Showing papers on "Scattering published in 1973"

Spectrum of light scattered from a viscoelastic gel

Abstract: We report measurements of the spectrum of light scattered from thermally excited displacement fluctuations in polyacrylamide gels. These measurements have been carried out on the polarized scattered light as a function of scattering angle and temperature for 5% and 2.5% polyacrylamide gels using the methods of optical mixing spectroscopy. We also present a theory for the amplitude and time dependence of the thermally excited longitudinal and transverse displacements of the gel fiber network. These displacements are responsible, respectively, for the polarized and depolarized scattered light. The correlation function for the displacements having wave vector q is predicted for these gels to have the form of an exponential decay: exp(− Γt). The decay rate is given by Γ = Glq2/f or Gtq2/f, where f is the frictional force per unit volume on the fiber network as it moves with unit velocity relative to the gel liquid. Gl is the longitudinal compressional modulus for longitudinal displacements and Gt is the shear...

Intermediate Quantum Mechanics

Abstract: Theory Of Atomic Structure * Miscellaneous Results From Elementary Quantum Mechanics * Identical Particles and Symmetry * Two-Electron Atoms * Self-Consistent Field * Statistical Models * Addition of Angular Momenta * Theory of Multiplets, Electrostatic Interaction * Theory of Multiplets, Spin-Orbit Interaction, and Interactions with External Fields * Molecules Semiclassical Radiation Theory * Semiclassical Theory of Radiation * Intensity of Radiation, Selection Rules * Photoelectric Effect Atomic Collisions * Elastic Scattering at High Energies * Elastic Scattering at Low Energies * Further Corrections to Elastic Scattering Formulas * Elastic Scattering of Spin 1/2 Particles * Inelastic Scattering at High Energies * Inelastic Scattering at Low Energies * Semiclassical Treatment of Inelastic Scattering * Classical Limit of Quantum Mechanical Scattering Summary Relativistic Equations * Klein-Gordon Equation * Dirac Equation, Formal Theory * Solutions of the Dirac Equation

Charged-Particle Scattering in the Presence of a Strong Electromagnetic Wave

Abstract: A simple and convenient approximation is obtained for the multiphoton energy-transfer processes which accompany the scattering of a charged particle by a scattering potential in the presence of a strong external electromagnetic field. It is expressed in terms of the differential elastic-scattering cross section combined with known functions, and is valid when the scattering potential is weak or when the wave frequency is small. A detailed form of the classical limit is obtained.

Semiconductor Physics: An Introduction

Abstract: 1. Elementary Properties of Semiconductors.- 2. Energy Band Structure.- 3. Semiconductor Statistics.- 4. Charge and Energy Transport in a Nondegenerate Electron Gas.- 5. Carrier Diffusion Processes.- 6. Scattering Processes in a Spherical One-Valley Model.- 7. Charge Transport and Scattering Processes in the Many-Valley Model.- 8. Carrier Transport in the Warped-Sphere Model.- 9. Quantum Effects in Transport Phenomena.- 10. Impact Ionization and Avalanche Breakdown.- 11. Optical Absorption and Reflection.- 12. Photoconductivity.- 13. Light Generation by Semiconductors.- 14. Surface and Interface Properties and the Quantum Hall Effect.- 15. Miscellaneous Semiconductors.- Appendices.- A. Table A: Physical Constants.- B. Envelope wave function for Quantum Wells.- C. Table C: Semiconductor and Semimetal Data.- References.- About the Author.

Semiphenomenological optical model for electron scattering on atoms

Abstract: It is shown that it is possible to derive from first principles a form for a local, central, complex potential that fits elastic electron scattering on hydrogen at various energies with two free parameters. The energy-dependence of the parameters is discussed. Understanding of the optical model based on hydrogen enables the authors to use published Hartree-Fock calculations to construct a potential that gives excellent fits to argon at several energies with no free parameters. In all cases, the total reaction cross section, obtained from independent experimental information, is used to determine the strength of the imaginary part of the potential.

Structure Factor and Radial Distribution Function for Liquid Argon at 85 °K

Abstract: The structure factor $S(Q)$ for liquid argon at 85 \ifmmode^\circ\else\textdegree\fi{}K has been determined in a neutron scattering experiment to an accuracy of \ensuremath{\sim}0.01. The problem of obtaining $S(Q)$ from the results of neutron scattering measurements, made as a function of scattering angle using a detector with an energy-dependent efficiency, is considered in detail. Smooth curves for $S(Q)$ and its Fourier transform, the radial distribution function $g(r)$, were obtained from the experimental data by an iterative procedure suggested by Verlet and carried out by Schiff, and are tabulated for convenience. The experimental results are in excellent agreement with the predictions of computer simulations based on either the Lennard-Jones two-body interaction, or on the Barker, Fisher, and Watts potential with corrections for three-body and quantum effects included.

