Showing papers on "Scattering published in 1970"

Relativistic Calculation of Anomalous Scattering Factors for X Rays

Abstract: Anomalous scattering factors Δf′ and Δf″ have been calculated relativistically for Cr, Fe, Cu, Mo, and Ag Kα radiations for the atoms Li through Cf. An interpolation scheme for other wavelengths is included in a separate report. Relativistic calculations of the photoelectric cross section have been made and the integral for the principal contribution to Δf′ has been evaluated numerically without approximation to the form of the cross section‐vs‐energy curve, as has been done in previous calculations. Many of the results are significantly different from previous calculations. Where experimental values exist, agreement for Δf″ is improved. For the rare gases, except for xenon, agreement between Δf′ and experiment is improved. Because of the more rigorous evaluation of Δf′ from cross‐section information, it is presumed that the present Δf′ values are more accurate than previous calculated values. Calculated mass absorption coefficients for the elements are included as incidental information.

Superlattice and negative differential conductivity in semiconductors

Abstract: We consider a one-dimensional periodic potential, or "superlattice," in monocrystalline semiconductors formbeyd a periodic variation of alloy composition or of impurity density introduced during epitaxial growth. If the period of a superlattice, of the order of 100A, is shorter than the electron mean free path, a series of narrow allowed and forbidden bands is expected duet o the subdivision of the Brillouin zone into a series of minizones. If the scattering time of electrons meets a threshold condition, the combined effect of the narrow energy band and the narrow wave-vector zone makes it possible for electrons to be excited with moderate electric fields to an energy and momentum beyond an inflection point in the E-k relation; this results ina negative differential conductance in the direction of the superlattice. The study of superlattices and observations of quantum mechanical effects on a new physical scale may provide a valuable area of investigation in the fieId of semiconductors.

Electrical-Resistivity Model for Polycrystalline Films: the Case of Arbitrary Reflection at External Surfaces

Abstract: In this paper, the total resistivity of a thin metal film is calculated from a model in which three types of electron scattering mechanisms are simultaneously operative: an isotropic background scattering (due to the combined effects of phonons and point defects), scattering due to a distribution of planar potentials (grain boundaries), and scattering due to the external surfaces. The intrinsic or bulk resistivity is obtained by solving a Boltzmann equation in which both grain-boundary and background scattering are accounted for. The total resistivity is obtained by imposing boundary conditions due to the external surfaces (as in the Fuchs theory) on this Boltzmann equation. Interpretation of published data on grain-boundary scattering in bulk materials in terms of the calculated intrinsic resistivity, and of thin-film data in terms of the calculated total resistivity suggests that (i) the grain-boundary reflection coefficient in Al is \ensuremath{\approx} 0.15, while it is somewhat higher in Cu; (ii) the observed thickness dependence of the resistivity in thin films is due to grain-boundary scattering as well as to the Fuchs size effect; and (iii) the common observation that single-crystal films possess lower resistivities than polycrystalline films may be accounted for by grain-boundary effects rather than by differences in the nature of surface scattering.

Electromagnetic and acoustic scattering by simple shapes

Abstract: : The book represents an exhaustive study of the scattering properties of acoustically soft and hard bodies and of perfect conductors, presented for 15 geometrically-simple shapes Such shapes are important in their own right and as a basis for synthesizing the radiation and scattering properties of more complex configurations Each shape is treated in a separate chapter whose contents are presented in stylized format for easy reference Emphasis is placed on results in the form of formulae and diagrams Although no detailed derivation are included, an outline of methods in scattering theory is given in the Introduction

Side-Jump Mechanism for the Hall Effect of Ferromagnets

Abstract: The center of mass of a wave packet undergoes a discontinuous and finite sideways displacement on scattering by a central potential, in the presence of spin-orbit interaction. This is the main Hall-effect mechanism (${\ensuremath{\rho}}_{H}\ensuremath{\propto}{\ensuremath{\rho}}^{2}$) for Fe, Ni, and their alloys above 100 K, while asymmetric scattering dominates below 100 K. Displacement $\ensuremath{\Delta}y$ per actual collision is calculated by partial waves. In the case of Born expansion, the leading term of $\ensuremath{\Delta}y or \frac{{\ensuremath{\rho}}_{H}}{{\ensuremath{\rho}}^{2}}$ is of zero order in the scattering potential. The magnitude is predicted correctly ($\ensuremath{\Delta}y\ensuremath{\approx}{10}^{\ensuremath{-}10}\ensuremath{-}{10}^{\ensuremath{-}11}$ m) when using the effective spin-orbit Hamiltonian derived by Fivaz from spin-orbit interband mixing. The calculation of ${\ensuremath{\rho}}_{H}$ is extended to arbitrary ${\ensuremath{\omega}}_{c}\ensuremath{\tau}$ for compensated and un-compensated metals. Other nonclassical physical mechanisms proposed by Karplus and Luttinger and by Doniach and by Fivaz are spurious for the dc Hall effect.

