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Scattering, elastic

Since the wavelength (energy) of the incident beam can be varied (e.g., when using a synchrotron as the photon source) the scattering vector rather than the angle is often used as the variable  [Pg.458]

Here X is the wavelength of the incident beam, 6 is half of the scattering angle, and e is the unit vector characterizing the direction of the vector q. The latter is defined by the difference of the wave vectors of the incident and the scattered beam, k k = 2nlX) and kf, respectively, since we are dealing with elastic scattering fc = fc.  [Pg.458]

To change the resolution in q, or to extend the q-range, the wavelength of the incident beam or the sample-detector distance can be adjusted. The colUmation of the incident beam can have either point or slit geometry. In the case of sUt geometry, the measured scattered intensity represents the convolution of the scattering pattern of the sample for point collimation with the slit profile [23]. [Pg.458]

In the SAS regime, the angular characteristic of the individual scatterer can be disregarded and an angle independent amplitude A, can be attributed to each wave emitted. The scattered intensity is given by the square of the sum of overall waves emitted from the sample volume irradiated (21.2) as a consequence, the phase shift information between the individual waves is lost and only the autocorrelation function of the system under investigation (in case of a two-phase media, e.g., solid and voids) can be extracted from the experimental data. As the phase information is missing, the autocorrelation function cannot be unequivocally related to a three-dimensional backbone stractore. [Pg.458]

Here dE/dQcoh is the coherent differential cross-section per sample volume irradiated, Vj, Psld( ) represents the autocorrelation function of the so-called scattering length density, and r is the difference between pairs of position vectors For isotropic systems, the vector in (21.2) can be simplified  [Pg.459]

Burcham Nuclear Reactions, Levels, and Spectra of Light Nuclei. Sect. 16. [Pg.36]

The differential cross section for elastic scattering of a charged particle by a nucleus is given in terms of the asymptotic phase shifts di of the partial wave of angular momentum 1% by the formula (Schiff ) [Pg.36]

The phase shift di represents the refraction of the incident partial wave of angular momentum I by the non-CouLOMB field if all di are zero (l6.1) reduces to the Rutherford scattering formula. If the non-CouLOMB field is due to a nucleus of radius R, and if X R, then the phase shifts are important up to an Z-value given by [Pg.36]

The quantities Fi,Gi,F, j.es defined in Sect. 9- The separation into hard sphere scattering (phase shift (pi) and nuclear resonant scattering (phase shift i) is a mathematically convenient way of distinguishing between potential scattering [Pg.36]

Schiff Quantum Mechanics, p. 120. New York McGraw Hill 1949  [Pg.36]


Bragg scattering Coherent elastic scattering of monochromatic neutrons by a set of crystal planes. [Pg.66]

If a beam of monoenergetic ions of mass A/, is elastically scattered at an angle 6 by surface atoms of mass Mg, conservation of momentum and energy requires that... [Pg.308]

Buck U 1974 Inversion of molecular scattering data Rev. Mod. Phys. 46 369 Buck U 1975 Elastic scattering Adv. Chem. Phys. 30 313... [Pg.215]

Electrons interact with solid surfaces by elastic and inelastic scattering, and these interactions are employed in electron spectroscopy. For example, electrons that elastically scatter will diffract from a single-crystal lattice. The diffraction pattern can be used as a means of stnictural detenuination, as in FEED. Electrons scatter inelastically by inducing electronic and vibrational excitations in the surface region. These losses fonu the basis of electron energy loss spectroscopy (EELS). An incident electron can also knock out an iimer-shell, or core, electron from an atom in the solid that will, in turn, initiate an Auger process. Electrons can also be used to induce stimulated desorption, as described in section Al.7.5.6. [Pg.305]

