Hubbard relations for linear molecules

The Hubbard relations for linear molecules in the cases of the extended diffusion model (EDM) and Ivanov's theory are derived. The M-diffusion variant of the EDM leads to an unphysical result as the dielectric and Raman correlation times approach infinity and it is suggested that M-diffusion is not a realistic model. The J-diffusion is almost the same as for spherical molecules. When the reduced angular momentum correlation time, τ _J *, is very much less than unity both EDM and Ivanov theory give a relation similar to the friction model [2], i.e. the original Hubbard relations [14] with the coefficient 6^-1, instead of 2^-1 as obtained by O'Reilly [3]. For τ _J * > 1 the various versions of Hubbard's relations are different enough to be distinguished experimentally.     

Ab initio calculations of multipole moments,polarizabilities and long-range interaction coefficients for the azabenzene molecules

Using LCAO-SCF wave functions on the monomers and a non-empirical Unsöld procedure for the second-order properties we have calculated the (2 ^l ) multipole moments (up to l=6), the (l,l') multipole polarizabilities (up to l + l' = 6) and the related long-range coefficients describing the electrostatic, induction and dispersion interactions for the different azabenzene molecules. The agreement with available experimental data is good, in particular for the dipole polarizabilities. The anisotropy of the long-range interaction potential is dominated by the electrostatic contributions, although the dispersion terms, especially the mixed-pole terms (l≠l') for even n (C₈, C₁₀), also contribute significantly; the induction energy is rather small. The π contributions to the polarizabilities and the dispersion interactions are found to be larger than earlier estimates. Moreover, it is shown by calculating the dipole polarizabilities of some (aza)naphthalenes and (aza)anthracenes, that a bond polarizability model can be applied effectively only if the delocalized π electrons are considered separately from the σ electrons.     

厄米-高斯光束在非Kolmogorov大气湍流中的传输性质

基于广义惠更斯-菲涅尔原理和非Kolmogorov(非K)谱,推导出了厄米-高斯光束在非K大气湍流中传输的束宽、角扩展以及M²因子的解析表达式.数值计算表明,在传输距离比较远(如z≥3 km)时,厄米-高斯光束的束宽、角扩展和M²因子随广义指数参量α的增大而增加直到α=3.11时达到最大值后再随α的增大而减小;随湍流的内尺度l₀的减小而增大;随外尺度l₀的增加而增大(3.6<α<4).但是当广义指数参量α在3<α<3.6区间取值时,束宽和M²因子几乎不随外尺度的增加而变化.     

Rotational diffusion of carbon monoxide in various simple liquids

Infra-red spectra of CO dissolved in liquid N₂, O₂, Ar, Xe and CH₄ have been recorded both in the fundamental and the first overtone. From the band profiles, rotational correlation functions, band moments and intermolecular mean-square torques have been calculated. With the help of Gordon's rotational diffusion model [1] we computed the theoretical correlation functions in the ‘M-diffusion’ (including or not a distribution of angular momentum correlation times) and ‘J-diffusion’ limits. The validity of the Gordon and Debye diffusion models in the various dense gases is discussed.     

On the theory of light scattering in molecular liquids

The theory of light scattering for a system of linear molecules with anisotropic polarizabilities is considered. As a starting point for our theory, we express the result of a scattering experiment in VV and VH symmetry as dynamic correlation functions of tensorial densities ρ _lm(q) with l = 0 and l = 2. l, m denote indices of spherical harmonics. To account for all observed hydrodynamic singularities, a generalization of the theory of Schilling and Scheidsteger [1] for these correlation functions is presented, which is capable to describe the light scattering experiments from the liquid regime to the glassy state. As a microscopic theory it fulfills all sum rules contrary to previous phenomenological theories. We emphasize the importance of the helicity index m for the microscopic theory by showing, that only the existence of m = 1 components lead to the well known Rytov dip in liquids and to the appearance of transversal sound waves in VH symmetry in the deeply supercooled liquid and the glass. Exact expressions for the phenomenological frequency dependent rotation translation coupling coefficients of previous theories are derived. Received 3 July 2000 and Received in final form 7 November 2000     

Path integral treatment for the generalized Ginocchio potentials

The solution for the generalized Ginocchio potentials is exactly constructed by the path integral approach combined to the summation of the spectral representation. The energy spectrum and the wave functions of bound and scattering states are explicitly evaluated. The scattering functionS _l for each angular momentuml is also deduced.     