Aerodynamic sound generation by turbulent flow in the vicinity of a scattering half plane

Abstract: The presence of the edge of a half plane in a turbulent fluid results in a large increase in the noise generated by that fluid at low Mach numbers. The parameter which is important is the product then the farfield sound has the same features as would be predicted by geometrical acoustics. The edge does not produce any significant sound amplification.

Emission in the Region 4000 to 7000 Å Via Four-Photon Coupling in Glass

Abstract: Four-photon stimulated scattering has been observed in borosilicate glass under high-power 5300-\AA{} picosecond-pulse excitation. Parametric emission is generated from 4000 to 7000 \AA{} from filaments formed in the glass, the wavelength depending on the emission angle.

Interferometric displacement measurement on scattering surfaces utilizing speckle effect

Abstract: When a surface is illuminated with laser light it has a speckled appearance due to random interference. If two speckle patterns are superimposed the distribution of intensity in the resultant pattern depends on the relative phases of the component patterns. By measuring the correlation between the resultant patterns at two different times a change of relative phase is detected. This leads to a versatile method of measuring either the normal or in-plane components of displacement over the whole of a surface at one time.

Optical phonons of small crystals

Abstract: The long wavelength optical phonons of ionic crystals give rise to dipole-dipole forces, whose long range nature causes the vibrations to depend on the size and shape of the crystal sample. This dependence affects significantly most spectral properties of all crystals whose dimensions are of the order of or shorter than the wavelength of reststrahlen (characteristically several tens of micrometres). In experimental work in which the infrared properties of ionic crystals were examined on small samples, in powder form or in colloidal suspension or in the shape of thin layers, the peculiarities due to size and shape were not always properly recognized. The infrared frequencies of the material which are derived with disregard to these peculiarities may be in error by some tens of wavenumbers. In the experimental section of the review we interpret the general characteristics of the experimental spectra and analyse in detail some representative infrared measurements in the light of the theory. The theory of optical vibrations which takes account of the finiteness of the specimen is formulated firstly in general terms and then by special reference to samples which have one, two or three dimensions short (slab, cylinder and sphere-like geometries). Synthetic spectra are drawn whose characteristic features are interpreted in terms of bulk and surface modes. In the theory retardation effects, i.e. the coupling between lattice and electromagnetic waves, are also included, and the quantized modes are combinations of these, i.e. polaritons. For tiny crystallites of such size that the characteristic infrared radiation wavelength is much larger than the sample size, retardation effects can be neglected. The theory becomes much simpler and the spectrum sharper. Some of the absorption peaks are due to optical surface modes, and their positions are simply related to the characteristic shapes of the crystallites. The theory is so presented as to provide a practical aid in the correlation of spectra with sample shape. The consequences on the spectra of other, less common variables of experiments, for example, the refractive index of the environments, are also calculated. The role of optical surface modes in Raman - and electron - scattering is then discussed. Simple geometrical arrangements of small sized crystals enable the spectra of surface modes to be scanned.

Classical theory of the scattering of intense laser radiation by free electrons

Abstract: Thomson theory of arbitrarily intense elliptically polarized plane electromagnetic wave scattering by free electrons, solving electron equations of motion

Connection of Elastic Electromagnetic Nucleon Form Factors at Large Q 2 and Deep Inelastic Structure Functions Near Threshold

Abstract: It is suggested that if the structure function $\ensuremath{ u}{W}_{2}$ for deep inelastic electron-proton scattering behaves near threshold as $\ensuremath{ u}{W}_{2}\ensuremath{\sim}(\frac{1}{\ensuremath{\omega}}){(1\ensuremath{-}\frac{1}{\ensuremath{\omega}})}^{p} \mathrm{for} \ensuremath{\omega}\ensuremath{\equiv}\frac{2M\ensuremath{ u}}{{Q}^{2}}\ensuremath{\rightarrow}1,$ then the elastic electromagnetic form factor of the proton ${F}_{1}$ behaves for large momentum transfers as ${F}_{1}({Q}^{2})\ensuremath{\sim}{(\frac{1}{{Q}^{2}})}^{\frac{(p+1)}{2}} \mathrm{for} {Q}^{2}\ensuremath{\rightarrow}\ensuremath{\infty}$