Radiation probes such as neutrons, x-rays and visible light are used to see the structure of physical systems tlirough elastic scattering experunents. Inelastic scattering experiments measure both the structural and dynamical correlations that exist in a physical system. For a system which is in thennodynamic equilibrium, the molecular dynamics create spatio-temporal correlations which are the manifestation of themial fluctuations around the equilibrium state. For a condensed phase system, dynamical correlations are intimately linked to its structure. For systems in equilibrium, linear response tiieory is an appropriate framework to use to inquire on the spatio-temporal correlations resulting from thennodynamic fluctuations. Appropriate response and correlation functions emerge naturally in this framework, and the role of theory is to understand these correlation fiinctions from first principles. This is the subject of section A3.3.2. [Pg.716]

The time-dependent structure factor S k,t), which is proportional to the intensity I k,t) measured in an elastic scattering experiment, is a measure of the strength of the spatial correlations in the ordering system with wavenumber k at time t. It exliibits a peak whose position is inversely proportional to the average domain size. As the system phase separates (orders) the peak moves towards increasingly smaller wavenumbers (see figure A3.3.3. [Pg.733]

Approximate methods may be employed in solving tiiis set of equations for tlie (r) however, the asymptotic fonn of the solutions are obvious. For the case of elastic scattering... [Pg.1315]

To see how this works, consider elastic scattering in a situation where the electron-target interaction can be... [Pg.1320]

The ratio of elastically to inelastically scattered electrons and, thus, their importance for imaging or analytical work, can be calculated from basic physical principles consider the differential elastic scattering cross section... [Pg.1626]

In SEM and STEM, all detectors record the electron current signal of tire selected interacting electrons (elastic scattering, secondary electrons) in real time. Such detectors can be designed as simple metal-plate detectors, such as the elastic dark-field detector in STEM, or as electron-sensitive PMT. For a rigorous discussion of SEM detectors see [3],... [Pg.1633]

In the simplest case of bright-field imaging, the CTF can easily be deduced the elastically scattered electron... [Pg.1637]

Egerton R F 1976 Measurement of inelastic/elastic scattering ratio for fast electrons and its use in the study of radiation damage Phys. Status Solid a 37 663-8... [Pg.1650]

Figure Bl.24.4. Energy loss components for a projectile that scatters from depth t. The particle loses energy A E- via inelastic collisions with electrons along the inward path. There is energy loss A E in the elastic scattering process at depth t. There is energy lost to melastic collisions A along the outward path. For an incident energy Eq the energy of tlie exiting particle is = q - A iv - AE - A E. ... Figure Bl.24.4. Energy loss components for a projectile that scatters from depth t. The particle loses energy A E- via inelastic collisions with electrons along the inward path. There is energy loss A E in the elastic scattering process at depth t. There is energy lost to melastic collisions A along the outward path. For an incident energy Eq the energy of tlie exiting particle is = q - A iv - AE - A E. ...
Elastic scattering involves no pemianent changes in the internal structures (states a and P) of A and B. Both the energy rel and angular momentum L (AB) of relative motion are tiierefore all conserved. [Pg.2006]

The rate coefficient for elastic scattering between two species with non-isothennal Maxwellian distributions is then... [Pg.2009]

V..(R) is the static interaction for elastic scattering. The Bom scattering amplitude is a pure fiinction only of... [Pg.2020]

Since this agrees with the first Bom differential cross section for (in)elastic scattering, Femii s Rule 2 is therefore valid to first order in the interaction F. [Pg.2021]


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Acoustic scattering, elastic

Coherent Elastic Nuclear Resonant Scattering

Coherent elastic scattering

Coherently elastic neutron scattering

Cross section of elastic scattering

Diatomic molecules elastic scattering

Differential cross sections elastic scattering

Direct elastic scattering

Doppler shift, quasi-elastic laser scattering

Elastic (Diffractive) Scattering

Elastic Rutherford scattering

Elastic Scattering (Diffraction)

