Reconciliation of the forward scattering and wave theories of electric-field-gradient-induced birefringence

We consider propagation of a linearly polarized, harmonic, plane electromagnetic wave incident on a dilute gas subject to a non-uniform electrostatic field. We work to electric quadrupole–magnetic dipole order. In general, the wave is distorted to include a perpendicular component induced by the electrostatic field gradient, and the resultant is not a plane wave. Although the induced component is small, its contribution to the polarization-dependent refractive index of the gas in Buckingham's quadrupole experiment is significant. We show that distortion of the incident wave accounts exactly for the present discrepancy between wave theory and forward scattering theory of electric-field-gradient-induced birefringence in a gas: both theories yield the result obtained originally by Buckingham and Longuet-Higgins.     

Light scattering,flow birefringence and generalized hydrodynamics

The stress-optical coefficient ?, which is measured in flow birefringence experiments, is calculated using the generalized hydrodynamic equations which have been recently used to explain the k-dependent fine structure observed in depolarized (VH) light scattering. The resulting expressions allow a comparison of the strength of the birefiringence effect with that of the light scattering fine structure effect in a given liquid. It is seen that the combination of flow birefringence and VH scattering measurements yields the orientational structure factor g ⁽²⁾ of Ben-Reuven and Gershon. The theory is in reasonable agreement with experiment. The combination of our results with those of Raman and Krishnan yields a simple expression for the parameter δ which measures the strength of the stress-orientational effect. The dependence of the stress-optimal coefficient upon orientational order is briefly discussed.     

Electrically weak asymmetry in the elastic scattering of electrons by nuclei with multipole moments

The differential elastic-scattering cross section of longitudinally polarized electrons by nuclei of arbitrary spin and isospin is calculated in the Born approximation, taking into account the interference of electromagnetic interaction and the interaction of weak neutral currents. For a nucleus of spin J 3/2, explicit expressions are obtained for the interference terms in terms of the electromagnetic multipole form factors F_C, f_Q, f_M1 and f_M3. Using the example of the³He,¹¹B,¹⁹F and⁴⁰Ca nuclei, the behavior of electrically weak asymmetry of the cross section is investigated in detail in the framework of three gauge models. It is shown that the asymmetry of a_Rl is 10^–5 for E - 100 MeV, and is sensitive to the nuclear structure: By taking into account the contributions not only of the charge and magnetic-dipole scattering but also of the quadrupole and octupole scattering, one can obtain additional information on the structure of weak electron-nucleus interaction.This paper was presented at a conference on Investigations of Spin Phenomena in High-Energy Physics held at Protvino, November 23–26, 1982.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 79–84, April, 1984.     

Depolarized light scattering,flow birefringence and local order in molecular liquids

We propose a generalization of De Gennes' theory of flow birefringence [3] to the case of two distinct local anisotropy variables and also some extensions to the existing three variable theories of light scattering spectra. We show that the application of the theories with one or with two local anisotropy variables to analyse flow birefringence and light scattering spectra give numerically different results. We also show that it is possible to determinewhether the second local anisotropy variable is a primary or a secondary variable.

The VH and HH light scattering spectra of a number of symmetric top molecules are analysed. They show an unambiguous ‘shear mode coupling’ down to very small values of (q ²η/ρΦ). These results are discussed and compared to flow birefringence experiments in the light of our theoretical considerations. The three variable correction is shown to be small and within experimental error for all liquids studied except one (pyridine). The flow birefringence coefficient for CCl₄ is measured and found to be negative as predicted by our theory. Limitations to the formalism of generalized hydrodynamics are also discussed briefly.     

Light scattering spectrum of disordered molecular crystals: KCN

We have investigated the effect of the low temperature order-disorder phase transitions on the Raman spectrum of KCN. In the disordered cubic room temperature phase we only find a broad central component in the spectrum which sharpens near the transition temperature at 168K. From the doubling of the librational mode of the CN^--molecules we conclude that an antipolar orientation of the CN^--molecules is probable for the low temperature phase below 83 K.     

吸收性海水中气泡光散射特性的理论研究

 给出了一种适合于吸收性介质内粒子散射的Mie级数新的表示形式。利用Mie理论研究了吸收性海水中气泡的单散射特性和气泡群的相位函数。与非吸收性海水中气泡的光散射特性相比,分析了海水折射率虚部对气泡光散射的影响。结果表明：180°后向散射的增强是气泡固有的光学性质,与所处介质无关,可以利用后向散射的增强来探测气泡。     

Rovibrational matrix elements of multipole moments of the HD,HT and DT molecules

Rovibrational matrix elements of the multipole moments Q _? of HD, HT and DT for ranks 2 ≤ ? ≤ 11 have been computed. Since the present calculations have been performed with the nuclear centre of mass (rather than the geometric centre) as the origin, the computations had to include even as well as odd values of ?. The results are used to correlate the absorption intensities of the zero-phonon single transitions in solid HD to theory.     

Nonlinear refractive index and light scattering due to fluctuations of molecular multipole electric fields

Statistical fluctuations of multipolar electric molecular fields, leading to variations of isotropic and anisotropic light scattering, are moreover shown to give rise to a temperature-dependent nonlinear refractive index of dense fluids. Some selected models of dipolar and quadrupolar molecules, linearly and nonlinearly polarizable and correlated in binary as well as ternary assemblages, are discussed. The formulae derived for the isotropic and anisotropic scattering constants are applicable to one-and many-component fluids, consisting of atoms and polar molecules, and provide the basis for a deeper interpretation of the latest experimental results.     