Compton Scattering of X Rays from Bound Electrons

Abstract: Exact and approximate methods for determining the momentum distribution of electronic systems from Compton scattering measurements are presented. The method used previously to analyze Compton scattering measurements, the impulse approximation (IA), is derived from first principles, and its accuracy is compared with the exact calculations for Compton scattering from a hydrogenic system. It is shown that the IA gives very accurate results for weakly bound electrons and that exact calculation may only be necessary to substract out the contributions to Compton scattering from deeply bound core electrons. Experimental results for Compton scattering from helium are presented as a test of the above ideas. Analyzing the results of the experiment in the IA gives a momentum distribution for the weakly bound helium electrons which is in excellent agreement with the momentum distribution obtained from Clementi Hartree-Fock wave functions.

Equatorial spread F: Implications of VHF radar observations

Abstract: VHF radar measurements of scattering by field aligned irregularities associated with equatorial spread F

Scaling, duality, and the behavior of resonances in inelastic electron-- proton scattering.

Abstract: We propose that a substantial part of the observed behavior of inelastic electron-proton scattering is due to a nondiffractive component of virtual photon-proton scattering. The behavior of resonance electroproduction is shown to be related in a striking way to that of deep inelastic electron-proton scattering. We derive relations between the elastic and inelastic form factors and the threshold behavior of the inelastic structure functions in the scaling limit.

Electron Mobility in Direct-Gap Polar Semiconductors

Abstract: The electron drift mobilities of the five direct-gap III-V semiconductors GaAs, GaSb, InP, InAs, and InSb are presented as a function of temperature. Polar-mode, deformation-potential acoustic, and piezoelectric scattering are included, as well as nonparabolic conduction bands and the corresponding electron wave functions. The drift mobility follows exactly from the assumed model by a simple iterative technique of solution which retains all the advantages of variational techniques without, however, the need for excessive mathematical detail. Piezoelectric scattering is shown to be considerable in GaAs for temperatures below 100 \ifmmode^\circ\else\textdegree\fi{}K. The agreement between theory and experiment for GaAs is satisfactory.

The Optical Array: An Alternative to Scattering or Extinction for Airborne Particle Size Determination

Abstract: An electro-optical technique is described for the measurement of the size distributions of cloud and precipitation particles. The technique utilizes a linear array of photodetectors as a size measuring grid in a typical shadowgraph-type imaging system. Several instruments have been designed and are described in various stages of testing and development. A thorough description of one such instrument and preliminary field data are given.

Structural Investigation of Noncrystalline Nickel‐Phosphorus Alloys

Abstract: The structure of noncrystalline electrodeposited Ni–P alloys, 73.8–81.4 at.% Ni, has been investigated by x‐ray scattering and by physical density measurements. The x‐ray interference functions, I(k), are qualitatively inconsistent with those calculated for fcc‐, hcp‐, and Ni3P‐type crystallites. Calculated radial distribution functions RDF(r) indicate that the alloys have a better defined short‐range order than that observed in liquid noble metals above their melting points. The observed I(k) are very similar to the I(k) calculated by Dixmier, Doi, and Guinier [in Physics of Noncrystalline Solids, J. A. Prins, Ed. (North‐Holland Publ. Co., Amsterdam, 1965), p. 67] from their model. However, the parameters needed to fit the experimental results are inconsistent with the atomic sizes expected for nickel and phosphorus. The noncrystalline alloys are between 0.6% and 1.4% less dense than the corresponding mixtures of fcc Ni and Ni3P, both of which are essentially close packed. A grain boundary density defici...

Temperature Dependence of the Transport Properties of Gallium Arsenide Determined by a Monte Carlo Method

Abstract: Transport properties of gallium arsenide in an electric field have been calculated in the temperature range 77°–500°K using a Monte Carlo technique. In intrinsic material it is found that the threshold field for the onset of negative differential mobility changes only slightly over this temperature range increasing from 3.1 kV/cm at 77°K to 3.7 kV/cm at 500°K, while the negative differential mobility reduces from 4200 to 1000 cm2/V sec over the same temperature rise. The influence of impurity scattering on the velocity field characteristic has been considered at 77°K for impurity concentrations of 1015 and 1017 cm−3 and at 300°K for concentrations for 1013, 1015, and 1017cm−3. The threshold field for the onset of negative differential mobility is found to change only slightly while the peak‐to‐valley ratio decreases significantly with increasing impurity concentration. The temperature dependence of the low‐field mobility has been calculated for impurity concentrations of 1015, 1016, and 1017 cm−3.

