Showing papers on "Scattering published in 1975"

Atomic form factors, incoherent scattering functions, and photon scattering cross sections

Abstract: Tabulations are presented of the atomic form factor,F (α,Z), and the incoherent scattering function, S (x,Z), for values of x (=sin ϑ/2)/λ) from 0.005 A−1 to 109 A−1, for all elements A=1 to 100. These tables are constructed from available state‐of‐the‐art theoretical data, including the Pirenne formulas for Z=1, configuration‐into action results by Brown using Brown‐Fontana and Weiss correlated wavefunctions for Z=2 to 6 non‐relativistic Hartree‐Fock results by Cromer for Z=7 to 100 and a relativistic K‐shell analytic expression for F (x,Z) by Bethe Levinger for x≳10 A−1 for all elements Z=2 to 100. These tabulated values are graphically compared with available photon scatteringangular distributionmeasurements. Tables of coherent (Rayleigh) and incoherent (Compton) total scattering cross sections obtained by numerical integration over combinations of F 2(x,Z) with the Thomson formula and S (x,Z) with the Klum‐Nishina Formual, respectively, are presented for all elements Z=1 to 100, for photon energies 100 eV (λ=124 A) to 100 MeV (0.000124 A). The incoherent scattering cross sections also include the radiative and double‐Compton corrections as given by Mork. Similar tables are presented for the special cases of terminally‐bonded hydrogen and for the H2 molecule, interpolated and extrapolated from values calculated by Stewart et al., and by Bentley and Stewart using Kolos‐Roothaan wavefunctions.

Origin of coda waves: Source, attenuation, and scattering effects

Abstract: Coda waves from small local earthquakes are interpreted as backscattering waves from numerous heterogeneities distributed uniformly in the earth's crust. Two extreme models of the wave medium that account for the observations on the coda are proposed. In the single backscattering model the scattering is considered to be a weak process, and the loss of seismic energy by scattering is neglected. In the diffusion model the seismic energy transfer is considered as a diffusion process. Both models lead to similar formulas that allow an accurate separation of the effect of earthquake source from the effects of scattering and attenuation on the coda spectra. A unique difference was found in the scaling law of earthquake source spectra between central California and western Japan, which may be attributed to the difference in inhomogeneity length of the earth's crust. The Q of coda waves in the two regions is strongly frequency dependent with values increasing from 50–200 at 1 Hz to about 1000–2000 at 20 Hz. This observation is interpreted as a combined effect of variation of Q with depth and frequency-dependent composition of coda waves described below. The turbidity coefficient of the lithosphere required at 1 Hz to explain the observed coda as body wave scattering is orders of magnitude greater than previously known values such as those obtained by Aki (1973) and Capon (1974) under the Montana Lasa from the amplitude and phase fluctuations of teleseismic P waves. From the high attenuation and turbidity obtained at this frequency we conclude that at around 1 Hz the coda is made of backscattering surface waves from heterogeneities in the shallow, low-Q lithosphere. The high Q observed for the coda at frequencies higher than 10 Hz, on the other hand, eliminates the possibility that these waves are backscattering surface waves. We conclude that at these high frequencies the coda must be made of backscattering body waves from heterogeneities in the deep lithosphere. The low turbidities found for deep earthquake sources under western Japan are consistent with this model of coda wave generation.

Theory of the extended x-ray absorption fine structure

Abstract: The extended x-ray absorption fine structure is a consequence of the modification of the photoelectron final state due to scattering by the surrounding atoms. We present a theory of the absorption fine structure starting from theoretically obtained electron-atom scattering phase shifts. The electron scattering is treated using a spherical wave expansion which takes into account the finite size of the atoms. Multiple-scattering effects are included by classifying multiple-scattering paths by their total path lengths. Their effects are quite large but appear to make quantitative but not qualitative changes on the single-scattering contribution. The exceptional case is the fourth shell in fcc or bcc structure, where it is shadowed by the first-shell atom and is profoundly affected by forward scattering due to the first shell. This may account for the anomaly observed experimentally at the fourth-shell radius in metals. A detailed numerical calculation is carried out for copper and is shown to agree quite well with experiment.

Computed relationships between the inherent and apparent optical properties of a flat homogeneous ocean.

