Scattering independent

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... 

We have found that display of nuclear trajectories and the simultaneous evolution of charge distributions to yield insightful details of complicated processes. Such descriptions also map more readily to the actual experimental conditions than do the more conventional time-independent scattering matrix descriptions. 

The first thing to realize about scattering by liquids is that individual molecules can no longer be viewed as independent scatterers. If a liquid were perfectly uniform in density at the molecular level, its molecules could always be paired in such a way that the light scattered by each member of a pair would be exactly out of phase with the other, resulting in destructive interference. No net scattering results in this case. The second thing to realize, however, is that density is not perfectly uniform at the molecular level. 

The theory discussed in this paper treats the biased superlattices as onedimensional systems in a single particle envelope approximation in which the electrons and holes act independently. Scattering mechanisms, which cause a loss of coherence, have not yet been included in the formalism. Loss of coherence represents a significant obstacle to quantum control in... 

Within the multichannel Bayesian formalism of structure determination, it is indeed possible to make use ofMaxEnt distributions to model systems whose missing structure can be reasonably depicted as made of random independent scatterers. This requires that the structural information absent in the diffraction data be obtained from some other experimental or theoretical source. The known substructure can be described making use of a parametrised model. 

Brewster, M. O., and Tien, C. L., Radiative Heat Transfer in Packed Fluidized Beds Dependent Versus Independent Scattering, J. Heat Transfer, 104(4) 574-580 (1982)... 

Time-Independent Scattering Wave Packet Technique Using Real Operators and Wave Functions. 

Next, consider a polymer sample which is heterodisperse both in molecular weight and composition. In the limit of vanishing concentration. Equation 1 gives, for independent scatterers, i ... 

Mandelkow et alP provided direct kinetic studies of nucleation by using 1 A synchrotron radiation to obtain time-resolved scattering data during cycles of assembly and disassembly after temperature shifts between 4 and 36°C. Small-angle scattering theory requires independent scattering from all particles in the solution, and the theory relates the intensity of scattering to other parameters as follows ... 

For independently scattering systems, without specific phase relation, we get for the total intensity in the scattered beam... 

For a system of independently scattering electrons, the resonance scattering amplitude, ignoring the second term, becomes... 

After a correction similar to that for the PDF for sample independent scattering, absorption, multiple scattering, and incoherent scattering one obtains a dynamic structure factor ... 

As in the case of photodissociation, the quantum theory of reactive molecular scattering was initially entirely based on time-independent scattering theory [4-7,100-123]. There were several early attempts to apply time-dependent quantum theory to reactive scattering processes [124—131]. But the modern era of the field really began with the seminal work of Kosloff et al. [37] and the subsequent application of his grid-based methods to the reactive scattering problem by Neuhauser and Baer and coworkers [45,132]. There have been many developments in the field [93,133-138], and several reviews and a book have been written on the topic [10,139-141]. My aim in the next section will be to outline the basic methods of time-dependent quantum theory used in reactive scattering calculations. While the review will cover many aspects of the theory, it will not cover all the approaches currently in use (as of 2003). 

For lattice acoustic-mode deformation potential scattering, s =, giving r = /8 = 1.18. For ionized-impurity scattering, s = —f, giving rn0 = 315 /512 = 1.93. For a mixture of independent scattering processes we must... 

Scale up for independent scatterers Multiply by number of sites per unit volume (subscript 5 on i)... 

Johnson and Rice used an LCAO continuum orbital constructed of atomic phase-shifted coulomb functions. Such an orbital displays all of the aforementioned properties, and has only one obvious deficiency— because of large interatomic overlap, the wavefunction does not vanish at each of the nuclei of the molecule. Use of the LCAO representation of the wavefunction is equivalent to picturing the molecule as composed of individual atoms which act as independent scattering centers. However, all the overall molecular symmetry properties are accounted for, and interference effects are explicitly treated. Correlation effects appear through an assigned effective nuclear charge and corresponding quantum defects of the atomic functions. 

So, the scattering matrix in our problem is described by 7 independent real parameters. For a point scatterer with energy independent scattering amplitudes (to, ro) one readily gets that t 2 = to 2 = D (D is the junction transparency). The phases are... 

Independent scattering refers to the scattering from a single particle in a cloud which is not affected by the neighboring particles, whereas dependent scattering refers to the scattering... 

Qs,D Qs.i Efficiency factor for dependent scattering Efficiency factor for independent scattering a Greek Symbols Volume fraction of the gas phase... 

Tien, C. L. and Drolen, B. L. (1987). Thermal Radiation in Particulate Media with Dependent and Independent Scattering. In Annual Review of Numerical Fluid Mechanics and Heat Transfer. Ed. T. C. Chawla. Washington, D.C. Hemisphere. 

Application of SVD analysis to the time-resolved SAXS data of Russell et al. (2002) clearly indicated two significant singular values, and therefore enabled data analysis by projection of each independent scattering profile onto two states. The folded and unfolded states were selected because of... 

Figure 16.17. Complementarity of direct and indirect neutralino dark matter searches. The figure shows that several supersymmetric models that are within the (expected) reach of a big neutrino telescope of 10 km2 yr exposure are beyond the reach of current and future direct detection experiments. The vertical axis is the product of the neutralino-proton spin-independent scattering cross section

Here 4iir/>incl is the structure-independent scattering, while Pstr(r) is the structure-dependent part. For a disordered liquid or solid, as r increases—say, beyond 10 or 15 A—the peaks in R(r) fade into the structureless scattering from electrons Ircr2p[nd, as the short-range order is exceeded. The area under the first few peaks of R(r) will yield the coordination number of the atoms in the peak. 

The parameter Z represents a field-independent scattering length of the carriers. The factor 1/6 is included to account for the statistical distribution of motion directions. The net carrier flux in field direction is... 

A second assumption is that the particles act as independent scattered, i.e., the scattering of light by one particle does not influence the scattering by another. If particles are separated by more than about 2 diameters, this assumption is met (Van de Hulst, 1957). For 1-p.m-diameter particles, this means concentration on the order of 1.25 x 1011 particles per cubic centimeter before this assumption breaks down. At a concentration of this magnitude, other factors such as coagulation (see Chap. 18) come into play to reduce the concentration, so the assumption is always valid. 

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