Scattered wave

The beam-defect interaction is modelled using Kirchhoff s diffraction theory applied to elastodynamics. This theory (see [10] for the scattering by cracks and [11] for the scattering by volumetric flaws) gives the amplitude of the scattered wave in the fonn of coefficients after interaction with defects and takes account of the possible mode-conversion that may occur. 

In the usual approximation of the object as a weak phase/weak amplitude object, this scattered wave can be used to calculate the intensity of the image transfomi as... 

This relation is a direct consequence of the conservation of flux. The target casts a shadow in the forward direction where the intensity of the incident beam becomes reduced by just that amount which appears in the scattered wave. This decrease in intensity or shadow results from interference between the incident wave and the scattered wave in the forward direction. Figure B2.2.2 for the density P (r) of section B2.2.6 illustrates... 

Kroes G J and Neuhauser D 1996 Performance of a time-independent scattering wave packet technique using real operators and wave functions J. Chem. Phys. 105 8690... 

The energy and state resolved tiansition probabilities are the ratio of two quantities obtained by projecting the initial wave function on incoming plane waves (/) and the scattered wave function on outgoing plane waves [F)... 

Transmission electron microscopy (tern) is used to analyze the stmcture of crystals, such as distinguishing between amorphous siUcon dioxide and crystalline quartz. The technique is based on the phenomenon that crystalline materials are ordered arrays that scatter waves coherently. A crystalline material diffracts a beam in such a way that discrete spots can be detected on a photographic plate, whereas an amorphous substrate produces diffuse rings. Tern is also used in an imaging mode to produce images of substrate grain stmctures. Tern requires samples that are very thin (10—50 nm) sections, and is a destmctive as well as time-consuming method of analysis. 

Assuming kinematical diffraction theory to be applicable to the weakly scattering CNTs, the diffraction space of SWCNT can be obtained in closed analytical form by the direct stepwise summation of the complex amplitudes of the scattered waves extended to all seattering centres, taking the phase differenees due to position into aeeount. 

EXAFS is observed as a modulating change in the absorption coefficient caused by the ejected electron wave back-scattering from the surrounding atoms, resulting in interference between ejected and back-scattered waves. It is defined as ... 

Sun, C., and Su, C., 1978, Overlapping muffin tin multiple scattering wave Xo method, Scienta Sinica 21 327. 

The Doppler meter may be used wherever small particulate solids, bubbles or droplets are dispersed in the fluid and are moving at essentially the same velocity as the fluid stream which is to be metered. A continuous ultrasonic wave is transmitted, again at an acute angle to the wall of the duct, and the shift in frequency between the transmitted and scattered waves is measured. This method of measurement of flowrate is frequently used for slurries and dispersions which present considerable difficulties when other methods are used. 

Section IIC showed how a scattering wave function could be computed via Fourier transformation of the iterates q k). Related arguments can be applied to detailed formulas for S matrix elements and reaction probabilities [1, 13]. For example, the total reaction probability out of some state consistent with some given set of initial quantum numbers, 1= j2,h), is [13, 17]... 

This oscillating dipole will radiate a secondary wave of the same frequency, which may be observed along the direction OP making an angle 6 with the direction (x-axis) of the incident wave. The scattered wave will be polarized in the plane defined by P and the 2 -axis. The electric intensity Es c of the scattered wave will depend on the acceleration of the induced electric moment, i.e., on d pldC-. Specifically the amplitude o.sec of the wave scattered in the direction OP will depend on the amplitude of (1/c ) d pldt ) calculated from Eq. (14), on the projection of the moment perpendicular to the direction P in the plane, and inversely on the distance r from the scatterer. Thus,... 

During an NFS experiment with a sample that contains more than one kind of scatterer (i.e., HS and LS isomer), the superposition of forward scattered waves could occur coherently or incoherently. Longitudinal scattering is always coherent, because there is no path-length difference for nuclei located along the X-ray beam. 

When, however, phonons of appropriate energy are available, transitions between the various electronic states are induced (spin-lattice relaxation). If the relaxation rate is of the same order of magnitude as the magnetic hyperfine frequency, dephasing of the original coherently forward-scattered waves occurs and a breakdown of the quantum-beat pattern is observed in the NFS spectrum. 

In the case of coherent scattering, which observes the pair-correlation function, interference from scattering waves emanating from various segments complicates the scattering function. Here, we shall explicitly calculate S(Q,t) for the Rouse model for the limiting cases (1) QRe -4 1 and (2) QRe > 1 where R2 = /2N is the end-to-end distance of the polymer chain. 

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