Abstract: Monte Carlo simulations of the transfer of radiation in the ocean are used to compute the apparent optical properties of a flat homogeneous ocean as a function of the inherent optical properties. The data are used to find general relationships between the inherent and apparent optical properties for optical depths tau

Scattering of electromagnetic waves by arbitrarily shaped dielectric bodies

Abstract: The differential scattering characteristics of closed three-dimensional dielectric objects are theoretically investigated. The scattering problem is solved in a spherical basis by the Extended Boundary Condition Method (EBCM) which results in a system of linear equations for the expansion coefficients of the scattered field in terms of the incident field coefficients. The equations are solved numerically for dielectric spheres, spheroids, and finite cylinders to study the dependence of the differential scattering on the size, shape, and index of refraction of the scattering object. The method developed here appears to be most applicable to objects whose physical size is on the order of the wavelength of the incident radiation.

Theory of stimulated scattering processes in laser‐irradiated plasmas

Abstract: Analytic theory of the linear and nonlinear behavior of the one‐dimensional Brillouin and Raman scattering instabilities is given. Results are presented for the problems of an infinite homogeneous plasma and of a finite inhomogeneous plasma. Nonlinear fluid equations can predict backscatter energies the order of the incident laser energy; however, the size of the interaction region and nonlinear effects on the excited electrostatic wave are very important in determining the amount of backscatter. In many cases of contemporary interest for a high power laser incident on a target plasma, the latter effects can play a crucial role in reducing backscatter to a tolerable level.

Three-Dimensional Induced Polarization and Electromagnetic Modeling

Abstract: The induced polarization (IP) and electromagnetic (EM) responses of a three‐dimensional body in the earth can be calculated using an integral equation solution. The problem is formulated by replacing the body by a volume of polarization or scattering current. The integral equation is reduced to a matrix equation, which is solved numerically for the electric field in the body. Then the electric and magnetic fields outside the inhomogeneity can be found by integrating the appropriate dyadic Green’s functions over the scattering current. Because half‐space Green’s functions are used, it is only necessary to solve for scattering currents in the body—not throughout the earth. Numerical results for a number of practical cases show, for example, that for moderate conductivity contrasts the dipole‐dipole IP response of a body five units in strike length approximates that of a two‐dimensional body. Moving an IP line off the center of a body produces an effect similar to that of increasing the depth. IP response va...

Electron drift velocity in silicon

Abstract: Experimental results for electrons obtained with the time-of-flight technique are presented for temperatures between 8 and 300\ifmmode^\circ\else\textdegree\fi{}K and fields ranging between 1.5 and 5 \ifmmode\times\else\texttimes\fi{} ${10}^{4}$ V ${\mathrm{cm}}^{\ensuremath{-}1}$ oriented along $〈111〉$, $〈110〉$, and $〈100〉$ crystallographic directions. At 8\ifmmode^\circ\else\textdegree\fi{}K the dependence of the transit time upon sample thickness has allowed a measurement of the valley repopulation time when the electric field is $〈100〉$ oriented. These experimental results have been interpreted with Monte Carlo calculations in the same ranges of temperature and field. The theoretical model includes the many-valley structure of the Si conduction band, acoustic intravalley scattering with correct momentum and energy relaxation and correct equilibrium phonon population, several intervalley scatterings, and ionized impurity scattering.

Approximations for the exchange potential in electron scattering

Abstract: Four new exchange potentials (the semiclassical exchange approximation, the asymptotically adjusted free‐electron–gas exchange approximation, the second‐order free‐electron–gas exchange approximation, and the high‐energy exchange approximation) are derived. Calculations are performed for elastic electron scattering from helium and argon. The results are compared to one another and to calculations using Hara’s free‐electron–gas approximation and the exact nonlocal exchange potential. Three of the approximations to exchange are in good agreement with the exact exchange —except at very low energy— but are much easier to use. Thus they should be very useful in electron–atom and electron–molecule scattering calculations.

Scattering and absorption of electromagnetic radiation by a semi-infinite medium in the presence of surface roughness

Abstract: In this paper, we present a theoretical description of the scattering and absorption of electromagnetic radiation induced by roughness on the surface of a semi-infinite medium. We approach the problem by the use of scattering theory applied to the classical Maxwell equations. We obtain formulas for the roughness-induced scattering from the surface of an isotropic dielectric for both $s$- and $p$-polarized waves incident on the surface at a general angle of incidence. When the real part of the dielectric constant of the material is negative and its imaginary part small (as in a simple nearly-free-electron metal), we extract from the expressions for the total absorption rate that portion which describes roughness-induced absorption by surface polaritons (surface plasmons). We compare our results with those recently published by Ritchie and collaborators for the case of normal incidence, and we present a series of numerical studies of the roughness-induced scattering and absorption rates in aluminum.

