Showing papers on "Scattering published in 1988"

Numerically stable algorithm for discrete-ordinate-method radiative transfer in multiple scattering and emitting layered media.

Abstract: The transfer of monochromatic radiation in a scattering, absorbing, and emitting plane-parallel medium with a specified bidirectional reflectivity at the lower boundary is considered. The equations and boundary conditions are summarized. The numerical implementation of the theory is discussed with attention given to the reliable and efficient computation of eigenvalues and eigenvectors. Ways of avoiding fatal overflows and ill-conditioning in the matrix inversion needed to determine the integration constants are also presented.

X-ray and neutron scattering from rough surfaces

Abstract: The scattering of x rays and neutrons from rough surfaces is calculated. It is split into specular reflection and diffuse scattering terms. These are calculated in the first Born approximation, and explicit expressions are given for surfaces whose roughness can be described as self-affine over finite length scales. Expressions are also given for scattering from liquid surfaces, where it is shown that ``specular'' reflections only exist by virtue of a finite length cutoff to the mean-square height fluctuations. Expressions are also given for the scattering from randomly oriented surfaces, as studied in a typical small-angle scattering experiment. It is shown how various well-known asymptotic power laws in S(q) are obtained from the above theory. The distorted-wave Born approximation is next used to treat the case where the scattering is large (e.g., near the critical angle for total external reflection), and its limits of validity are discussed. Finally, the theory is compared with experimental results on x-ray scattering from a polished Pyrex glass surface.

Atomic and Molecular Beam Methods

Abstract: Part I: Spectroscopy. 1: Spectroscopy of molecular beams: an overview. 2: Magnetic and electric resonance spectroscopy. 3: Beam-maser spectroscopy. 4: Quantum amplifiers and oscillators. 5: Metrology with molecular beams. 6: Infrared laser spectroscopy. 7: Visible and UV spectroscopy: physical aspects. 8: Photofragment spectroscopy. 9: Fourier-transform microwave spectroscopy. 10: Fourier-transform methods: infrared. Part II: Surface Scattering. 11: General principles and methods. 12: Elastic scattering of atoms. 13: Rotational inelastic scattering. 14: Single phonon inelastic helium scattering. 15: Multiple phonon inelastic scattering. 16: Scattering from disordered surfaces. 17: Reactive scattering

The discrete-dipole approximation and its application to interstellar graphite grains

Abstract: The discrete dipole approximation (DDA), a flexible method for computing scattering of radiation by particles of arbitrary shape, is extended to incorporate the effects of radiative reaction and to allow for possible anisotropy of the dielectric tensor of the material. Formulas are given for the evaluation of extinction, absorption, scattering, and polarization cross sections. A simple numerical algorithm based on the method of conjugate gradients is found to provide an efficient and robust method for obtaining accurate solutions to the scattering problem. The method works well for absorptive, as well as dielectric, grain materials. Two validity criteria for the DDA are presented. The DDA is then used to compute extinction cross sections for spherical graphite grains and to calculate extinction cross sections for nonspherical graphite grains with three different geometries. It is concluded that the interstellar 2175 A extinction feature could be produced by small graphite grains which should have aspect ratios not far from unity. 35 references.

Diffusing wave spectroscopy

Abstract: We obtain useful information from the intensity autocorrelations of light scattered from systems which exhibit strong multiple scattering. A phenomenological model, which exploits the diffusive nature of the transport of light, is shown to be in excellent agreement with experimental data for several different scattering geometries. The dependence on geometry provides an important experimental control over the time scale probed. We call this technique diffusing wave spectroscopy, and illustrate its utility by studying diffusion in a strongly interacting colloidal glass.

Small‐angle scattering by fractal systems

Abstract: Fractal structures are characterized by self similarity within some spatial range. The mass distribution in a fractal object varies with a power D of the length R, smaller than the dimension d of the space. When the range of physical interest falls below 1000 A, scattering techniques are the most appropriate way to study fractal structures and determine their fractal dimension D. Small-angle neutron scattering (SANS) is particularly useful when advantage can be taken of isotopic substitution. It is easy to show that the scattering law for a fractal object is given by S(Q), ~ Q−D, where Q is the magnitude of the scattering vector. However, in practice some precautions must be taken because, near the limits of the fractal range, there are important deviations from this simple law. Some relations are derived which can be applied in relatively general situations, such as aggregation and gelation. The effects of polydispersity, important, in particular, in situations described by percolation models, are also shown.

