Showing papers on "Scattering published in 1977"

A new method for the evaluation of small-angle scattering data

Abstract: A new numerical method is presented for simultaneous smoothing, desmearing and Fourier transformation of X-ray and neutron small-angle scattering data. The method can only be applied to scattering curves from dilute particle systems, i.e. for scattering media whose distance distributions are zero beyond a certain value. The distance distribution of the scattering medium is approximated by a linear combination of about 20 to 30 cubic B-splines. These spline functions have a restricted extension in real space. Their coefficients are adjusted by a weighted least-squares operation so that the series, after being Fourier transformed and smeared according to the geometry and wavelength distribution, represents an optimum smoothed approximation of the experimental data. Tendencies towards oscillations in the least-squares operation are suppressed by a new stabilization routine. The method offers a new possibility for the estimation of the radius of gyration, which is generally superior to the Guinier approximation.

Inverse Problems in Quantum Scattering Theory

Abstract: The physical importance of inverse problems in quantum scattering theory is clear since all the information we can obtain on nuclear, particle, and subparticle physics is gathered from scattering experiments Exact and approximate methods of investigating scattering theory, inverse radial problems at fixed energy, inverse one-dimensional problems, inverse three-dimensional problems, and construction of the scattering amplitude from the cross section are presented The methods often apply to other fields, eg applied mathematics and geophysics The book will therefore be of interest to theoretical and mathematical physicists, nuclear particle physicists, and chemical physicists For the second edition the chapters on one-dimensional and three-dimensional scattering problems have been rewritten and considerably expanded Furthermore, two new chapters on spectral problems and on numerical aspects have been added; in the sections on classical methods the comments and references have been updated

Energy propagation including scattering effects sengle isotropic scattering approximation

Abstract: The elastic energy propagation in a three dimensional infinite elastic medium, in which scatterers are distributed homogeneously and randomly, is investigated by a statistical method. A single isotropic scattering process is investigated. The elastic medium is characterized by the wave velocity V and the distribution of the scatterers is characterized by the mean free path l. It is assumed that the elastic energy is radiated spherically from the source at a time t=0 in a short time duration. A space-time distribution of the mean energy density of the scattered waves is obtained as Es(r, t)=(W0/4πlVtr)1n((Vt+r)/(Vt-r)) for Vt≥r, where r is the distance from the source and W0 is the total energy radiated. A uniform spatial distribution is constructed far behind the wave front and near the source. The mean energy density Es is proportional to t-2 for t_??_2r/V and independent of r and W0. Several important properties of coda waves observed near the hypocenter are explained qualitatively by this solution when heterogeneities in the earth are interpreted as the scatterers and Es corresponds to the power spectrum of coda waves.

Light scattering by small particles in an absorbing medium.

Abstract: Extinction for the scattering by small particles embedded in an absorbing medium is defined and a generalized form of an optical theorem is derived. In general, the extinction is related to both the forward and the backward scattering amplitude.

A new theoretical and practical approach to the multislice method

Abstract: The multislice formulation of Cowley and Moodie for high-energy electron scattering is rederived from the Schrodinger equation, and the validity of the finite slice approach in practical computation is theoretically proved by the stationary-phase approximation. A set of computer programs for the multislice method is developed, where the convolution integral is carried out through the fast Fourier transform. The following conditions are required to obtain a sufficiently accurate result in multislice calculations: (1) the maximum slice thickness should be about kd2, where k is the wavenumber of the incident electrons and d is the distance over which the potential does not change appreciably; (2) there must be a sufficient number of beams in the multislice iteration to prevent the aliasing effect of convolution. The multiple scattering masks the real specimen structure when the specimen thickness exceeds a certain value. This effect of multiple scattering is recognized from the probability distribution of the scattered electrons in addition to the scattering amplitudes obtained through the procedure developed in the present work.

Interstellar Scattering and Scintillation of Radio Waves

Abstract: A review is presented of interstellar scattering and scintillation observations in the light of modern theory for extended, spatially homogeneous, power law inhomogenieties. Formulas are presented for the experimentally observable quantities and are compared with data. A general discussion of the model is given. (GHT)

Effects of laser-modulated particulate incandescence on Raman scattering diagnostics

Abstract: Laser‐modulated particulate (soot) incandescence has been studied by measuring the laser‐driven particle surface temperature in a propane diffusion flame as a function of laser focal flux. The experimental results display fair agreement with an analytical model of the process. Quite importantly, the absolute incandescence level displays a saturation behavior with increasing laser pulse energy. For laser Raman scattering diagnostics, this behavior means that the S/N ratio will increase with increasing laser flux level. Thus, for highest S/N ratio, it is preferable to operate at the highest possible flux short of gas breakdown and/or optical‐component damage levels.