Self-consistent molecular Hartree—Fock—Slater calculations II. The effect of exchange scaling in some small molecules

Abstract: The effect of varying the scaling parameter a in the Xα exchange expression has been studied in a number of SCF LCAO MO Hartree—Fock—Slater calculations on the diatamic molecules CO, NO, N2, O2, LiF and the hydro- carbon C2H4. The calculated ionization potentials and charge distribution of these molecules are in excellent agree- ment with experiment for α = 0.70. From a comparison with results of the multiple scattering technique (MSXα), it appears that removing the muffin-tin approximations considerably improves the results of Hartree—Fock—Slater calculations.

Elastic and Inelastic Cross Sections for Electron-Hg Scattering from Hg Transport Data

Abstract: Elastic- and inelastic-scattering cross sections for low-energy electrons in Hg have been obtained through comparison of experimental and calculated transport data. Electron-electron interactions and superelastic collisions are incorporated into the numerical solution for the electron-energy distribution. The electron-electron interactions are shown to have a pronounced effect upon computed drift velocity and characteristic energies at low $\frac{E}{N}$, while superelastic collisions principally alter the cascade ionization rate. Details of the present method for solving the dc Boltzmann equation, including the above process, are discussed.

Radiation Pressure on a Free Liquid Surface

Abstract: The force of radiation pressure on the free surface of a transparent liquid dielectric has been observed using focused pulsed laser light. It is shown that light on either entering or leaving the liquid exerts a net outward force at the liquid surface. This force causes strong surface lens effects, surface scattering, and nonlinear absorption. The data relate to the understanding of the momentum of light in dielectrics.

The theory of diffuse X-ray scattering and its application to the study of point defects and their clusters

Abstract: The theory of the diffuse scattering by point defects and by defect clusters is reviewed. For a small concentration of statistically distributed point defects the symmetry of the long ranging part of the displacement field and the strength of the defects can be obtained from scattering measurements close to the reciprocal lattice points (Huang scattering). In addition to the (symmetrical) Huang scattering an asymmetry of the scattering is observed. For defects with sufficiently large displacements, the sign of this asymmetric scattering determines the sign of the displacement field around the defect and its magnitude yields information about the magnitude of the displacements close to the defect. For defect clusters the diffuse scattering is strongly modified. The Huang scattering very near to the Bragg reflection increases in direct proportion to the number of point defects in the cluster. For larger distances q from the Bragg reflection the intensity decreases as 1/q4.

Investigation of non-ideal two-phase polymer structures by small-angle X-ray scattering

Abstract: The mean square of the electron-density gradient, 〈|grad η|2〉 in isotropic structures is shown to be proportional to the fourth moment of the SAXS intensity distribution in reciprocal space ∫s4I(s)ds, as well as to the second derivative of the correlation function in the origin. In the case of two-phase structures with unsharp phase boundaries, these relations may be used to find the thickness E of the transition regions. As was shown by Ruland [J. Appl. Cryst. (1971). 4, 70–73] E can also be determined by analysis of the intensity in the tail of the SAXS pattern. This approach is used here to investigate the effect of E on the one-dimensional correlation function. In the application of both methods, separation of the SAXS intensity from the continuous background of liquid scattering constitutes a critical step. A procedure in which the background is represented by a curve of the type a + bsn, where n is an even number, is found to work well for a number of polymers.

On the possibility of measuring gas concentrations by stimulated anti‐Stokes scattering

Abstract: A novel and very sensitive method for gas concentration measurements is proposed. Intense light scattering is obtained through a stimulated interaction. The method appears more practical than spontaneous Raman scattering for gas flow analysis with fine spatial resolution. Experimental results with the detection of H2 are given.

Rayleigh scattering

Abstract: By using a computer program, the authors intend to compute quantities specifying the low frequency scattering behavior of rotationally symmetric bodies which are metallic (electromagnetic scattering), soft, or hard (acoustic scattering)

Charge-Carrier Transport Phenomena in Amorphous Si O 2 : Direct Measurement of the Drift Mobility and Lifetime

Abstract: A report of the first direct measurement of the drift velocity of excess electrons is given as a function of applied field in amorphous Si${\mathrm{O}}_{2}$ using a transit-time technique. The drift mobility is found to be 20 \ifmmode\pm\else\textpm\fi{} 3 ${\mathrm{cm}}^{2}$/V sec at 300 K, the highest known for a solid amorphous material, and it decreases with increasing temperature. These results can be explained by a model involving LO phonon scattering at high temperatures and boundary scattering at lower temperatures.