The validity of the perturbation approximation for rough surface scattering using a Gaussian roughness spectrum

Abstract: The validity of the perturbation approximation for rough surface scattering is examined (1) by comparison with exact results obtained by solving an integral equation and (2) through comparison of low‐order perturbation predictions with higher‐order predictions. The pressure release boundary condition is assumed, and the field quantity calculated is the bistatic scattering cross section. A Gaussian roughness spectrum is used, and the surfaces have height variations in only one direction. It is found, in general, that the condition kh≪1 (k is the acoustic wavenumber, h is the rms surface height) is insufficient to guarantee the accuracy of first‐order (or higher‐order) perturbation theory. When the surface correlation length l becomes too large or too small with h held fixed, higher‐order perturbation terms can make larger contributions to the scattering cross section than lower‐order terms. An explanation for this result is given. The regions of validity for low‐order perturbation theory are also given. Th...

Calculations of electron inelastic mean free paths for 31 materials

Abstract: We present new calculations of electron inelastic mean free paths (IMFPs) for 200–2000 eV electrons in 27 elements (C, Mg, Al, Si, Ti, V, Cr, Fe, Ni, Cu, Y, Zr, Nb, Mo, Ru, Rh, Pd, Ag, Hf, Ta, W, Re, Os, Ir, Pt, Au and Bi) and four compounds (LiF, SiO2, ZnS and Al2O3). These calculations are based on an algorithm due to Penn which makes use of experimental optical data (to represent the dependence of the inelastic scattering probability on energy loss) and the theoretical Lindhard dielectric function (to represent the dependence of the scattering probability on momentum transfer). Our calculated IMFPs were fitted to the Bethe equation for inelastic electron scattering in matter; the two parameters in the Bethe equation were then empirically related to several material constants. The resulting general IMFP formula is believed to be useful for predicting the IMFP dependence on electron energy for a given material and the material-dependence for a given energy. The new formula also appears to be a reasonable but more approximate guide to electron attenuation lengths.

The physics of charged-particle beams

Abstract: Introduction Beam optics and focusing systems Laminar beams with self-fields Non-Laminar beams without collisions Beams with scattering or dissipation Waves and instabilities in beams

Light scattering from a sphere arbitrarily located in a Gaussian beam, using a Bromwich formulation

Abstract: We present a theoretical description of the scattering of a Gaussian beam by a spherical, homogeneous, and isotropic particle. This theory handles particles with arbitrary size and nature having any location relative to the Gaussian beam. The formulation is based on the Bromwich method and closely follows Kerker’s formulation for plane-wave scattering. It provides expressions for the scattered intensities, the phase angle, the cross sections, and the radiation pressure.

X-ray resonance exchange scattering.

Abstract: Large resonant magnetization-sensitive x-ray scattering is predicted to occur in the vicinity of the L/sub II/, L/sub III/, and M/sub II/--M/sub V/ absorption edges in the rare-earth and actinide elements, and at the K and L edges in the transition elements. These ''magnetic'' resonances result from electric multipole transitions, with the sensitivity to the magnetization arising from exchange. For some transitions, the magnetic scattering will be comparable to the charge scattering. The general features of the observed L/sub III/ resonance in Ho are discussed.

Effective permittivity of dielectric mixtures

Abstract: General mixing formulas are derived for discrete scatterers immersed in a host medium. The inclusion particles are assumed to be ellipsoidal. The electric field inside the scatterers is determined by quasi-static analysis, assuming the diameter of the inclusion particles to be much smaller than one wavelength. The results are applicable to general multiphase mixtures, and the scattering ellipsoids of the different phases can have different sizes and arbitrary ellipticity distribution and axis orientation, i.e. the mixture may be isotropic or anisotropic. The resulting mixing formula is nonlinear and is suitable for iterative solutions. The formula contains a quantity called the apparent permittivity, and with different choices of this quantity, the result leads to the generalized Lorentz-Lorenz formula, the generalized Polder-van Santen formula, and the generalized coherent potential-quasicrystalline approximation formula. The results are applied to calculating the complex effective permittivity of dry and wet snow, and sea ice. >

Intensity images and statistics from numerical simulation of wave propagation in 3-D random media

Abstract: An extended random medium is modeled by a set of 2-D thin Gaussian phase-changing screens with phase power spectral densities appropriate to the natural medium being modeled. Details of the algorithm and limitations on its application to experimental conditions are discussed, concentrating on power-law spectra describing refractive-index fluctuations of the neutral atmosphere. Inner and outer scale effects on intensity scintillation spectra and intensity variance are also included. Images of single realizations of the intensity field at the observing plane are presented, showing that under weak scattering the small-scale Fresnel length structure of the medium dominates the intensity scattering pattern. As the strength of scattering increases, caustics and interference fringes around focal regions begin to form. Finally, in still stronger scatter, the clustering of bright regions begins to reflect the large-scale structure of the medium. For plane waves incident on the medium, physically reasonable inner scales do not produce the large values of intensity variance observed in the focusing region during laser propagation experiments over kilometer paths in the atmosphere. Values as large as experimental observations have been produced in the simulations, but they require inner scales of the order of 10 cm. Inclusion of an outer scale depresses the low-frequency end of the intensity spectrum and reduces the maximum of the intensity variance. Increasing the steepness of the power law also slightly increases the maximum value of intensity variance.