Elastic Scattering of Electromagnetic Radiation by Single Electron

Elastic and inelastic neutron scattering

Elastic and inelastic scattering of two molecules

Elastic electron scattering

Elastic electron-proton scattering

Elastic interband scattering

Elastic intraband scattering

Elastic light-scattering detection

Elastic light-scattering detection methods

Elastic molecular light scattering

Elastic molecular light scattering information from

Elastic neutron scattering

Elastic or Rayleigh scattering

Elastic peak scattering

Elastic positron scattering

Elastic scatter

Elastic scattering Subject

Elastic scattering amplitudes

Elastic scattering approximate methods

Elastic scattering potential, with

Elastic scattering, angular distribution

Elastic scattering, molecule surface

Elastic single scattered intensity

Elastic small-angle neutron scattering

Elastic, Inelastic, and Reactive Scattering

Electron Elastic-Scattering Cross-Section

Electron Elastic-Scattering Cross-Section Database (SRD

Excitation-transfer systems elastic scattering

Forward recoil elastic scattering

Incoherent quasi-elastic neutron scattering

Incoherent quasi-elastic neutron scattering IQENS)

Light scattering elastic

Light scattering elastic constants

Light-scattering detectors elastic

Micelles quasi-elastic light scattering

Multiple elastic scattering, effect

Near-Field Microscopy by Elastic Scattering from a Tip

Neutron elastic scattering from actinides and anomalous lanthanides

Neutron scattering elastic incoherent structure factor

Neutrons, capture reaction elastic scattering

Non-elastic scatter

Nuclear elastic scattering

Nuclear resonant elastic scattering

Nuclear resonant inelastic and quasi-elastic scattering

Nucleus elastic scattering

Polar systems, elastic scattering

Polymer Dynamics-Quasi-Elastic Scattering

Proteins Quasi-elastic light scattering

QELS = quasi-elastic scattering

Quantum Elastic Scattering on Fixed Target

Quasi elastic neutron scattering experiments

Quasi-Elastic Light Scattering (QELS) Method

Quasi-Elastic Neutron Scattering Studies of H2 Exchange with cis Hydrides

Quasi-elastic Laser Scattering (QELS)

Quasi-elastic electron scattering

Quasi-elastic laser scattering

Quasi-elastic light scattering

Quasi-elastic light scattering , Photon correlation

Quasi-elastic light scattering , interface

Quasi-elastic light scattering QELS)

Quasi-elastic light scattering distributions

Quasi-elastic light scattering from gels

Quasi-elastic light scattering particles

Quasi-elastic light scattering spectroscopy

Quasi-elastic light scattering spectroscopy QELSS)

Quasi-elastic light scattering studies

Quasi-elastic light scattering technique

Quasi-elastic neutron scattering

Quasi-elastic neutron scattering QENS)

Quasi-elastic neutron scattering adsorbates

Quasi-elastic neutron scattering benzene

Quasi-elastic neutron scattering diffusion

Quasi-elastic neutron scattering rates

Quasi-elastic neutron scattering self-diffusion coefficients

Quasi-elastic neutron scattering short-range H motion

Quasi-elastic neutron scattering spectra

Quasi-elastic neutron scattering temperature dependence

Quasi-elastic scattering

Quasi-elastic scattering approximation

Quasi-elastic scattering from droplets theory

Quasi-elastic scattering measurements

Quasi-elastic scattering measurements on hydrogen diffusing in hydrides

Rayleigh elastic scattering

Scatter elastically

Scatter elastically

Scattering elastic and inelastic

Scattering elastic/inelastic

Scattering residual elastic

Slow electrons elastic scattering

Surface Quasi-Elastic Light Scattering (SQELS)

Surface quasi-elastic light scattering

Time quasi-elastic neutron scattering

Time-resolved quasi-elastic laser scattering

Time-resolved quasi-elastic laser scattering interface

Time-resolved quasi-elastic laser scattering measurements

Time-resolved quasi-elastic laser scattering method

Time-resolved quasi-elastic laser scattering principle

Transmission electron microscopy elastic scattering

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