N维各向同性谐振子径向平均值的递推关系和解析表达式

推导出了用于N维各向同性谐振子径向平均值计算的二个递推关系,并在-3≤s≤3的条件下,给出了平均值〈n_rJ_N-2|r^2s|n_rJ_N-2〉的值.二维和三维各向同性谐振子的相关结果均作为特例包含在结论中.     

Theoretical study of stereodynamics for the reaction O(3P) +D2 (v=0, j=0) to OD+D and isotope effect

Quasi-classical trajectory (QCT) calculations have been performed to study the product polarization behaviours in the reaction O(³P) + D₂ (v= 0, j= 0)→OD + D. By running trajectories on the ³A′ and ³A″ potential energy surfaces (PESs), vector correlations such as the distributions of the polarization-dependent differential cross sections (PDDCSs), the angular distributions of P(θ_r) and P(ø_r) are presented. Isotope effect is discussed in this work by a comprehensive comparison with the reaction O(³P) + H₂ (v= 0, j= 0) → H + H. Common characteristics as well as differences are discussed in product alignment and orientation for the two reactions. The isotope mass effect differs on the two potential energy surfaces: the isotope mass effect has stronger influence on P(θ_r) and PDDCSs of the ³A′ PES while the opposite on P(ø_r) of the ³A″ potential energy surface.     

氮原子在800 nm附近的同位素位移

The Doppler-limited absorption spectra of ¹⁴N and ¹⁵N atoms were measured around 800 nm using concentration modulation spectroscopy to study their isotope shifts. The nitrogen atoms were generated by discharging molecular nitrogen buffered with helium in a homemade discharge tube. The isotope shifts of four multiplets (3s⁴P_J→3p⁴D_J^o, 3s⁴P_J→3p⁴P_J^o, 3s²D_J→5s²P_J^o, and 3p²P_J^o→5s²D_J^o) were measured and their J-dependent specific mass shifts were observed and discussed.     

hcp结构的Co磁性膜表面和界面的非线性克尔旋转及SHG的研究

本文基于对称性理论、磁性表面的菲涅耳反射和折射定律,研究了hcp(密排六方体)Co结构的χ⁽²⁾、SHG(二次谐波振荡)信号强度和非线性磁光克尔旋转角Φ_k,α⁽²⁾与入射角、偏振角及光子能量的关系.结果表明,Φ_k,α⁽²⁾比线性克尔角有巨大的增强;当接近垂直入射时,Φ_k,α⁽²⁾接近90°;Φ_k,α⁽²⁾灵敏地依赖于M的影响,从而可以通过Φ_k,α⁽²⁾来决定薄膜中的晶轴方向和磁化强度的取向.     

带栅极纳米线冷阴极的场增强因子研究

场增强因子是体现场发射冷阴极器件性能优劣的重要参数.利用静电场理论给出了一种带栅极(normal-gated)纳米线冷阴极的场增强因子表示式β=k₁{N²·(L-d₁)²+［1/k₁+(L-d₁)］²}^1/2，且进一步分析了几何参数对场增强因子的影响.结果表明，纳米线突出栅孔的部分(L-d₁)与栅孔半径越大，则场增强因子越大；而纳米线半径越小，则场增强因子越大；当L远大于d₁时满足β∝L/r₀.其中N=N₁(k₁r₀)/N₀(k₁r₀)，N₀(k₁r₀)和N₁(k₁r₀)分别代表零阶和一阶Neumann函数，k₁=0.8936/R，R为栅孔半径，L为纳米线长度，r₀为纳米线半径，d₁表示阴极与栅极间距.     

DsJ(2632)强衰变的研究

SELEX合作组发现的D_sJ(2632)引起了很多的讨论, 同时也带来了激烈的争论. 它的自旋宇称还没有最后确定, 如果它真的存在, 它的夸克结构可能是奇特的. 以前有的文献假定D_sJ(2632)是1^－的径向激发态, 我们假定它可能是夸克结构为qq,J^P为2⁺的基态或者0⁺D_sJ(2317)的第一径向激发态, 用Bethe-Salpeter方程重新计算了它的衰变宽度. 计算结果表明, 理论值和实验数据还是存在尖锐的矛盾.     