The dopant density and temperature dependence of electron mobility and resistivity in n-type silicon

Abstract: Traditional analysis of electron mobility in n -type silicon neglects the effect of electron-electron scattering in the mobility calculations. As a result, theory fails to conform with experiment when dopant density exceeds 2 × 10 16 cm −3 . In this work, an improved theoretical model for computing mobility and resistivity as functions of dopant density and temperature has been developed for n -type silicon. The model has been applied to phosphorus-doped silicon for dopant densities from 10 13 to 10 19 cm −3 , and temperatures between 100 and 500 K. The mobility was calculated analytically by appropriately combining lattice, ionized impurity and neutral impurity scattering contributions. The effect of electron-electron scattering was incorporated empirically for dopant densities greater than 2 × 10 16 cm −3 . Additionally, the anisotropic scattering effect was included in the mobility formulations. Resistivity measurements on seven phosphorus-doped silicon wafers with dopant densities from 1.2 × 10 14 to 2.5 × 10 18 cm −3 were carried out for temperatures from 100 to 500 K. Electron mobility at 300 K was deduced from resistivity and junction C-V measurements for dopant densities from 10 14 to 10 18 cm −3 . Agreement between theoretical calculations and experimental data for both electron mobility and resistivity of phosphorus-doped silicon was within ±7% in the range of dopant densities and temperatures studied.

The evaluation of the small-angle scattering of anisotropic lamellar two-phase systems by means of interface distribution functions

Abstract: The application of the concept of interface distribution functions for the evaluation of the small-angle scattering of lamellar two-phase systems has been extended to structures with preferred orientation. For measurements with pin-hole collimation, the evaluation is analogous to that for random orientation. It produces direction dependent interface distribution functions from which the preferred orientation and possible correlations between orientation and structure can be determined. For measurements with slit collimation approximations are given for the direct determination of interface distribution functions from the slit-smeared intensity distributions. The evaluation of Porod's law in the slit-smeared anisotropic intensity distributions and possible errors due to the tangent plane approximation in the case of high preferred orientation are discussed.

Formal aspects of the theory of the scattering of ultrasound by flaws in elastic materials

Abstract: An integral equation is used to derive formal expressions for the scattering of a plane wave from a single homogeneous flaw embedded in an isotropic elastic medium. Expressions are found for the scattered amplitudes and differential cross sections. An optical theorem is also derived.

The Born approximation in the theory of the scattering of elastic waves by flaws

Abstract: We used the integral equation formulation of the scattering of elastic waves to generate an approximate solution analogous to the Born approximation in quantum mechanics. This solution is attractive because of the ease with which it may be applied to scatterers of complicated shapes. We investigated the validity of the approximation by comparing it with exact results for spherical scatterers. Our conclusion for voids in elastic media is that the approximation describes well the scattering when the wavelength of the incident wave is approximately an order of magnitude larger than the scatterer and when the scattering is viewed in the backscattered directions. For many applications this range of validity is experimentally accessible. For elastic inclusions, however, where the properties of defect and host differed by 20–40%, the Born approximation is surprisingly good for all angles and even at short wavelengths.

Multiple scattering in reflection nebulae. I - A Monte Carlo approach. II - Uniform plane-parallel nebulae with foreground stars. III - Nebulae with embedded illuminating stars

Abstract: A method for calculating the surface brightness distribution on a plane-parallel reflection nebula of uniform density illuminated by a star located either in front of, behind, or arbitrarily inside the scattering medium is proposed. The Monte Carlo technique is used to find solutions to the radiative transfer problem. The scattering properties of the nebular particles are parameterized by the albedo for single scattering and a three-parameter analytic phase function. Calculations are then presented for the surface brightness distribution across the face of such nebulae with (1) a foreground star and (2) immersed stars. The calculations include the full effects of multiple scattering, are independent of a particular assumed grain material or size distribution, and are applicable to any wavelength region for which observations can be obtained.

On the factorization and fitting of molecular scattering information

Abstract: The reported analysis is based on the factored IOS T-matrix. It is shown that line shape measurements may be used over a range of temperatures to evaluate inelastic scattering cross sections. Basic factorization or parameterization relations are derived by considering the wavefunction equations. The parameterization of cross sections is considered, taking into account the differential scattering amplitude and cross section, integral cross sections, phenomenological cross sections for general relaxation processes, and viscosity and diffusion cross sections. Thermal averages and rates are discussed, giving attention to integral cross sections and rates, and general phenomenological cross sections. The results of computational studies are also presented.

