Showing papers on "Scattering published in 1987"

Structure Analysis by Small-Angle X-Ray and Neutron Scattering

Abstract: Small-angle scattering of X rays and neutrons is a widely used diffraction method for studying the structure of matter. This method of elastic scattering is used in various branches of science and technology, includ ing condensed matter physics, molecular biology and biophysics, polymer science, and metallurgy. Many small-angle scattering studies are of value for pure science and practical applications. It is well known that the most general and informative method for investigating the spatial structure of matter is based on wave-diffraction phenomena. In diffraction experiments a primary beam of radiation influences a studied object, and the scattering pattern is analyzed. In principle, this analysis allows one to obtain information on the structure of a substance with a spatial resolution determined by the wavelength of the radiation. Diffraction methods are used for studying matter on all scales, from elementary particles to macro-objects. The use of X rays, neutrons, and electron beams, with wavelengths of about 1 A, permits the study of the condensed state of matter, solids and liquids, down to atomic resolution. Determination of the atomic structure of crystals, i.e., the arrangement of atoms in a unit cell, is an important example of this line of investigation."

Origin of the scattering peak in microemulsions

Abstract: From a Landau theory the static scattering intensity distribution I(q) of microemulsions is obtained. As essential ingredient we have included a negative gradient term in the free energy expression. The form of I(q)∼(a2+c1q2+c2q4)−1 yields for a2>0, c1 0 a single broad scattering peak and a q−4 decay at large q, both properties experimentally observed for a variety of microemulsions containing comparable amounts of water and oil. The peak originates from the modulation in the corresponding space correlation function given by γ(r)=(d/2πr)⋅e−r/ξ⋅sin(2πr/d). It is shown that the scattering intensity relation describes experimental literature data remarkably well, using only three fit parameters.

Black-hole normal modes: A WKB approach. I. Foundations and application of a higher-order WKB analysis of potential-barrier scattering.

Abstract: We present a semianalytic technique for determining the complex normal-mode frequencies of black holes. The method makes use of the WKB approximation, carried to third order beyond the eikonal approximation. Mathematically, the problem is similar to studying one-dimensional quantum-mechanical scattering near the peak of a potential barrier, and determining the scattering resonances. Under such conditions, a modification of the usual WKB approach must be used. We obtain the connection formulas that relate the amplitudes of incident, reflected, and transmitted waves, to the third WKB order. By imposing the normal-mode (resonance) boundary condition of a zero incident amplitude with nonzero transmitted and reflected amplitudes, we find a simple formula that determines the real and imaginary parts of the normal-mode frequency of perturbation (or of the quantum-mechanical energy of the resonance) in terms of the derivatives (up to and including sixth order) of the barrier function evaluated at the peak, and in terms of the quantity (n+(1/2)), where n is an integer and labels the fundamental mode (resonance), first overtone, and so on. This higher-order approach may find uses in barrier-tunneling problems in atomic and nuclear physics.

Absolute calibration of small‐angle neutron scattering data

Abstract: Absolute calibration forms a valuable diagnostic tool in small-angle neutron scattering (SANS) experiments, and allows the parameters of a given model to be restricted to the set which reproduces the observed intensity. Discrepancies between the observed and calculated intensities may arise from potential artifacts or even new physical processes and absolute calibration methods are useful in delineating these circumstances. General methods which are available for absolute scaling are discussed along with estimates of the degree of internal consistency which may be achieved between the various standards. In order to minimize the time devoted to calibration in a given experimental program, emphasis is placed on developing a set of precalibrated strongly scattering standards which may be run in the chosen experimental geometry. Comparison of such a set developed at the National Center for Small-Angle Scattering Research (Oak Ridge) with independent determinations by SANS users indicates consistency to within ± 5%.

