Zero-order scattering

Here, Jo(x) is the Bessel function of zero order, r7- kf-ki is the momentum transfer, which depends on the scattering angle 6, and 6 b) is the semiclassical phase shift, which is given in terms of the deflection function as b) = dd b)Hk , db. 

The dynamic calculations include all beams with interplanar distances dhki larger than 0.75 A at 120 kV acceleration voltage and thickness between 100 A and 300 A for the different zones. The structure factors have been calculated on the basis of the relativistic Hartree - Fock electron scattering factors [14]. The thermal difiuse scattering is calculated with the Debye temperature of a-PbO 481 K [15] at 293 K with mean-square vibrational amplitude

= 0.0013 A following the techniques of Radi [16]. The inelastic scattering due to single-electron excitation (SEE) is introduced on the base of real space SEE atomic absorption potentials [17]. All calculations are carried out in zero order Laue zone approximation (ZOLZ). 

As described in the main text of this section, the states of systems which undergo radiationless transitions are basically the same as the resonant scattering states described above. The terminology resonant scattering state is usually reserved for the case where a true continuum is involved. If the density of states in one of the zero-order subsystems is very large, but finite, the system is often said to be in a compound state. We show in the body of this section that the general theory of quantum mechanics leads to the conclusion that there is a set of features common to the compound states (or resonant scattering states) of a wide class of systems. In particular, the shapes of many resonances are very nearly the same, and the rates of decay of many different kinds of metastable states are of the same functional form. It is the ubiquity of these features in many atomic and molecular processes that we emphasize in this review. 

In summary, we have shown how the absorption of a photon leads to the formation of a resonant scattering state. Explicit formulas involving quadrature over the system energy spectrum have been presented but not evaluated. When the resonant scattering state may be approximated in terms of a set of quasistationary bound states, an explicit relationship is obtained for the rate of dissociation in terms of the matrix elements coupling zero-order states and the corresponding densities of states. In principle this permits the use of experimental rate data to evaluate the matrix elements vx and v2, if px and p2 can be estimated. 

In this case we recover the result by Feuchtwang [12], that the Bardeen method is just the zero order approximation to a full scattering treatment [13,14],... 

This result and its interpretation in terms of scattering theory is well accepted. Here, it shows once more that the choice for the zero order Green s function of the interface is justified. In case of non-zero bias the scattering approach leads in addition to a bias dependent term, which increases the current and leads to a quadratic relation between current derivative dl/dV and bias V. Though this result has been well documented in experiments,... 

When the grating is illuminated with one of the two original waves, some of the wave will be scattered into a reconstruction of the other wave, some of the wave will pass through the grating unaffected (the zero-order beam), and some of the beam may be scattered into other directions corresponding to the other various orders of the grating (Fig. 2b). 

NIR has been used to determine the mass median diameter of a micronized active compound contained in a lactose monohydrate at a concentration of 4% by weight and a size between 8 and 20 pm [223]. Multivariate statistical analysis was applied to zero order NIR spectra using particle size distributions by low angle laser light scattering as a reference technique. Due to its speed, simplicity and low operating costs it was demonstrated that this is a viable alternative to other methods used to carry out this type of analysis. 

Subsequently, wc use the expression (9.148) as the zero order approximation for the scattered field inside the inhomogeneity,... 

A very peculiar dynamics has been revealed in the Ca(OH)2 crystal by means of inelastic neutron scattering technique [26]. It has been found that anharmonic terms must be included, which mix the vibrational states of the OH and lattice modes. In particularly, the lattice modes have successfully been represented as the superposition of oxygen and proton synchronous oscillators, and it appears that the proton bending mode Eu is strongly coupled to the lattice modes. The contribution of the proton harmonic wave functions has been taken as the zero-order approximation. 

The Franck-Condon A term will now be written in the overlap picture for the case of fundamental scattering in the low temperature limit where excitation occurs only from the 0) level of the ground state. It must be remembered that the ground levels are true in the zero-order, i.e. there is no vibronic coupling in the ground state. 



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