Screening Effect and Quantum Transport in a Silicon Inversion Layer in Strong Magnetic Fields

Abstract: The broadening of Landau levels and the transport quantities, such as the transverse and Hall conductivity and cyclotron resonance linewidth, are calculated in an inversion layer on the (100) surface of p -type Si at zero temperature. Main scattering mechanisms are assumed to be charged impurity scattering and surface roughness scattering. A new expression for the surface roughness scattering is obtained. The self-consistent Born approximation is employed for the effect of scattering, and the random phase approximation for the screening. Because of the singular density of states the screening depends on the position of the Fermi level and becomes weak when it lies at the tail region of each Landau level. Scattering potentials become strong and of slowly varying type in this case. Except such a special case, overall features agree with the results obtained for short-ranged scatterers.

Reconciliation of the Conwell-Weisskopf and Brooks-Herring formulae for charged-impurity scattering in semiconductors: Third-body interference

Abstract: The divergence at small scattering angles for unscreened charged-impurity scattering may be removed by including the probability that a closer scattering centre does not exist. This introduces an exponential function like the screening factor, which allows a straightforward bridging to be made between non-screening and screening situations. An expression for the mobility which encompasses the Conwell-Weisskopf and Brooks-Herring results is derived.

Direct Observation of Multiphoton Processes in Laser-Induced Free-Free Transitions

Abstract: Multiphoton processes are detected in the scattering of electrons on argon atoms in the presence of a strong CO/sub 2/-laser field. The observations are in accordance with a recently developed semiclassical model.

Independent electron approximation for atomic scattering by heavy particles

Abstract: Scattering from a multielectron target by a heavy particle is approximated in terms of amplitudes for scattering from individual target electrons. By treating the motion of the projectile classically and ignoring correlations, the wave function for the system is expressed as a product of single-electron wave functions. The probability amplitude for scattering into specific states is then a product of single-electron scattering amplitudes. In this approximation, cross sections for excitation and ionization involving many electrons are expressed in terms of a binomial distribution of single-electron probabilities. The standard connection of this amplitude for multiple excitation and ionization, ${A}^{\mathrm{if}}(B)$, to the corresponding scattering amplitude, $f(\ensuremath{\theta})$, is given, and the validity of this approximation is discussed.