Interface roughness scattering in GaAs/AlAs quantum wells

Abstract: We study experimentally and theoretically the influence of interface roughness on the mobility of two‐dimensional electrons in modulation‐doped AlAs/GaAs quantum wells. It is shown that interface roughness scattering is the dominant scattering mechanism in thin quantum wells with a well thickness Lw<60 A, where electron mobilities are proportional to L6w, reaching 2×103 cm2/V s at Lw∼55 A. From detailed comparison between theory and experiment, it is determined that the ‘‘GaAs‐on‐AlAs’’ interface grown by molecular beam epitaxy has a roughness with the height of 3–5 A and a lateral size of 50–70 A.

Multiple Light Scattering from Disordered Media. The Effect of Brownian Motion of Scatterers

Abstract: We have measured the time autocorrelation function of the light intensity multiply scattered from turbid aqueous suspensions of submicron size polystyrene spheres in directions near backscattering. It is found strongly non-exponential at short times revealing the very fast decay of coherence in extended scattering loops due to the thermal motion of the many spheres involved; the longest living decay time is found remarkably close to the single particle backscattering relaxation time even under conditions of interparticle interactions. These features are only weakly affected by the particular interference effect between time-reversed pairs of loops giving rise to the coherent backscattering enhancement. A simple argument is presented which accounts for these observations.

Imaging radar polarization signatures: Theory and observation

Abstract: Radar polarimetry theory is reviewed, and comparison between theory and experimental results obtained with an imaging radar polarimeter employing two orthogonally polarized antennas is made. Knowledge of the scattering matrix permits calculation of the scattering cross section of a scatterer for any transmit and receive polarization combination, and a new way of displaying the resulting scattering cross section as a function of polarization is introduced. Examples of polarization signatures are presented for several theoretical models of surface scattering, and these signatures are compared with experimentally measured polarization signatures. The coefficient of variation, derived from the polarization signature, may provide information regarding the amount of variation in scattering properties for a given area.

Quantum reactive scattering in three dimensions using hyperspherical (APH) coordinates. Theory

Abstract: The theory of reactive (rearrangement) scattering for three atoms in three physical dimensions using adiabatically adjusting, principal axes hyperspherical (APH) coordinates is given. The relationships of the APH coordinates to Delves and Jacobi coordinates are given, and the kinetic energy operator is shown to be relatively simple. Procedures for solving the equations via either an exact coupled channel (CC) method or an optimum centrifugal sudden (CSAPH) approximation are given as well as procedures for applying scattering boundary conditions. Surface functions of two angles are obtained using a finite element method with an optimized, nonuniform mesh, and the CC equations are solved using the efficient VIVAS method. Sample CC results are given for the H3 system. The present approach has the advantages that all arrangements are treated fully equivalently; it is a principal axis system, so that both axes and internal coordinates swing smoothly with the reactions; it is directly applicable to both symmetric and unsymmetric systems and mass combinations and all total angular momenta; it gives convenient mappings for visualization of potential energy surfaces and wave functions; only regular radial solutions are required; all coordinate matching is by simple projection; and the expensive parts of the calculation are energy independent, so that, once they are done, the scattering matrices can be rapidly generated at the large numbers of energies needed to map out reactive thresholds and resonances. Accurate reactive scattering calculations are now possible for many chemically interesting reactions that were previously intractable.

Scattering from fractals

Abstract: The concepts of dilation symmetry and the fractal dimension are introduced, and from these basic concepts scattering functions are computed for surface and mass fractals. It is then shown how the fractal structure of various random media has been elucidated from scattering measurements, and how these observations relate to specific models of fractal geometry. Examples include colloidal aggregates, gels, soot and the fractal porosity of rocks of various sorts.

