 718 )   Rehybridization of electronic orbitals in carbon nanotubes contains tilting angles of $\pi $ orbital, electrons wavefunctions of $\pi $ orbital and $\sigma $ orbital, degrees of hybridization, etc. In this paper, we have obtained analytical formulas of tilting angle of $\pi $ orbital relative to tube surface, electrons wavefunctions of $\pi $ orbital and $\sigma $ orbital, degrees of hybridization, separately, as well as the numerical results.

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Observation of a diverse deviation from macropore-formation theory in silicon electrochemistry Bao Xiao-Qing(包晓清), Ge Dao-Han(葛道晗), and Jiao Ji-Wei(焦继伟) Chin. Phys. B, 2008, 17 (8):  3130-3137.  DOI: 10.1088/1674-1056/17/8/060 Abstract ( 987 )   PDF (4166KB) ( 476 )   Via anodizing patterned and unpatterned samples with a high HF concentration ([HF]), the degree of deviation from pore-formation theory was found to be markedly different. Based on the analysis of scanning electron microscope (SEM) micrographs and current--voltage ($I-V$) curves, the variation of physical and chemical parameters of patterned and unpatterned substrates was found to be crucial to the understanding of the observations. Our results indicate that the initial surface morphology of samples can have a considerable influence upon pore formation. The electric-field effect as well as current-burst-model was employed to interpret the underlying mechanism.

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The effect of composition on structural and electronic properties in polycrystalline CuGaSe2 thin film Zhang Li(张力), He Qing(何青), Xu Chuan-Ming(徐传明), Xue Yu-Ming (薛玉明), Li Chang-Jian(李长健), and Sun Yun(孙云) Chin. Phys. B, 2008, 17 (8):  3138-3142.  DOI: 10.1088/1674-1056/17/8/061 Abstract ( 1102 )   PDF (3354KB) ( 746 )   Polycrystalline CuGaSe$_{2}$ thin films on Mo-coated soda-lime glass substrates have been synthesized by co-evaporation process from Cu, Ga and Se sources. Structural and electrical properties of the as-grown CuGaSe$_{2}$ films strongly depend on the film composition. Stoichiometric CuGaSe$_{2}$ is fabricated, as indicated by x-ray diffraction spectroscope (XRD) and x-ray fluorescence (XRF). A two-phase region is composed of CuGaSe$_{2}$ and Cu$_{2 - x}$Se phases for Cu-rich films, and CuGaSe$_{2}$ and CuGa$_{3}$Se$_{5}$ phases for Ga-rich films，respectively. Morphological properties are detected by scanning electron microscope (SEM) for various compositional films, the grain sizes of the CuGaSe$_{2 }$films decrease with the extent of deviation from stoichiometric composition. Raman spectroscopy of Cu-rich samples shows that there exist large Cu-Se particles on the film surface. The results from Hall effect measurements for typical samples indicate that CuGaSe$_{2}$ films are always of p-type semiconductor from Cu-rich to Ga-rich. Stoichiometric CuGaSe$_{2}$ films exhibit relatively large mobility than any other compositional films. Finally, polycrystalline CuGaSe$_{2}$ thin film solar cell with a best conversion efficiency of 6.02% has been achieved under the standard air mass (AM)1.5 spectrum for 100 mW/cm$^{2 }$ at room temperature (aperture area, 0.24 cm$^{2})$. The open circuit voltage of the CuGaSe$_{2}$ solar cells is close to770 mV.

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Self-organization effect in poly(3-hexylthiophene): methanofullerenes solar cells Yu Huang-Zhong(於黄忠) and Peng Jun-Biao(彭俊彪) Chin. Phys. B, 2008, 17 (8):  3143-3148.  DOI: 10.1088/1674-1056/17/8/062 Abstract ( 1200 )   PDF (1027KB) ( 574 )   This paper studies the self-organization of the polymer in solar cells based on poly(3-hexylthiophene): [6, 6]-phenyl C$_{61}$-butyric acid methyl ester by controlling the growth rate of active layer. These blend films are characterized by UV-vis absorption spectroscopy, charge-transport dark $J-V$ curve, x-ray diffraction pattern curve, and atomic force microscopy. The results indicate that slowing down the drying process of the wet films leads to an enhanced self-organization, which causes an increased hole transport. Increased incident light absorption, higher carrier mobility, and balanced carrier transport in the active layer explain the enhancement in the device performance, the power conversion efficiency of 3.43% and fill factor up to 64.6%are achieved under Air Mass 1.5, 100 mW/cm$^{2}$.

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The fluid phenomena in the crystallization of the protein crystal Duan Li(段俐) and Kang Qi(康琦) Chin. Phys. B, 2008, 17 (8):  3149-3155.  DOI: 10.1088/1674-1056/17/8/063 Abstract ( 883 )   PDF (6605KB) ( 385 )   This paper reports that an optical diagnostic system consisting of Mach--Zehnder interferometer with a phase shift device and image processor has been used for study of the kinetics of protein crystal growing process. The crystallization process of protein crystal by vapour diffusion is investigated. The interference fringes are observed in real time. The present experiment demonstrates that the diffusion and the sedimentation influence the crystallization of protein crystal which grows in solution, and the concentration capillary convection associated with surface tension occurs at the vicinity of free surface of the protein mother liquor, and directly affects on the outcome of protein crystallization. So far the detailed analysis and the important role of the fluid phenomena in protein crystallization have been discussed a little in both space- and ground-based crystal growth experiments. It is also found that these fluid phenomena affect the outcome of protein crystallization, regular growth, and crystal quality. This may explain the fact that many results of space-based investigation do not show overall improvement.

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The study on optically stimulated luminescence dosimeter based on the SrS:Eu, Sm and CaS:Eu, Sm Liu Yan-Ping(刘艳平), Chen Zhao-Yang(陈朝阳), Fan Yan-Wei(范艳伟), Ba Wei-Zhen(巴维真), Gou Qi(郭旗), Lu Wu(陆妩), Tang Xin-Qiang(汤新强), and Du Yan-Zhao(杜彦召) Chin. Phys. B, 2008, 17 (8):  3156-3162.  DOI: 10.1088/1674-1056/17/8/064 Abstract ( 1070 )   PDF (269KB) ( 596 )   With the increasing use of nuclear energy, there is a need for a wider range of efficient dosimeters for radiation detection and assessment. There has been a tremendous growth in the development of radiation detectors and devices in the past few decades. In recent years, the development of new materials for radiation dosimetry has progressed significantly. Alkaline earth sulfides (AES) have been known for a long time as excellent and versatile phosphor materials. In the present investigation, a number of phosphor samples such as mono-, binary and ternary sulfides of alkaline earths (II$^{\rm a}$-VI$^{\rm b})$ have been prepared and their TL properties have been studied with respect to exposure (x-ray) response and fading. In this paper, some results on SrS:Eu, Sm and CaS:Eu, Sm phosphors are presented. A type of novel OSL dosimeter is described. The dosimeter takes advantage of the characteristics of charge trapping materials SrS:Eu, Sm and CaS:Eu, Sm that exhibit optically stimulated luminescence (OSL). The measuring range of the dosimeter is from 0.01 to 1000 Gy. The OSL dosimeters provide capability for remote monitoring radiation locations which are difficult to access and hazardous. This equipment is relatively simple, small in size and has low power consumption. The device is suitable for space radiation dose exploration. In addition, it also can be used in IC and other radiation occasions and has good prospects.