Exact Rayleigh scattering calculations for use with the Nimbus-7 Coastal Zone Color Scanner

Abstract: For improved analysis of Coastal Zone Color Scanner (CZCS) imagery, the radiance reflected from a planeparallel atmosphere and flat sea surface in the absence of aerosols (Rayleigh radiance) has been computed with an exact multiple scattering code, i.e., including polarization. The results indicate that the single scattering approximation normally used to compute this radiance can cause errors of up to 5% for small and moderate solar zenith angles. At large solar zenith angles, such as encountered in the analysis of high-latitude imagery, the errors can become much larger, e.g.,>10% in the blue band. The single scattering error also varies along individual scan lines. Comparison with multiple scattering computations using scalar transfer theory, i.e., ignoring polarization, show that scalar theory can yield errors of approximately the same magnitude as single scattering when compared with exact computations at small to moderate values of the solar zenith angle. The exact computations can be easily incorporated into CZCS processing algorithms, and, for application to future instruments with higher radiometric sensitivity, a scheme is developed with which the effect of variations in the surface pressure could be easily and accurately included in the exact computation of the Rayleigh radiance. Direct application of these computations to CZCS imagery indicates that accurate atmospheric corrections can be made with solar zenith angles at least as large as 65 degrees and probably up to at least 70 degrees with a more sensitive instrument. This suggests that the new Rayleigh radiance algorithm should produce more consistent pigment retrievals, particularly at high latitudes.

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

Lattice Vibrations and Heat Transport in Crystals and Glasses

Abstract: in all processes that involve temperature. The purpose of this paper is to review and illustrate the models developed for the description of lattice vibrations and their interactions. Because of our personal involvement we discuss measurements of specific heat, thermal conductivity, and the propagation of heat pulses, the subjects of our own work. We begin our historical review with the earliest model, as proposed by Einstein, and then show why for crystalline solids it had to be replaced by a model employing elastic travelling waves. We review scattering experiments that demonstrate the wave-like character of these excitations, and other experiments that are more readily understood with the particle picture of quantized vibrations.

Polarization and resonance properties of magnetic x-ray scattering in holmium.

Abstract: Be measuring the degree of linear polarization we identify the orbital and spin contributions to the x-ray magnetic scattering in holmium. When the incident x-ray energy is tuned through the ${L}_{\mathrm{III}}$ absorption edge, we observe a fiftyfold resonant enhancement of the magnetic signal, and resonant integer harmonics. The line shapes of the two linear components scattered parallel and perpendicular to the diffraction plane are distinct in energy with a 6-eV splitting.

Theoretical study of the coherent backscattering of light by disordered media

Abstract: A theoretical study of the coherent backscattering effect of light from disordered semi-inifinite media is presented for various situations including time-dependent effects as well as absorption and amplitude modulation. Particular attention is devoted to the case of anisotropic scattering and to polarization in order to explain quantitatively experimental results. A microscopic derivation of the coherent albedo is given which strongly supports the heuristic formula previously established. In addition the coherent albedo of a fractal system is predicted. The validity of the different approximations used are discussed and some further theoretical developments are presented On inclut les effets dependant du temps, les milieux absorbants et les effets lies a la modulation d'amplitude de la lumiere

Femtosecond photon echoes from band-to-band transitions in GaAs.

Abstract: We report the first observation of femtosecond photon echoes from the band-to-band transitions in a bulk semiconductor. The time decay of the echo, found to vary from 3.5 to 11 fs, has allowed us to determine the polarization dephasing rate in GaAs. This rate was found to depend on the carrier density in the experimental range covered, 1.5\ifmmode\times\else\texttimes\fi{}${10}^{17}$ to 7\ifmmode\times\else\texttimes\fi{}${10}^{18}$ ${\mathrm{cm}}^{\ensuremath{-}3}$, indicating the dominance of carrier-carrier scattering as the principal dephasing mechanism. The observed functional dependence of the dephasing rate on the carrier density has yielded previously unavailable information on Coulomb screening in a nonequilibrium carrier distribution.

Light scattering in strongly scattering media: Multiple scattering and weak localization

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Polarization dependence of magnetic x-ray scattering.