Three-dimensional radiative heat transfer solutions by the discrete-ordinates method

Abstract: Radiative heat transfer in a three-dimensional participating medium was predicted using the discrete-ordinates method. The discrete-ordinates equations are formulated for an absorbing, anisotropically scattering, and re-emitting medium enclosed by gray walls. The solution strategy is discussed and the conditions for computational stability are presented. Several test enclosures are modeled. Results have been obtained for the S2, S4, S6, and S8 approximation s that correspond to 8, 24, 48, and 80 fluxes, respectively, and are compared with the exact-zone solution and the P3 differential approximation. Solutions are found for conditions that simulate absorbing media and isotropically and anisotropically scattering media. Solution accuracy and convergence are discussed for the various flux approximations. The S4, S6, and S8 solutions compare favorably with the other methods and can be used to predict radiant intensity, incident energy, and surface heat flux. A an bn B C E G / L n q r S x y z a /U,,£,TJ p a a © V Nomenclature = north-south areas, m2 = coefficients of a Legendre series = coefficients of a modified Legendre series = east-west areas, m2 = front-back areas, m2 = emissive power ( = aT4), W/m2 = incident energy, /4w/d6, W/m2 = radiant intensity, W/(m2 • Sr) = enclosure dimension, m = unit normal = heat flux, W/m2 = position vector, m = source term, W/m3 = volume of pth control volume, m3 = weight function in a direction - m (fractional area of a unit sphere) = coordinate, m = coordinate, m = coordinate, m — finite-difference weighting factor = extinction coefficient, a -f K,m~l = surface emittance = absorption coefficient, m"1 = ordinates p = cos0, £ = sin0 sin , TJ = sinG cos = outgoing direction of radiation = phase function = surface reflectance = scattering coefficient, m"1 = Boltzmann's constant, 5.669 X 1(T 8 W/(m2

Experimental study of scattering from characterized random surfaces

Abstract: An experimental investigation of light scattering from random rough surfaces is described. The surfaces, whose height fluctuations approximately follow Gaussian statistics, are fabricated in photoresist with a metal overcoating. When the lateral correlation length is larger than a wavelength and the surface slopes are mild, measurements of diffuse scattering are found to agree with the Beckmann theory, as long as the angle of incidence is not too large. For other surfaces that have stronger slopes, depolarization and enhanced backscattering may be observed in the diffuse scattering. Though we are unaware of theoretical calculations that compare with the measurements, the effects of multiple scattering are shown to be consistent with the major features of the observations.

Radiation and scattering from a microstrip patch on a uniaxial substrate

Abstract: The problem of a rectangular microstrip antenna printed on a uniaxially anisotropic substrate is treated. The effect of anisotropy on the resonant frequency and surface wave excitation of the antenna is considered, and the radar cross section (RCS) of the antenna is calculated. The RCS calculation includes the effect of the load impedance (antenna mode scattering). Results for the resonant frequency of a patch on a uniaxial substrate are compared with measurements, and the RCS of a patch on an isotropic substrate is compared with measurements. The derivation of the uniaxial Green's function in spectral form, the associated moment method analysis for the input impedance and scattering of the microstrip patch, and the expressions for the far-zone fields of a source on a uniaxial substrate are presented.