Dynamics of solids and liquids by neutron scattering

Abstract: 1 Introduction- 11 Prologue- 12 Correlation Functions- 13 Nuclear Scattering- 131 Scattering by Phonons- 132 Phonon Interactions- 133 Electron-Phonon Interactions- 134 Monoatomic Liquids- 135 Molecular Gases- 14 Polarization Effects- 15 Magnetic Scattering- 151 Ferromagnetic Spin Waves- 152 Antiferromagnetic Spin Waves- 153 Paramagnetic Scattering- Appendix A: Crystal Lattices and Reciprocal Lattices- References- 2 Phonons- 21 Lattice Dynamics and Neutron Scattering- 211 General Model- 212 Rigid-Ion and Shell Models- 213 Experimental- 22 Lattice Dynamics of Crystals of the Rutile Type - TiO2, MgF2, and MnF2- 221 TiO2- 222 MgF2- 223 MnF2- 224 Conclusions- 23 Phonon Anomalies in Superconducting Materials- 231 Transition Metal Carbides- 232 A-15 Compounds- 233 Niobium-Alloys, Other Compounds, and Impurities- 234 Other Superconductors - Tc, Mo-Re, Hg- 235 Conclusions- 24 Layered Compounds- 241 MoS2- 242 NbSe2- 243 Graphite- 244 PbI2- 245 Concluding Remarks- 25 Effects of Pressure on Phonon Spectra- 251 Experimental Aspects- 252 Phonon Shifts and Widths in Neon- 253 Selected Phonons in Rubidium as a Function of Temperature and Volume- 254 Conclusions- References- 3 Phonons and Structural Phase Transformations- 31 Relation Between Neutron and X-Ray Scattering Techniques- 311 Elastic and Inelastic Scattering- 312 Experimental Technique- Inelastic Neutron Scattering- X-Ray Scattering- 313 Correlations and Dimensionality in Real and Reciprocal Space- 32 Fluctuations and Order- 321 Soft Modes- 322 Critical Slowing Down- 323 Eigenvector and Order Parameter- 33 Experimental Results- 331 Ferrodistortive Transformations- 332 Antiferrodistortive Transformations- 333 Modulated Lattices and Low Dimensional Systems- References- 4 Dynamics of Molecular Crystals, Polymers, and Adsorbed Species- 41 Molecular Crystals- 411 Models for the Lattice Dynamics in Molecular Crystals- 412 The Lattice Dynamics of ?-Paradichlorobenzene- 413 The Dynamics of Hexamethylenetetramine- 414 Incoherent Neutron Scattering, Phonon Density of States, and Intramolecular Vibrations- 415 Molecular Torsional Motions and Tunneling Spectroscopy- 416 Phonon Density of States Measurements by Optical Spectroscopy- 42 Polymers- 421 Polyethylene - the Isolated Chain and Incoherent Scattering Studies- 422 Polyoxymethylene- 423 Biopolymers- 43 Structure and Dynamics of Adsorbed Species- 431 Substrates- 432 Physisorption- 433 Incoherent Scattering- 44 Chemisorption- 441 Hydrocarbons Adsorbed on Zeolites- 442 Hydrogen Adsorbed on Metals- 45 Intercalation Compounds- 451 Tantalum Disulphide-Ammonia- 452 Translational Diffusion in Alumino-Silicate Minerals- 46 Conclusions- References- 5 Molecular Rotations, and Diffusion in Solids, in Particular Hydrogen in Metals- 51 Diffusion in Solids, in Particular Hydrogen in Metals- 511 General Aspects- 512 Experiments on Hydrogen in Pd, a fcc-Lattice- 513 Hydrogen in the bcc Metals Ta, Nb, and V- 514 The Temperature- and Q-Dependence of the Quasielastic Intensity- 515 Conclusions on H-Metal Systems Other Problems of Diffusion in Solids- 52 Rotations in Molecular Solids- 521 Rotations and Hindrance Potential Scattering Law- 522 High Temperatures: Rotational Jumps and Rotational Diffusion- 523 Fixed-Window-Method- 524 Low Temperature Experiments Quantum Rotations- 53 Liquids, Liquid Crystals, and Related Problems- 531 The Scattering Law for Molecular Liquids- 532 Liquid Crystals, Polymers- References- 6 Collective Modes in Classical Monoatomic Liquids- 61 Collective Modes- 611 Collective Variables- 612 Generalized Hydrodynamics- 62 Coherent Scattering- 621 Insulating Liquids- 622 Liquid Metals- 623 Comparison of Systems Studied- 63 Transverse Current Correlations- 64 Relations Between S(Q,?) and Ss(Q,?)- 65 Current Issues- References- 7 Magnetic Scattering- 71 Magnons in Ionic Compounds- 72 Quasi One- and Two-Dimensional Systems- 721 Magnetic Linear-Chain Systems- 722 Layered Magnetic Systems- 73 Magnons in Metals- 74 Crystal Field Levels in Rare Earth Compounds- 75 Magnons and Excitons in Rare Earth Metals- 76 Critical Magnetic Scattering- 77 Hyperfine Field Measurements- References

Interstellar grains The interaction of light with a small-particle system

Abstract: Interstellar dust is suggested to be one of the most thoroughly studied of all small-particle systems, whose characteristics have in some ways not been duplicated in our laboratories. The particles are maintained in complete isolation from one another, in ultra-high vacuum and at low temperature, and have been studied spectroscopically from far infra-red to far ultra-violet. Optical properties of the interstellar dust which are surveyed include effects interpreted as due to surface plasmon bands in the ultra-violet, surface phonon bands and other vibrational absorption bands in the infra-red, linear and circular polarization caused by aligned particles, impurity absorption, and defect absorption possibly caused by radiation damage. A discussion of the possible origins for interstellar grains leads to speculation on their relationship to certain meteorites. Absorption and scattering effects from small particles in general are surveyed by way of Mie calculations for a representative insulator, MgO,...

Scattering of a Dirac particle with charge Ze by a fixed magnetic monopole

Abstract: The helicity-flip and helicity-nonflip scattering amplitudes of a Dirac particle with spin 1/2 and charge $Ze$ by a fixed magnetic monopole field are calculated. To make the Hamiltonian meaningful an infinitesimal extra magnetic moment is added to the charged particle. The sign of this extra term has measurable consequences. The differential cross section, which is independent of the sign of $Ze$, is tabulated. The helicity-flip amplitude vanishes at all angles for incoming beam helicity = +1 if $Zegg0$, and for incoming beam helicity = -1 if $Zegl0$.