Abstract: We calculate the polarization dependence of the x-ray scattering cross section, including magnetic terms, using the Poincar\'e representation for the polarization. General expressions are given for the polarization dependence of the cross section of the pure magnetic scattering and of the interference between charge and magnetic scattering, and for the polarization of the scattered beam in both cases. These expressions are compared to the equivalent results for magnetic neutron scattering. The general results are then specialized to several typical cases, including the scattering of linearly and circularly polarized radiation from spiral, uniaxially modulated, and ferromagnetic structures. It is shown that detailed magnetic-structure determinations are possible using synchrotron radiation. It is further demonstrated that the orbital- and spin-angular-momentum contributions of both ferromagnets and antiferromagnets may be separately measured in a variety of simple geometries. It is found that, although the efficiency is very low, linearly polarized radiation can be completely converted to circular polarization by scattering from a magnetic spiral. Finally, it is shown that, in addition to the interference between charge and magnetic scattering, there is an interference involving the spin- and orbital-angular-momentum scattering, which can couple moments in different spatial directions.

Anisotropic normal-state transport properties predicted and analyzed for high-Tc oxide superconductors.

Abstract: Electronic energy bands calculated from local-density-functional (LDF) theory are used to predict anisotropic transport properties of the oxide superconductors La/sub 2/..sqrt../sub x/Sr/sub x/CuO/sub 4/ and YBa/sub 2/Cu/sub 3/O/sub 7/. Calculations of the magnitude of the resistivity tensor rho/sub ..cap alpha..//sub ..beta../ (assuming only electron-phonon scattering) lead to results smaller than given by current experiments, suggesting that LDF theory overestimates the Drude plasma frequency (or Fermi velocity), or else that another scattering mechanism dominates. Determinations of the Fermi velocity from critical field measurements suggest however that it is close to the LDF value. Quantities which are independent of the scattering are calculated with more success: the resistivity anisotropy rho/sub z//sub z/rho/sub xx/, the Hall tensor R/sub ..cap alpha..//sub ..beta..//sub ..gamma..//sub '//sup H/ and the thermopower S/sub ..cap alpha..//sub ..beta../. It is predicted that R/sup H/ should appear ''holelike'' when electrons orbit in metallic planes but S should appear ''electronlike'' for thermal gradients in the plane. When fields are tipped 90/sup 0/, all coefficients change sign. There is not very much single-crystal data to compare with, but what exists is qualitatively consistent, including anomalous signs of the Hall tensor. Polycrystalline data for R/sup H/ seem completely at variance with the LDF results,more » so it is surprising how well single-crystal results agree« less

Classical and quantum scattering on a cone

Abstract: The “topological” scattering of a quantized test particle in the locally flat conical geometry of a localized source in 2+1-dimensional gravity is analyzed. Wave functions and scattering amplitudes are obtained and compared with those recently found in a different approach by ‘t Hooft. The propagator [heat kernel] is also determined.

Electromagnetic scattering from a layer of finite length, randomly oriented, dielectric, circular cylinders over a rough interface with application to vegetation

Abstract: A scattering model for defoliated vegetation is developed by treating a layer of defoliated vegetation as a collection of randomly oriented dielectric cylinders of finite length over an irregular ground surface. Both polarized and depolarized backscattering are computed and their behavior versus the volume fraction, the incidence angle, the frequency, the angular distribution and the cylinder size are illustrated. It is found that both the angular distribution and the cylinder size have significant effects on the backscattered signal. The present theory is compared with measurements from defoliated vegetations.

X-ray diffraction study of the polymorphic behavior of N-methylated dioleoylphosphatidylethanolamine.

Abstract: The polymorphic phase behavior of aqueous dispersions of dioleoylphosphatidylethanolamine (DOPE) and its N-methylated analogues, DOPE-Me, DOPE-Me/sub 2/, and DOPC, has been investigated by X-ray diffraction. In the fully hydrated lamellar (L/sub ..cap alpha../) phase at 2/sup 0/C, the major structural difference is a large increase in the interlamellar water width from DOPE to DOPE-Me, with minor increases with successive methylation. Consistent with earlier reports, inverted hexagonal (H/sub II/) phases are observed upon heating at 5-10 /sup 0/C in DOPE and at 65-75 /sup 0/C in DOPE-Me and are not observed to at least 85 /sup 0/C in DOPE-Me/sub 2/ or DOPC. It is shown that, in copious water, the disordered state transforms very slowly into phases with cubic symmetry. This process is assisted by the generation of small amounts of lipid degradation products. The relative magnitudes of the monolayer spontaneous radius of curvature, are inferred from the H/sub II/ lattice spacings vs temperature and are shown to increase with increasing methylation. The relative magnitudes of R/sub 0/ are categorized as small for DOPE, intermediate for DOPE-Me, and large for DOPC. The relationship between the cubic phases and minimal periodic surfaces is discussed. The geometry of the equilibrium phases that occurmore » may be largely understood on the basis of a competition between a spontaneous tendency for the monolayers to curl to a radius, R/sub 0/, and the need to pack similar hydrocarbon chains at near constant density and at a uniform mean length.« less