Classical Light Scattering from Polymer Solutions

Abstract: 1. Physical principles of light scattering. Interaction of electromagnetic radiation with a small isolated molecule. Light scattering in ensembles of small molecules. Light scattering from solutions of macromolecules. The Rayleigh ratio. Basic equation for light scattering from solutions of small macromolecules. Turbidity. Light scattering by large particles. Particle scattering function. Particle size parameters. Particle scattering function and radius of gyration. Particle scattering functions for basic particle shapes. Information on particle shape from P(C). Basic equation for light scattering from solutions of large molecules. Some terms relating to polydisperse systems. Molar-mass average from light scattering. Particle scattering functions of polydisperse systems. Second virial coefficient of polydisperse systems. Typical shapes of angular dependences of light scattering. Optical anisotropy of scattering particles. 2. Principles of measurement. Light-scattering photometers. Preparation and clarification of solutions. Refractive index increment. Light-scattering standards. Correction factors. Computation of the Rayleigh ratio. Transmission measurements. Preliminary tests. 3. Fundamental light-scattering methods. Single-angle method. Dissymmetry method. Zimm's method. 4. Light scattering from polymer solutions in mixed solvents. Selective sorption: a qualitative concept. Some thermodynamic aspects of selective sorption. Different ways of description of the extent of selective sorption. Coefficient of selective sorption. Selective sorption and changes of intensive properties of the system. Determination of the coefficient of selective sorption by increment methods. Types of selective sorption behaviour. Effect of molecular weight on the extent of selective sorption. Light scattering and mixed solvents. Light scattering and the coefficient of selective sorption. Solvents with three and more components. Notes on the equilibrium dialysis technique. 5. Light scattering from dilute copolymer solutions. Heterogeneity of chemical composition of copolymers and its origin. Distribution functions for copolymers. Heterogeneity parameters. Molecular weights of parts of a binary copolymer. Approximate extent of the compositional heterogeneity of typical copolymers. Light scattering and heterogeneous copolymers: a qualitative concept. Basic equations for light scattering from copolymer solutions. Some characteristic features of light scattering from copolymer solutions. Determination of parameters of heterogeneous copolymers by means of light scattering. Light scattering from copolymer solutions in mixed solvents. Angular dependence of light scattering from copolymer solutions. Block- and graft-copolymer micelles. 6. Some other applications of light scattering. Light scattering and intrinsic viscosity. Branching. Coupling of gel permeation chromatography and light scattering. Polyelectrolytes. Asymptotic methods.

Energy-flux model of seismic coda: Separation of scattering and intrinsic attenuation

Abstract: A new model of seismic coda is presented, based on the balance between the energy scattered from the direct wave and the energy in the seismic coda. This energy-flux model results in a simple formula for the amplitude and time decay of the seismic coda that explicitly differentiates between the scattering and intrinsic (anelastic) attenuation of the medium. This formula is valid for both weak and strong scattering and implicitly includes multiple scattering. The model is tested using synthetic seismograms produced in finite difference simulations of wave propagation through media with random spatial variations in seismic velocity. Some of the simulations also included intrinsic dissipation. The energy-flux model explains the coda decay and amplitude observed in the synthetics, for random media with a wide range of scattering Q. In contrast, the single-scattering model commonly used in the analysis of microearthquake coda does not account for the gradual coda decay observed in the simulations for media with moderate or strong scattering attenuation (scattering Q less than or equal to 150). The simulations demonstrate that large differences in scattering attenuation cause only small changes in the coda decay rate, as predicted by the energy-flux model. The coda decay rate is sensitive, however, more » to the intrinsic Q of the medium. The ratio of the coda amplitude to the energy in the direct arrival is a measure of the scattering attenuation. Thus, analysis of the decay rate and amplitude of the coda can, in principle, produce separate estimates for the scattering and intrinsic Q values of the crust. We analyze the coda from two earthquakes near Anza, California. Intrinsic Q values determined from these seismograms using the energy-flux model are comparable to coda Q values found from the single-scattering theory. The results demonstrate that coda Q values are, at best, measures of the intrinsic attenuation of the lithosphere and are unrelated to the scatteing Q. « less

On the variability of desert aerosol radiative characteristics

Abstract: Size distributions of desert aerosol observed in arid regions of Senegal, Mali, and Niger under different weather conditions are classified in terms of visibility ranges into three categories and converted to lognormal distributions. The resulting curves are considered to represent average distributions encountered during fair weather, wind carrying dust, and sandstorm episodes. By means of the Mie theory, main radiative characteristics, i.e., attenuation coefficients, single scattering albedo, asymmetry factor, and phase functions, are computed for the spectral range between 0.3 and 40 μm. Regardless of the prevailing atmospheric conditions, extinction and scattering coefficients indicate a nearly wavelength independent pattern in the solar spectral range due to the large and effective particle scattering diameter. All size distributions yield strong absorption peaks at 10 μm, clogging the atmospheric window. Moreover, the temporal variation of single scattering albedo and asymmetry factor is most sensitive in the solar spectrum. For climate modeling purposes, average values are computed for seven spectral bands of the European Centre for Medium Range Weather Forecast radiation scheme. In addition, phase functions for eight characteristic wavelengths are presented and show predominantly forward scattering properties. Optical depth measurements performed in the framework of the African turbidity monitoring network between November 1980 and February 1984 indicate a high space and time fluctuation of aerosol concentration over the Sahara and surrounding areas. Daily average optical depth values (base e) between 0.03 in the Hoggar mountains and 3.5 during sandstorms in Boutilimit (Mauritania) have been observed for the mandatory wavelength 0.5 μm. Turbidity values in Zaria (Nigeria) indicate that the Sahel region is an insignificant area for mineral dust production.