Rotational excitation in H2–H2 collisions: Close‐coupling calculations

Abstract: Rotational excitation in molecule−molecule collisions has been treated for the first time by accurate quantum close−coupling scattering calculations, employing an expansion basis set of two to three rotational levels for each molecule and correctly accounting for exchange of identical particles. Elastic and inelastic cross sections have been computed for collisions of para−para, ortho−ortho, and para−ortho hydrogen molecules assuming an intermolecular potential suggested previously. The accuracy of recent ’’effective potential’’ calculations is demonstrated by comparison with the exact quantum results.

Scattering of surface waves by a conical island

Abstract: A model equation is derived which approximately describes the propagation of periodic surface waves in water of slowly varying depth. Numerical solutions to the model equation are obtained for the scattering of an incident plane wave by a conical island.

Light scattering study of dynamic and time-averaged correlations in dispersions of charged particles

Abstract: Several aqueous dispersions of charged polystyrene spheres (mean radius =250 aa) have been studied at very low ionic strength by conventional light scattering and photon correlation spectroscopy. Plotted as a function of scattering angle, the mean scattered intensity exhibited maxima similar to those found in the structure factor of simple liquids determined by X-ray or neutron scattering. Fourier transformation of the corrected intensity data yielded radial distribution functions whose structure indicated considerable short-range ordering of the particles due to repulsive coulombic interactions. The reciprocal of the effective particle diffusion coefficient (determined from the initial decay rate of the non-exponential temporal autocorrelation function of the scattered light field) showed angular dependence similar to the mean intensity, in agreement with recent theoretical predictions.

Pure-state analysis of resonant light scattering: Radiative damping, saturation, and multiphoton effects

Abstract: A fully quantum-mechanical treatment of resonant light scattering is presented. The incident field is assumed to be described by a coherent state, and is allowed to be intense enough to cause saturation. Complete solutions are obtained for the correlated atom-field pure state vector, including multiphoton contributions of arbitrary order. The frequency spectrum of the scattered field is evaluated and is found to agree exactly with the result previously obtained by means of the quantum fluctuation-regression theorem. A derivation of the fluctuation-regression theorem and of the optical Bloch equations is given which is fully quantum mechanical and which relies upon no assumption of statistical factorization of atom and field states. The accuracy of the result found for the scattered - field spectrum is thus shown to be limited only by the assumption of the smallness of the saturated linewidth compared to the (optical) atomic resonance frequency. The one-photon approximation is analyzed in some detail. The method of adding an imaginary term to the upper-atomic-state energy is clarified, and it is shown how the vacuum and one-photon amplitudes thereby obtained may be used, within a simple and plausible iteration scheme, to construct the complete multiphoton spectrum. A variety of commonly used injection schemes and methods of representing atomic relaxation are discussed, and comparisons are made with results found by other authors. The entire analysis is performed with the aid of a canonical transformation which replaces the applied field by a $c$ number. It is thus proved quite rigorously and generally that the use of a $c$-number applied field is a fully quantum-mechanical procedure, provided only that radiation-reaction terms are retained.

X-Ray-Diffuse-Scattering Evidence for a Phase Transition in Tetrathiafulvalene Tetracyanoquinodimethane (TTF-TCNQ).

Abstract: X-ray-diffuse-scattering measurements of tetrathiafulvalene tetracyanoquinodimethane (TTF-TCNQ) show structural evidence of a phase transition. The low-temperature three dimensional superlattice ($2a\ifmmode\times\else\texttimes\fi{}3.7b\ifmmode\times\else\texttimes\fi{}\mathrm{Xc}$) is found to be preceded above 40 K by one-dimensional fluctuations or a one-dimensional distortion visible up to 55 K.

Microwave scattering and the straining of wind-generated waves

Abstract: The modulation in backscattered power from wind-generated waves due to the presence of a 0.575-Hz plunger-generated wave has been measured in a wave tank as a function of air friction velocity and plunger wave amplitude. The measurements were made at 9.375 GHz, a depression angle of 45° and vertical polarization. The straining of the wind waves is treated by a first-order perturbation of the Boltzmann transport equation and the scattering is calculated from a simple application of composite surface scattering theory utilizing first-order Bragg scattering. The theory predicts a characteristic relaxation behavior for the wind-speed dependence of the components of the modulation amplitude in phase and out of phase with the horizontal component of orbital velocity of the plunger wave. This relaxation behavior is closely followed by the observed modulation amplitudes for air friction velocities less than about 40 cm sec−1, i.e., winds less than about 7 m sec−1.