“全同”超形变核转动带的量子群Uqp(u2)模型的理论分析

利用量子群U_qp(u₂)模型计算了^{191-192-193-194Hg}超形变(SD)带的γ跃迁能E_γ,运动学转动惯量J⁽¹⁾和动力学转动惯量J⁽²⁾,顺排角动量之差(i=ω(J⁽¹⁾(^{191-192-193-194}Hg)-J⁽¹⁾(¹⁹²Hg))),并与实验值进行比较得到了满意的结果,此外,还利用U_qp(u₂)模型的形变参量与核软度的关系式,计算出各SD带的核软度参数σ₁与唯象分析给出的组态结构进行了比较分析.     

高分辨的一氧化二氮光解离实验研究

利用"时间切片"离子速度成像技术研究了N₂O分子在134.20、135.20和136.43 nm波长下的真空紫外光解动力学. 实验中通过采集解离产物O(¹S_J=0)的离子影像来研究O(¹S_J=0)+N₂(X¹∑_g⁺)这一解离通道. 从各个波长下的实验影像可获得产物N₂(X¹∑_g⁺)的振动态分辨的结构,进而得到产物的总平动能谱和产物N₂的振动态布居. 实验结果表明在实验的光解波长下,产物N₂(X¹∑_g⁺)主要布居在v=2和v=3. 此外,还得到了产物N₂的振动态分辨的各向异性参数β,从中发现产物N₂的β值在三个解离波长下均表现出相似的特征,即随着振动量子数的增大,β值从趋近于2逐渐减小至1.4. 这一现象表明低振动态产物是通过一个以平行跃迁解离为主的解离过程产生的,而高振动态的产物来自于一个更加弯曲的中间构型的解离. 此推论与在平动能谱中所见到的最强转动态布居随着振动量子数的增大而出现的位移是相一致的.     

Spectroscopic investigations on NO+(x1∑+,a3∑+,A1Ⅱ) ion using multi-reference configuration interaction method and correlation-consistent sextuple b

Three low-lying electronic states (x¹∑⁺,a³∑⁺,and A¹Ⅱ) of NO⁺ ion are studied using the complete active space self-consistent-field (CASSCF) method followed by highly accurate valence internally contracted multi-reference configuration interaction (MRCI) approach in combination of the correlation-consistent sextuple basis set augmented with diffuse functions, aug-cc-pV6Z. The potential energy curves (PECs) of the NO⁺(x¹∑⁺,a³∑⁺,A¹Ⅱ) are calculated. Based on the PECs, the spectroscopic parameters R_e, D_e, ω_e, ω_eχ_e, α _e, B_e, and D₀ are reproduced, which are in excellent agreement with the available measurements. By numerically solving the radial Schrödinger equation of nuclear motion using the Numerov method, the first 20 vibrational levels, inertial rotation and centrifugal distortion constants of NO⁺(x¹∑⁺,a³∑⁺,A¹Ⅱ) ion are derived when the rotational quantum number J is equal to zero (J = 0) for the first time, which accord well with the available measurements. Finally, the analytical potential energy functions of these states are fitted, which are used to accurately derive the first 20 classical turning points when J = 0. These results are compared in detail with those of previous investigations reported in the literature.     

一种用于零差干涉型光纤传感器动态相移线性测量的J1～J6法

本文介绍一种用于零差干涉型光纤传感器动态相移线性测量的方法:J₁～J₆法.该方法同时测量干涉仅输出的一到六次谐波,并用三个奇次谐波或三个偶次谐波来计算动态相移的幅值.这一方法克服了以前提出的J₁～J₄法的缺点,可以在任何相位偏置的条件下对动态相移进行稳定测量.     

Mössbauer analysis and magnetic properties of Invar Fe–Ni–C and Fe–Ni–Mn–C alloys

The saturation magnetization and the hyperfine magnetic field of different f.c.c. Fe–Ni based alloys containing nearby 29 at .% Ni were studied as a function of temperature and for different Carbon and Manganese contents. We have observed abnormal behaviors that are explained in terms of mixed exchange interactions between atomic spins: J _NiNi(r _i ) < 0, J _FeFe(r _i ) > 0, J _NiFe(r _i ) < 0.     