Impulsive stimulated light scattering. I. General theory

Abstract: Theoretical analysis of the time‐resolved impulsive stimulated light scattering (ISS) method is presented. A general theoretical framework is developed to describe ISS experiments on any type of material mode which is active in light scattering and conforms to linear response theory. ISS experiments permit time‐resolved observation of material motion through the dielectric response function Gee(q,t). In the simplest case of ideal time and wave vector resolution, ISS signal gives ‖Gee(q,t)‖2 directly. Various consequences of limited t and q resolution are discussed in detail. ISS experiments on acoustic and optic phonons, Debye relaxational modes, and some combinations of modes are treated explicitly. A detailed comparison of time‐domain impulsive stimulated scattering and frequency‐domain spontaneous light‐scattering spectroscopy is presented in the companion paper.

Expanding Protons: Scattering at High Energies

Abstract: This book presents an original theory, based on more than a decade of research, of the behavior of strongly interacting particles in high-energy collision processes. Using gauge field theories, the authors systematically study elastic as well as multiparticle production processes and diffractive scattering, arriving at the conclusion that the total cross section should rise, that is, the particles should "expand," as energies increase.Cheng and Wu compare their results with experimental data, including the outcomes of a series of experiments conducted in the mid-1970s that dramatically confirmed their predictions of rising total cross section at high energies and the dependence of cross sections on the momenta of incoming and outgoing particles. The presentation is systematic and mathematically rigorous yet broad enough to be accessible to graduate students.After a clear presentation of the basic elements of particle physics as well as the quantum theory of gauge fields, the authors take up fermion-fermion elastic scattering, high-energy scattering models, multiparticle production, elastic amplitude, the rising total cross section, phenomenology, the scattering of particles with a structure, the method of calculation by means of momentum variables, tower diagrams, quarkquark scattering in non-Abelian gauge field theories, and multiparticle unitarity and the eikonal formula. included in the appendixes is a detailed discussion of the Feynman parameter method, the power of which is fully illustrated by examples drawn from the authors' experiences.Hung Cheng is Professor of Applied Mathematics at MIT. Tai Tsun Wu is Cordon McKay Professor of Applied Physics at Harvard University.

Differential inelastic electron scattering cross sections from experimental reflection electron-energy-loss spectra: Application to background removal in electron spectroscopy

Abstract: The possibility of extracting absolute inelastic electron scattering cross sections K(T) (differential in energy loss T and path length) for solids from experimental electron spectra is studied. Assuming homogeneous scattering properties for the solid, a formula is found, which allows a direct determination of [\ensuremath{\lambda}L/(\ensuremath{\lambda}+L)]K(T) from a measured reflected electron-energy-loss spectrum (REELS) resulting from a monoenergetic beam of electrons incident on the surface of the solid. Here \ensuremath{\lambda} is the inelastic electron mean free path and L\ensuremath{\simeq}2${\ensuremath{\lambda}}_{1}$ where ${\ensuremath{\lambda}}_{1}$ is the transport mean free path for elastic electron scattering. The formula is applied to experimental REELS spectra of aluminum. The resulting cross sections are discussed in relation to a theoretical calculation based on dielectric-response theory. The determined cross sections are applied to remove the inelastic background signal from Mg--K\ensuremath{\alpha}(h\ensuremath{ u}\ensuremath{\simeq}1254 eV) and synchrotron-radiation-excited (h\ensuremath{ u}\ensuremath{\simeq}250 eV) photoelectron spectra of aluminum. The resulting primary excitation spectra are discussed in relation to the results of existing procedures.