Molecular dynamics of liquids modelled by ‘2-Lennard-Jones centres’ pair potentials

The molecular dynamics study based on two-Lennard-Jones (12-6) centres pair potentials, with reduced bond lengths in the range 0·5 ?l/σ?0[sbreve]d8, and with ε, σ-parameters simulating liquid F₂, Cl₂, Br₂ and CO₂ (14) is extended to time correlation functions. The calculated properties include: translational velocity and force self correlation functions; orientational self-correlation functions <P _1,2(Î . Î(t))>, a cross correlation function for P ₂, angular momentum (J), and torque self-correlation functions. Diffusion constants (D) and rotational relaxation times (τ₁, τ₂, τ _J ) have been evaluated and where possible compared with experimental data (D and τ _J for F₂, τ₂ for Cl₂). Calculations with 108 or 256 molecules are reported for several densities and temperatures for four model liquids. The nature of the one-particle motion is analysed qualitatively in terms of quasi-oscillations and -librations. It is difficult to fit the observed features into the framework of physical models proposed in the literature. The parametrization in terms of memory functions will be reported in a subsequent paper.     

Chaotic properties of multipoint correlation functions of an Ising model with long-range interactions on the Sierpiński—Gasket lattice

A class of multispin correlation functions of an Ising model with ferromagnetic nearest neighbor interactionsK and constant (distance-independent) long-range interactionsQ ₁=Q,l=1,2,..., on the Sierpiski-gasket lattice is considered. Using an exact method for calculating thermodynamic functions of hierarchically constructed Ising systems, it is shown that, for a set of values ofQ and for almost all values ofK, someM _k-spin correlation functions, whereM _k=3 ^k +3 withk=1,2,...,n andn=1,2,... being the order of lattice construction, change chaotically asn, k, and therebyM _k increase to infinity. Accordingly, in the thermodynamic limit, these correlation functions prove to be nonanalytic for appropriate values ofQ andK. SinceM _k-point correlation functions withk being finite, i.e., correlation functions involving finite numbers of spins, remain analytic asn tends to infinity, there is a smooth crossover between analytic properties of correlation functions of the two types.     

Simulation of molecular orientational dynamics in a model polar fluid

A molecular dynamics simulation of a Stockmayer fluid with μ* = 1·0, ρ* = 0·7 and T* = 1·13 (±0·03) is reported. In addition to evaluations of a number of static properties, orientational time correlation functions C_l (t) = <P(cos δθ(t))> were calculated for l = 1 through 4 ; P_l is a Legendre polynomial and δθ(t) is the angle of reorientation of the dipole in time t. These time correlation functions are characteristic of nearly free rotation and agree well with curves calculated from a perturbation theory for the memory functions that utilizes the simulated value of the mean square torque. The angular velocity autocorrelation function for this fluid was also simulated and compared with perturbation theory. Agreement is not good, primarily because of the presence of a pronounced long time tail in the simulated function. The relationship between these results and those of other simulations and theories is discussed.     

The mean squared torque in pure and mixed dense fluids

The mean squared torque on a molecule can be obtained from infra-red or Raman band moments, and provides a direct measure of the strength of the anisotropic intermolecular forces. The expression for the mean squared torque on a molecule of species α in a fluid mixture is given in terms of the intermolecular potential and the angular pair correlation functions. This relation is made tractable by introducing a perturbation expansion in powers of the anisotropic potential strength for the angular pair correlation functions. Monte Carlo calculations of the mean squared torque are presented for a liquid of linear molecules having dipolar, quadrupolar and anisotropic overlap interactions. Comparison of the perturbation expansion to second order with these ‘exact’ results shows good agreement for μ*=μ/(εσ³)^1/2 and Q*=Q/(εσ⁵)^1/2 values less than about 0·5, and for values of the dimensionless overlap constant |δ| less than about 0·2. Finally, experimental values of the mean squared torque for both pure and mixed liquids are compared to the Monte Carlo and to the perturbation theory results.     