Désordre linéaire dans les cristaux (cas du silicium, du quartz, et des pérovskites ferroélectriques)

Abstract: Many crystals produce a diffuse scattering of X-rays which is localized in a series of relplanes. It is shown that the corresponding linear disorder in the crystal may have various origins. In silicon, the scattering is due to thermal vibrations and is well explained by the elastic properties of the crystal. In neutron irradiated quartz the radiation damage is responsible for the major part of the scattering. The case of BaTiO3 and KNbO3 is discussed in detail. A linear disorder is proposed which accounts better for the different distributions of the scattering in the 4 allotropic phases than the alternative explanation of the soft mode. In spite of some neutron inelastic scattering results it is not yet possible to distinguish between static and dynamic disorder.

Absorption and Multiple Scattering by Biological Suspensions

Abstract: We first specialize multiple-scattering theory for uncorrelated distributions of large, low-refracting, absorbing particles to similarly and randomly aligned spheroids. The theory takes into account backscattering interface effects, but neglects the smaller coherent reflection effects. Then we illustrate how the results can be used in optical diagnostics on suspensions of cells for biomedical purposes. We consider the isolation of molecular absorption coefficients for transmission and reflection oximetry on whole blood, scattering-shifted absorption extrema, cell-membrane fragilometry and the effects of osmotic swelling, and some asymmetrical scattering effects for optical monitoring of cell alignment in fluid-transport processes. In measurements on thin samples at wavelengths corresponding to relatively small absorption, pronounced minima in transmission and maxima in reflection have been observed for suspensions about half-full of cells; we discuss simple approximations that indicate the essentials of the phenomena.

Resonance Raman Effect and Resonance Fluorescence in Halogen Gases

Abstract: The various output frequencies of the argon ion laser at 5145, 5017, 4965, 4880, and 4765 A lie in the absorption bands of the heavier halogen gases. With the appropriate choice of exciting line, either resonance Raman effect or resonance fluorescence can be observed. The difference between the two types of spectra are discussed in some detail. In the case of a strong resonance Raman effect, overtone sequences up to the 14th harmonic could be observed. Raman frequencies, depolarization ratios, and relative scattering cross sections are given for the fundamentals and overtones of Cl2, Br2, I2, BrCl, ICI, and IBr at 4880 A excitation.

Electron Mobility in High‐Purity GaAs

Abstract: The combination of polar optical phonon, piezoelectric acoustic photon, deformation potential acoustic phonon, ionized impurity, and neutral impurity scattering in the relaxation time approximation is shown to give results which are in good agreement with the temperature and concentration dependence of the electron mobility in high‐purity GaAs. For polar optical phonon scattering a relaxation time is defined at each temperature from Ehrenreich's variational calculation. Since most of the parameters are well known, the only adjustable parameter in the calculation is the conduction band deformation potential with the best agreement with experiment given by | E1 | = 7.0 eV. Using this value a 77°K lattice scattering limited mobility of 240 000 cm2/V sec is obtained.

The scattering of polarized light by polydisperse systems of irregular particles

Abstract: The elements of the Mueller matrix for polydisperse systems of irregular, randomly oriented particles have been measured in absolute terms as a function of scattering angle for two wavelengths. These results have been compared to the matrix elements that were calculated for assemblies of spherical particles that fit the same particle size distribution function and have the same (real) refractive index.

Scattering by a two-dimensional periodic array of conducting plates

Abstract: The boundary value problem of an infinite array of thin plates arranged in a doubly periodic grid along any two coordinates is formulated in a general form for an arbitrarily polarized plane wave incident from any oblique angle. The induced current on the plate, the near-field distribution, and the distant reflected waves can be obtained to a very close accuracy. Both magnitudes and phases of the reflection coefficients for some specific examples are determined explicitly. For the case of a wave incident normally on a rectangular lattice array of narrow rectangular plates, the calculated values are in excellent agreement with the measurements in a previously published paper.

Limit of Cross Sections at Infinite Energy

Abstract: At infinite energy, we predict: (1) ${\ensuremath{\sigma}}_{\mathrm{tot}}$ approaches infinity; (2) the ratio of the real part to the imaginary part of the forward elastic amplitude approaches zero; (3) $\frac{{\ensuremath{\sigma}}_{\mathrm{el}}}{{\ensuremath{\sigma}}_{\mathrm{tot}}}$ approaches \textonehalf{}; (4) the width of diffraction peak approaches zero; its product with ${\ensuremath{\sigma}}_{\mathrm{tot}}$ is a constant. We give theoretical evidence based on massive quantum electrodynamics as well as experimental evidence in support of these predictions, and a physical picture for high-energy scattering.