On the structure and multipole moments of axially symmetric stationary metrics

The structure of the stationary metrics [1], generated from Laplace’s solutions as seed, is investigated. The expressions for the equatorial and polar circumferences, the surface area of the event horizon, location of singular points and the Gaussian curvatures of the metrics [1] are derived and their variations with the field parameter α₀ are studied. The multipole moments are calculated with the help of coordinate invariant Geroch-Hansen technique. These investigations expose some interesting properties of the metrics, some of which are known in the literature and some deserve a new interpretation.     

Calculations of molecular multipole electric moments of a series of exo-insaturated four-membered heterocycles,Y = CCH2CH2X

The influence of ring puckering angle on the multipole moments of sixteen four-membered heterocycles (1-16) was theoretically estimated using MP2 and different DFTs in combination with the 6-31+G(d,p) basis set. To obtain an accurate evaluation, CCSD/cc-pVDZ level and, the MP2 and PBE1PBE methods in combination with the aug-cc-pVDZ and aug-cc-pVTZ basis sets were performed on the planar geometries of 1-16. In general, the DFT and MP2 approaches provided an identical dependence of the electrical properties with the puckering angle for 1-16. Quantitatively, the quality of the level of theory and basis sets affects significant the predictions of the multipole moments, in particular for the heterocycles containing C=O and C=S bonds. Convergence basis sets within the MP2 and PBE1PBE approximations are reached in the dipole moment calculations when the aug-cc-pVTZ basis set is used, while the quadrupole and octupole moment computations require a larger basis set than aug-cc-pVTZ. On the other hand, the multipole moments showed a strong dependence with the molecular geometry and the nature of the carbon-heteroatom bonds. Specifically, the C-X bond determines the behavior of the μ(?), θ(?) and ?(?) functions, while the C=Y bond plays an important role in the magnitude of the studied properties.     

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.     

Light scattering and dielectric manifestations of secondary relaxations in molecular glassformers

Photon correlation data of the molecular glass-forming materials 2-picoline, dimethylphthalate (DMP) and salol are compared with their dielectric loss spectra in the time-frequency range where the dielectric data reveal secondary relaxations. Slow secondary relaxation processes in molecular liquids are commonly studied by dielectric spectroscopy (DS) and, based on such studies, believed to be characteristics of the deeply super-cooled liquid state. However, there has been no direct experimental evidence that they are similarly detected by other experimental techniques. In the present study, we experimentally address this question for the anisotropic (depolarized) light scattering (LS). In the first approximation, DS and LS probe the same molecular reorientation dynamics, and therefore are expected to provide qualitatively similar spectra. We find however that this is not the case, namely i) the magnitude of the slow secondary relaxations is much less in LS than in DS data, which is the opposite to expectations; ii) the shape of the relaxation spectrum is qualitatively different, concerning both the main and secondary processes. We discuss possible sources of these differences in the context of related data from the literature.Received: 21 July 2003, Published online: 23 December 2003PACS: 64.70.Pf Glass transitions - 77.22.Gm Dielectric loss and relaxation - 78.35. + c Brillouin and Rayleigh scattering other light scatteringJ. Mattsson: Presently at: DEAS and Physics Department, Harvard University, Cambridge, MA 02138, USA     

Light scattering from gaseous nitrogen: Effects of correlation between molecular and intermolecular axis

The depolarization ratio of light scattered from gaseous nitrogen has been measured at pressures up to 440 bar and 310 K. The molecular specific scattering (including the effects of the orientational pair correlations labelled OPC), the collision induced scattering (CIS), and their interferences are estimated in the DID approximation. The agreement with the experimental data is rather good.     

Rotation, scaling, and translation invariant local watermarking technique with Krawtchouk moments

A rotation, scaling, and translation invariant local watermarking is proposed with one or two Krawtchouk moment(s) of the original to estimate the geometric distortion parameters including rotation angle, scaling factor, and translation parameter. Krawtchouk moments can be used as private key of watermark extractor.Watermark is inserted into perceptually significant Krawtchouk moments of original, and watermark based on Krawtchouk moments is local. Independent component analysis (ICA) is utilized to extract watermark blindly. Experimental results show that this method has a good robustness against distortions preformed by watermark benchmark Stirmark.     

从流密度的Fourier分量出发导出多极矩表达式

从运动电荷产生的流密度入手,通过Fourier变换引入各级多极矩的表达式.     

从流密度的Fourier分量出发民出多极矩表达式

从运动电荷产生的流密度入手，通过Ｆｏｕｒｉｅｒ变换引入各级多极矩的表达式。     

Light scattering from anisotropic particles: propagation,localization, and nonlinearity

Plasmon resonances and extraordinary light scatterings of a nanoparticle with radial anisotropy are studied and summarized. The coupling between localized surface plasmons and far‐field quantities is discussed. It is found that the presence of radial anisotropy redistributes the localization of plasmons and also results in certain novel phenomena in the far zone, which provide the possibility of scattering control such as electromagnetic transparency, enhanced scattering cross section, etc. The nonlinear optical response is explored in order to yield deeper physical insight into the interaction between plasmons and incident light.     

Light cone,Regge contributions and large-angle scattering

The asymptotic behaviour of various three-particle vertices involving reggeons far off-mass-shell, and that of various exclusive reactions is found by using the light-cone algebra of the local and bilocal operators and supposing that the Regge contributions survive in the amplitude in the limit of large momentum transfer. The scaling behaviour (29), (34) is obtained in this way for the exclusive amplitudes. Besides, the asymptotic behaviour of hadronic form factors is obtained. The asymptotic behaviour of Regge-cut contributions and the region of applicability of the scaling behaviour (29) are found for the 2 → 2 amplitude. The relations between the dispersion contributions, Regge contributions, and those of quark diagrams, as well as the role of the signature are discussed. Predictions are given for the energy and the angular distributions for a number of two-particle reactions.