Dual-mode optical fibres with zero intermodal dispersion

An exact analytical approach to the synthesis of the refractive-index profile of dual-mode optical fibres with zero intermodal dispersion is presented, and the computer-aided, trial-and-error synthesis of the optimal profile is described. The synthesis is based on inverse scattering theory. Self-consistency of free potentials corresponding to individual modes was attained by numerical methods. The characteristics of the optical fibres with synthetized profiles were analysed, the optimization constraints were specified, and an optimum profile was found. The results can be used for the design of broadband optical fibres.Notation (r), (r) Single and double derivatives - C _l(r) Determinant of a matrix det - k _l (r) Vector - k _l (r) _l (r) The scalar products of the vectors - K _l(wr) The modified Bessel function of the second kind - _l(wr) The modified Bessel function of the first kind - J _l(uaR) The Bessel function of the first kind     

Acoustic radiation force of high-order Bessel beam standing wave tweezers on a rigid sphere

Background and objective

Particle manipulation using the acoustic radiation force of Bessel beams is an active field of research. In a previous investigation, [F.G. Mitri, Acoustic radiation force on a sphere in standing and quasi-standing zero-order Bessel beam tweezers, Annals of Physics 323 (2008) 1604–1620] an expression for the radiation force of a zero-order Bessel beam standing wave experienced by a sphere was derived. The present work extends the analysis of the radiation force to the case of a high-order Bessel beam (HOBB) of positive order m having an angular dependence on the phase ?.

Method

The derivation for the general expression of the force is based on the formulation for the total acoustic scattering field of a HOBB by a sphere [F.G. Mitri, Acoustic scattering of a high-order Bessel beam by an elastic sphere, Annals of Physics 323 (2008) 2840–2850; F.G. Mitri, Equivalence of expressions for the acoustic scattering of a progressive high order Bessel beam by an elastic sphere, IEEE Transactions on Ultrasonics Ferroelectrics and Frequency Control 56 (2009) 1100–1103] to derive the general expression for the radiation force function Y_Jm,st(ka,β,m), which is the radiation force per unit characteristic energy density and unit cross-sectional surface. The radiation force function is expressed as a generalized partial wave series involving the half-cone angle β of the wave-number components and the order m of the HOBB.

Results

Numerical results for the radiation force function of a first and a second-order Bessel beam standing wave incident upon a rigid sphere immersed in non-viscous water are computed. The rigid sphere calculations for Y_Jm,st(ka,β,m) show that the force is generally directed to a pressure node when m is a positive even integer number (i.e. Y_Jm,st(ka,β,m)>0), whereas the force is generally directed toward a pressure antinode when m is a positive odd integer number (i.e. Y_Jm,st(ka,β,m)<0).

Conclusion

An expression is derived for the radiation force on a rigid sphere placed along the axis of an ideal non-diffracting HOBB of acoustic standing (or stationary) waves propagating in an ideal fluid. The formulation includes results of a previous work done for a zero-order Bessel beam standing wave (m = 0). The proposed theory is of particular interest essentially due to its inherent value as a canonical problem in particle manipulation using the acoustic radiation force of a HOBB standing wave on a sphere. It may also serve as the benchmark for comparison to other solutions obtained by strictly numerical or asymptotic approaches.     

幂函数叠加势的径向薛定谔方程的解析解

研究多种正幂势函数与逆幂势函数紧密耦合条件下薛定谔径向方程解析解的求解方法.对势函数为V（r）=α₁r⁸＋α₂r³+α₃r²+β₃r^-1＋β₂r^-3＋β₁r^-4的径向薛定谔方程存在解析解的条件以及精确的解析解进行了研究. 根据量子系统波函数必须满足单值、有界和连续的标准条件,首先求出径向坐标r→∞以及r→0时的渐近解,然后采用非正则奇点邻域附近的波函数级数解法与求得的渐近解相结合,通过幂级数系数比较法得到径向薛定谔方程在势函数系数紧密耦合条件下的一系列定态波函数解析解以及相应的能级结构,并作适当讨论与结论. 关键词： 级数解法 幂势函数 径向波函数 渐近解     

A theorem on the order of levels in confining potentials

We prove that in a two-body, non-relativistic system interacting via a potential V = ?g²/r + V_c(r), where V_c is a confining potential non-singular at the origin, the 2S level is above the 2P level if V_c satisfies the following sufficient condition: This covers the well-known cases of linear potentials or harmonic oscillator potentials, which were considered in charmonium models, but also more generally, for instance, V_c(r) = r^α, α >0.     