Action of monoatomic cations on the structure and spectra of Mx(1)M1-x(2)UO2(NO3)3 crystals

The action of the monovalent M⁺ cations on the luminescent properties of the mixed M _x ⁽¹⁾ M _1-x ⁽²⁾ UO₂(NO₃)₃ crystals, where M is Na, K, Rb, Cs, or NH₄ , has been investigated. It has been established that the spectral positions of the bands of vibronic transitions depend linearly on the ratio between the concentrations of the M⁽¹⁰⁾ and M⁽²⁾ cations. It is shown that the crystals considered are composed of l[RbUO₂(NO₃)₃]n[CsUO₂(NO₃)₃] clusters, where l/n = x/(1 - x). The spectral regularities revealed are determined by the partial contributions of the M⁽¹⁾ and M⁽²⁾ cations to their combined, polarizing action on the uranyl complex and are explained by the ligand nature of its highest occupied molecular orbital.Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 71, No. 6, pp. 827–830, November–December, 2004.This revised version was published online in April 2005 with a corrected cover date.     

基于M2因子测量的大气湍流参数的确定方法

基于广义惠更斯-菲涅尔原理以及大气湍流理论,推导出部分相干光束在大气湍流中传输的光束传输M ^{2因子的解析表达式.定量分析了表征大气湍流参数的折射率结构常数 C2_n}和涡旋内尺度 l _{0对 M ^{2因子的影响,并由此提出了一种通过实验测量大气湍流中光束的 M 2因子,进而确定出大气湍流参数的新方法.研究结果表明,由于大气湍流对相干性好的光束影响更为明显,在测量中可采用具有高相干性的基模高斯光束作为测量光源,而测量装 关键词： 2因子')" href="#">光束传输 M 2因子 大气湍流参数 湍流折射率结构常数 湍流涡旋内尺度}}     

Spectral moments and orientation correlation functions of asymmetric top molecules

A method for calculating the spectral moments of dipole absorption and Raman scattering by asymmetric top molecules is proposed. The method is based on the calculation of coefficients of expansion of the corresponding orientation correlation functions in a Taylor series using the formalism of the angular momentum theory.     

柱坐标系中截断光束的广义M2因子

推导出截断圆对称光束二阶矩的传输方程，它们与无截断光束的二阶矩满足相似的传输定律.因此，基于广义截断二阶矩方法，将直角坐标系中截断二维光束的二阶矩特征参数推广到柱坐标系中的截断圆对称光束，类似方法定义的广义M²因子（M²_G因子）是一个传输不变量.对理论的自洽性作了物理解释.推导出柱坐标系中截断超高斯光束的二阶矩参数和M²_G因子.对一些有意义的特殊情况作了讨论，并以数值计算例作了说明. 关键词： 光束描述 截断光束 圆对称性 广义截断二阶矩(GTSM) 2因子（M²_G因子）')" href="#">广义M²因子（M²_G因子）     

Ab initio calculations on the ground and excited states of InI

Potential energy curves (PECs) of the ground and the low-lying excited states of the InI molecule are computed using the internally contracted multireference singles and doubles configuration interaction with the Davidson correction (ic-MR-CISD + Q) method based on the relativistic effective core potentials (RECPs). The spectroscopic constants are obtained, including the excitation energy (T _e), the equilibrium bond distance (R _e), the dipole moment (μ_e) and the vibrational constants (ω_e and ω_e). Finally, we predict the transition dipole moments, the radiative lifetimes, and the Franc-Condon factors for the transitions of A³Π₀+ ? X¹Σ₀ ⁺ and B³Π^l ? X¹Σ₀ ⁺,. The results reveal that A³Π₀+ and B³Π_l are long-lived states with the lifetimes being of the order of microseconds.     