Total attenuation coefficients and scattering phase functions of tissues and phantom materials at 633 nm

Abstract: Measurements have been made of the total attenuation coefficient sigma t and the scattering phase function, S(theta), of 632.8 nm of light for a number of animal model tissues, blood, and inert scattering and absorbing media. Polystyrene microspheres of known size and refractive index, for which sigma t and S(theta) can be calculated by Mie theory, were used to test the experimental methods. The purpose of the study was to define typical ranges for these optical properties of tissues, as a contribution to the development of experimental and theoretical methods of light dosimetry in tissue, particularly related to photodynamic therapy of solid tumors. The results demonstrate that, for the representative tissues studied, the total attenuation coefficients are of the order of 10-100 mm-1, and that the scattering is highly forward peaked, with average cosine of scatter in the range 0.6-0.97.

Resonant Raman scattering of hydrogenated amorphous carbon: Evidence for π‐bonded carbon clusters

Abstract: Resonant Raman spectroscopy has been used to study amorphous hydrogenated carbon films. For films containing both sp2 and sp3 bonded carbon a well‐defined high‐frequency shift of the main Raman peak is observed with increasing exciting photon energy. This shift is interpreted in terms of scattering from π‐bonded carbon clusters which is resonantly enhanced for incident photon energies approaching the π–π* resonance.

Theory of the Hall effect in heavy-fermion compounds.

Abstract: The Hall effect in the heavy-fermion compounds shows an anomalous behavior which can be ascribed to skew scattering. We calculate the Hall effect arising from skew scattering in cerium compounds. We compare our results with those of previous models and with experimental data.

Laser Diffraction Spectrometry: Fraunhofer Diffraction Versus Mie Scattering

Abstract: Laser diffraction spectrometry (LDS) is often claimed to operate on the principle of Fraunhofer diffraction. This is only true, however, if particles are large compared to the wavelength of light or if the ratio of the refractive indices of the disperse and continuous phases, m, is clearly different from unity. In this study it has been established that LDS, as applied to particle and droplet sizing in suspensions and emulsions, is based on Miescattering. Scattering patterns of single particles may be calculated if the refractive indices of both phases are known. Thus, a theoretical basis has been provided for the application of LDS to size-measurement in suspensions and emulsions, and for extension of this method to the lower size ranges and those cases in which the refractive indices of the disperse and continuous phases are similar. Extension of the work presented in this paper will enable the calculation of scattering matrices so that calibration of the apparatus with standard materials may be avoided.

Scattering from a microstrip patch

Abstract: A solution to the problem of plane wave scattering by a rectangular microstrip patch on a grounded dielectric substrate is presented. The model does not include the microstrip feed, and thus does not include the so-called "antenna mode" component of the scattering. The solution begins by formulating an electric field integral equation for the surface current density on the microstrip patch. The integral equation is solved using the method of moments. Computed data for the patch radar cross section (RCS) is found to be in close agreement with measurements over a broad frequency range. The microstrip RCS versus frequency consists of a number of large peaks which are identified as impedance or pattern factor resonance peaks.

A shading model for atmospheric scattering considering luminous intensity distribution of light sources

Abstract: Studio spotlights produce dazzling shafts of light, while light scattered from fog illuminated by automobile headlights renders driving difficult. This is because the particles in the illuminated volume become visible by scattering light. A shading model for scattering and absorption of light caused by particles in the atmosphere is proposed in this paper. The method takes into account luminous intensity distribution of light sources, shadows due to obstacles, and density of particles. The intensity at a viewpoint is calculated by integration of light scattered by particles between the viewpoint and a given point on an object. The regions to be treated in this manner are localized by considering illumination volumes and shadow volumes caused by obstacles in the illumination volumes.