Beam wander of J 0- and I 0-Bessel Gaussian beams propagating in turbulent atmosphere

Root mean square (rms) beam wander of J ₀-Bessel Gaussian and I ₀-Bessel Gaussian beams, normalized by the rms beam wander of the fundamental Gaussian beam, is evaluated in atmospheric turbulence. Our formulation is based on the first and the second statistical moments obtained from the Rytov series. It is found that after propagating in atmospheric turbulence, the collimated J ₀-Bessel Gaussian and the I ₀-Bessel Gaussian beams have smaller rms beam wander than that of the Gaussian beam, regardless of the choice of Bessel width parameter. However, the extent of such an advantage depends on the chosen width parameter, Gaussian source size, propagation distance and the wavelength. Focusing at finite distances of the considered beams causes the rms beam wander to decrease sharply at the propagation distances equal to the focusing parameter.     

Effect of high electric fields on the nematic to isotropic transition in a material exhibiting large negative dielectric anisotropy

We report the experimental high electric field phase diagram of a nematic liquid crystal which exhibits a large negative dielectric anisotropy. We measure simultaneously the birefringence (Δn) and the dielectric constant (epsilon_⊥) at various applied fields as functions of the local temperature of an aligned sample. We also measure the higher harmonics of the electrical response of the medium. The following experimental results are noted: (i) enhancement of orientational order parameter S in the nematic phase due to both the Kerr effect and quenching of director fluctuations; (ii) enhancement in the paranematic to nematic transition temperature (T_PN) with field; (iii) divergence of the order parameter susceptibility beyond the tricritical point as measured by third harmonic electrical signal; (iv) a small second harmonic electrical signal which also diverges near T_PN, indicating the presence of polarised domains. Our measurements show that ΔT_PN(= T_PN(E)-T_NI(0)) varies linearly with |E| whereas the Landau de Gennes theory predicts a dependence on E². It is argued that the quenching of director fluctuations by the field makes the dominant contribution to all the observations, including the thermodynamics of the transition.     

On the theory of the diffraction of light by two parallel ultrasonic waves,one being then th harmonic of the other

Assuming the validity ofRaman andNath's preliminary theory, the amplitudes of the light diffracted by two parallel ultrasonic waves consisting of a fundamental tone and its n^th harmonic are compared in the following cases:

1. (1)

   the sound waves are superposed;

2. (2)

   the sound waves are situated side by side.

The diffraction patterns are approximately the same if the condition πnL/λ^*¦sin ?_s¦?1 is fulfilled, where sin?_s=?sλ/μ₀λ^*(s being an integer);λ is the wave-lenght of the incident light in vacuum, λ^* is the wave-lenght of the fundamental tone of the sound waves, μ₀ is the refractive index of the medium andL the width of the sound field. The good agreement between recent experiments ofMurty andRao in the arrangement of case (2) and theoretical results calculated in case (1) is thus justified. The theoretical confirmation of older experiments byPande, Pancholy andParthasarathy is thereby established at the same time.

     

E.S.R. evidence for the planarity of the t-butyl radical

Monte Carlo calculations are reported for the radial distribution function g ₂(r; λ) of a fluid in which the intermolecular pair potential is [u ^ref(r) + λu ^p(r)], u ^ref(r) being the Weeks-Chandler-Andersen (WCA) reference fluid, and [u ^ref(r) + u ^p(r)] being the Lennard-Jones (6, 12) fluid. The calculations are performed for λ values in the range 0 to 1, at the state condition ρσ³ = 0·80, kT/ε = 0·719. It is shown that at high densities the perturbation expansion of g ₂(r; λ = 1) about g ₂(r; λ = 0) is rapidly convergent, but that the corresponding expansion for y ₂(r; λ) = exp [βu(r; λ)] × g ₂(r; λ) is not. In addition Monte Carlo estimates of the individual terms that contribute to the first-order perturbation term, (?g ₂/?λ)_λ=0, are presented. It is shown that these terms are individually large, but that (?g ₂/?λ)_λ=0 is small because there is strong cancellation between the various terms. Consequently, the calculation of (?g ₂/?λ)_λ=0 is highly sensitive to the approximation used to evaluate the individual terms.