The Rayleigh hypothesis and a related least‐squares solution to scattering problems for periodic surfaces and other scatterers

Abstract: The Rayleigh hypothesis is reviewed in relation to scattering by periodic surfaces, aperiodic surfaces, and bounded, two-dimensional bodies. Conditions for its validity are described, and explicit results are quoted for a sinusoidal grating. Some methods to solve scattering problems for periodic surfaces are outlined. One particular procedure for periodic surfaces and bounded scatterers is examined in detail. This involves an expansion for the scattered field in terms of the same sets of elementary wavefunctions that occur in connection with the Rayleigh hypothesis. The coefficients are determined by satisfying the boundary condition in the least-squares sense. It is shown that this solution converges uniformly to the scattered field at all points exterior to the boundary of the scatterer. Necessary completeness properties of the sets of wavefunctions are established in the appendices.

Scattering of P waves under the Montana Lasa

Abstract: The variations of amplitude and time delay of teleseismic P waves across the Montana Lasa (Large Aperture Seismic Array) were interpreted as being due to scattering by a random inhomogeneity in the earth's crust under the array The prediction of the Chernov [1960] theory explains well the observed statistical properties of P waves with a frequency of 05 Hz The inhomogeneity under Lasa has a correlation distance of about 10 km, with a fractional rms velocity fluctuation of 4% extending to a depth of about 60 km The turbidity coefficient under Lasa at 05 Hz is 0008 km−1, which is much greater than the values (10−3 to 10−4 km−1 at 5 to 10 Hz) observed for refracted waves in the crust and upper mantle in the USSR by Nikolayev and his colleagues The scattering under Lasa is so strong that the condition for the Born approximation is violated for frequencies higher than 05 Hz Accordingly, the observed statistical properties of 1-Hz waves show systematic departure from the prediction of the Chernov theory

Time dependent approach to scattering from impurities in a crystal

Abstract: A time dependent scattering theory for a quantum mechanical particle moving in an infinite, three dimensional crystal with impurity is given. It is shown that the Hamiltonian for the particle in the crystal without impurity has only absolutely continuous spectrum. The domain of the resulting wave operators is therefore the entire Hilbert space.

Intermolecular Potentials from Crossed Beam Differential Elastic Scattering Measurements. III. He+He and Ne+Ne

Abstract: High‐resolution differential cross sections for elastic scattering extending to wide scattering angles for He–He and Ne–Ne have been measured at two collision energies in the thermal range. The experiments were carried out by crossing two supersonic nozzle atom beams at right angles and detecting the atoms scattered in the plane of the beams with a rotatable electron‐bombardment mass‐filter universal detector. The results are analyzed to yield information on the interatomic potentials for these systems using a realistic and flexible potential function, and comparison is made with previously proposed potentials. For He2, a somewhat ``harder'' low‐energy repulsion than that of most such potentials is inferred, while for Ne2 the potential well depth found is ∼ 30 % larger than earlier estimates and in good agreement with a preliminary spectroscopic finding.

Amorphous germanium II. Structural properties

Abstract: The coherent X-ray scattering for momentum transfer, k, between 0·025 and 15·0 A−1 has been measured for a series of sputtered amorphous Ge films prepared at various substrate temperatures, T s, between 0 and 350°C. Differences in the radial distribution function (RDF) of films of different T s have been determined by an accurate differential scattering technique. The small angle scattering (SAS) of the films is less than 100 electron units for k < 1 A−1. From a combination of SAS, RDF and scanning electron microscope studies, it is concluded that an observed increase in film density with increasing T s occurs through a reduction in the number of voids about 7 A or less in diameter. No variation of bond length with T s is found. With increasing T s, there is an increase in first and second-neighbour coordination and a reduction in bond angle distortion. The rate of change of coordination, C, with density, ρ0, is found to be d ln C/d ln ρ0 = 0·6±0·2. Using a new, general theory of the dependence o...

Impurity and Lattice Scattering Parameters as Determined from Hall and Mobility Analysis in n-Type Silicon

Abstract: The carrier concentration and mobility, as determined from the Hall effect, have been analyzed using a computer for a series of $n$-type silicon samples doped with Sb, P, and As. Mobility calculations, performed numerically, were based on the general treatment given by Herring and Vogt. Ionized-impurity scattering was calculated from two theories and compared with experiment. Lattice-scattering parameters for intervalley and accoustic modes were determined from a comparison of the results between theory and experiment, using as many as four intervalley phonons. The conclusions support the earlier work of Long, and a partial explanation of the disagreement with parameters determined from other measurements is suggested. Scattering by neutral impurities is found to be temperature dependent, unlike the theoretical model of Erginsoy.