The distance dependence and spatial distribution of the molecular quadrupole moments of P2, S2 and Cl2

The quadrupole moments (Θ) of the molecules P₂, S₂ and Cl₂ have been computed at the SCF, CASSCF and CASSCF + 1 + 2 levels of theory, using augmented correlation consistent basis sets. The convergence of Θ as a function of basis set and level of theory is discussed. The variation of Θ from the separated atoms to the equilibrium region is reported. Θ is written as the sum of a sigma and pi contribution, and inaccuracies in the SCF values for P₂ and S₂ are due to the poor representation of the pi system in the SCF theory. A reference state dependent quadrupole moment density, - ½(3cos² θ- 1)r ²δη(r; R), is defined whose integral is the mole2 cular quadrupole moment, and the spatial distributions of the density and its relationship to the density difference δη(r; R) are examined.     

Effect of Coulomb forces on the position of the pole in the scattering amplitude and on its residue

The vertex constant for the virtual decay of a nucleus to two charged particles having an arbitrary orbital angular momentum l was explicitly obtained for the first time in the case of a standard expansion of the effective-range function K _l (k ²), as well as in the case where the function K ₀(k ²) has a pole. The bound state of the 3He nucleus and the resonance states of the ²He and ³He nuclei in the S wave, as well as the resonance states of the ⁵He and ⁵Li nuclei in the P wave, are studied as physical examples. For the Np and N d systems, the trajectories of the pole in the complex planes of the momentum and the corresponding renormalized vertex constant are constructed for the transition from a resonance state to a virtual state as the Coulomb interaction is switched off gradually.     

Exclusive radiativeB-decays in the light-cone QCD sum rule approach

We discuss vector, axial-vector, scalar and pseudoscalar two-point functions at low and intermediate energies. We first review what is known from chiral perturbation theory, as well as from a heat kernel expansion within the context of an extended Nambu-Jona-Lasinio (ENJL) model. We derive then these two-point functions to all orders in the momenta and to leading order in 1/N _c within the framework of this model. We find an improved high-energy behaviour and a general way of parametrizing them that shows relations between some of the two-point functions, which are also valid in the presence of gluonic interactions. The similarity between the shape of the experimentally known spectral functions and the ones we derive, is greatly improved with respect to those predicted by the usual constituent quark like models. We also obtain the scalar massM _s =2M _Q independent of the regularization scheme. In the end, we calculate fully an example of a nonleptonic matrix element in the ENJL-model, theπ ⁺?π ⁰ electromagnetic mass difference and find good agreement with the measured value.

     

Investigation of the impurity hyperfine field polarization in polycrystalline Rare Earth ferromagnets

Time differential perturbed angular correlation spectra of¹¹¹Cd in ferromagnetic polycrystalline Dy have been measured at 4.2 K in external magnetic fields up to 60 kG. The experimental data were well reproduced by a calculation which assumed that the angular distribution of the magnetic hyperfine fields is identical to that of the magnetic moments of the 4f-shells. The distribution of the 4f-moments was derived from magnetic anisotropy data. The results of this work seem to justify the application of the integral perturbed angular correlation technique for the determination of magnetic hyperfine fields in incompletely polarized ferromagnetic samples. The magnetic hyperfine fields of¹⁷⁷Hf:Gd and¹⁷⁷Hf:Dy have been measured by this method as:H _hf(Hf:Gd)=–375(60)kG andH _hf(Hf:Dy)=–225(45)kG.     

Moments of the Percus-Yevick hard-sphere correlation function

A simple recursive relation is derived for the momentsM _n ,n=1, 2,..., of the Percus-Yevick correlation functionh(r) for identical hard spheres. TheM _n are rational functions of the volume fractionw occupied by the spheres; the first ten are given explicitly, and a single-term asymptotic form is obtained to suffice for the rest. Applications of theM _n(w) include testing different approximations forh by numerical integration ofh(r) r ⁿ . We compare exact moments with shell approximationsM _n [h ^s ] corresponding to integration fromr=0 tos+1 fors=3–8, and with hybrid approximationsM _n [h ^s +h ^a ] which supplement the shell approximations with integrals of an asymptotic tail froms+1 to . For a givens, the hybrid approximation is better forw increasing than the shell approximation, andM _n [h ³+h ^a ] is even better thanM _n [h ⁸]