Theory of Hall Effect in a Two-Dimensional Electron System

Abstract: Hall conductivity σ XY is studied in various approximations. Characteristics of σ XY are obtained for the case of both short- and long-ranged scatterers in the self-consistent Born approximation, which is the simplest one free form the difficulty of divergence. In case of short-ranged scatterers, a relation is shown to hold between σ XY and σ XX within this approximation, if one uses a relaxation time under magnetic fields. Under strong magnetic fields, effects of higher Born scattering become important in low-lying Landau levels. They depend on the sign of scatterers and strongly on their concentrations. Effects of simultaneous scattering from many scatterers are calculated to the lowest order.

The two-stream approximation in radiative transfer Including the angle of the incident radiation

Abstract: The two-stream approximation has been applied to the equation of radiative transfer to obtain two–stream models for the transfer of radiation through an optically thin plane-parallel atmosphere. The models include the dependence of the reflection and the transmission of the atmosphere on the angle of the incident radiation and on the angular dependence of the scattering phase function of the medium. The two models arise from different methods for treating the incident radiation. It is shown that the models reduce to the thin-atmosphere approximation in the limit that the optical depth of the atmosphere approaches zero. In this limit the sign of the heating caused by the presence of a scattering and absorbing layer over a reflecting surface is derived. This reveals the importance of both the zenith angle and the angular dependence of the scattering phase function. The results obtained from the two-stream models are compared with those of numerical solutions to the equation of radiative transfer. I...

Laser irradiance propagation in turbulent media

Abstract: The results obtained in recent years on laser irradiance propagation in random weakly inhomogeneous media with large scale index of refraction fluctuations are reviewed. Of particular concern are the problems of the cozrelation theory of fluctuations of irradiance propagating over large distances, where the effects of multiple scattering are greatly pronounced. Much attention is paid to the results on laser beams spread and phase fluctuations. Consideration is given to problem of the study of spatial spikes of irradiance that had passed through a turbulent media; which is comparatively new but important for practical applications. Systematic comparison of the theory with experiment is given where appropriate. The methods of analyses reviewed in this paper are applicable to a class of stochastic and dynamic partial differential equations and thus may be of interest in other areas of engineering reseach.

Relationship of the relativistic Compton cross section to the momentum distribution of bound electron states

Abstract: An approximate relativistic treatment of the differential cross section for Compton scattering against bound electron states is discussed. A simple relationship between the cross section and the Compton profile is found. On contrast to previous work this relationship is valid for all scattering angles.

Electron Scattering and Nuclear Structure

Abstract: Electron scattering is treated within the framework of the one-photon exchange approximation. Electron excitation of collective particle-hole states (including the giant dipole resonance) is detailed. The process of quasi-elastic scattering is then discussed within the framework of the Fermi gas model. A brief review is presented of the relationship between electromagnetic interactions and semileptonic weak interactions, stressing the extra knowledge that the electron scattering yields. Finally, a few special topics of interest in intermediate energy physics are examined. 221 references. (SDF)

Scattering by periodic surfaces

Abstract: Reflection behavior is examined for an interface having periodic height variation. Upon employing the Bloch theorem, in conjunction with the extended boundary condition, exact matrix equations are obtained for surface fields, as well as transmitted and reflected wave amplitudes. Tunneling considerations then lead to new energy constraints for problems of this type, in which propagating waves are coupled with evanescent modes. In the limit of surface corrugations shallow compared with impinging wavelength, analytic results are obtained confirming both the energy constraints and early computations by Rayleigh. Numerical results demonstrate the efficiency of the method.Subject Classification: 20.30.

Measurement of the electron--deuteron elastic-scattering cross section in the range 0.8less than or equal toq$sup 2$less than or equal to6 GeV$sup 2$

Abstract: Preliminary results are reported of elastic e-d scattering at large momentum transfer performed at the Stanford Linear Accelerator Center with use of two high-resolution spectrometers in coincidence. Our results are in sharp disagreement with the meson-exchange calculations, they are in rough agreement with the nonrelativistic potential models, and they are in agreement with the predictions of the quark dimensional-scaling model which pictures the deuteron as a bound state of six quarks at large momentum transfer.

The absorption and scattering of light in bovine and human dental enamel

Abstract: The reflectance and transmission of thin slabs of dental enamel has been measured at all wavelengths between 220 and 700 nm by means of an integrating sphere. From the results the true scattering and absorption coefficients have been computed. The theoretical model used is an extended two-flux model, which is presented and discussed. The absorption spectrum of the dissolved organic component of enamel was also determined. An absorption peak at 270 nm is common to all the spectra. This peak in the bovine enamel spectrum is about three times as high as in the spectrum of human enamel. The peak of the dissolved material is about as high as the peak of the corresponding enamel. Hence it is concluded that the organic component, presumably aromatic amino acids, is responsible for most or all of the observed optical absorption.