Interference structural

Why should calculations of evidently converge more slowly than those for b, and both more slowly than cross-section calculations It seems likely that this is a consequence of the very different interference structure of these three terms and their different phase dependence— particularly the slower convergence of the sin(ri — riy /) terms in the b expression (see Section III.C). When phase differences are small, as they will be for higher (. waves that are partly attenuated in the molecular core region by centrifugal barriers, the rapidly varying sine term will lend them a disproportionate influence on the final... 

The four phases are Di thrust-related tight to isoclinal (Fi) folds and associated axial planar schistosity (Si). D2 tight-to-isoclinal folds (F2), with S2, are interpreted as high strain deformation with F1/F2 fold interference structure (Fig. 6) resulting in the development of SI/S2 composite fabric elements. D3 are recumbent and best developed in the west part of the BMC, and D4 are represented as kink-folds. 

In the region where water is weakly absorbing (between about 0.5 and 5 jum-1) the extinction curve for a 1.0 jum droplet has several features (1) a series of regularly spaced broad maxima and minima called the interference structure, which oscillates approximately about the value 2 (2) irregular fine... 

We shall defer detailed discussion of the ripple structure, which is considerably more complicated both mathematically and physically than the interference structure, until Chapter 11. Suffice it to say for the moment that the ripple structure has its origins in the roots of the transcendental equations (4.54) and (4.55), the conditions under which the denominators of the scattering coefficients vanish. 

Both the interference structure and the ripple structure are strongly damped when absorption becomes large, as it does in water if 1 /X is greater than about 6 pm x this is analogous to damping of interference bands in the transmission spectrum of a slab (see Fig. 2.8). If the droplet is small compared with the wavelength, then peaks in the bulk absorption spectrum are seen in the particle extinction spectrum for example, the extinction peaks in Fig. 4.6 at about 6 jam-1 for a 0.05-jum-radius droplet and at about 0.3 jum-1 for a 1.0-jam droplet are neither interference nor ripple structure but bulk absorption peaks. This illustrates the fact that absorption dominates over scattering for small a/X if there is any appreciable bulk absorption. 

The effect of averaging over one or more particle parameters—size, shape, orientation—is to efface details extinction fine structure, particularly ripple structure, to a lesser extent interference structure (Chapter 11) and undulations in scattering diagrams. If the details disappear upon averaging over an ensemble perhaps the best strategy in this instance would be to avoid the details of individual-particle scattering altogether and reformulate the problem statistically. 

The calculated extinction spectrum of a polydispersion of small aluminum spheres (mean radius 0.01 jam, fractional standard deviation 0.15) is shown in Fig. 11.4 both scales are logarithmic. In some ways spectral extinction by metallic particles is less interesting than that by insulating particles, such as those discussed in the preceding two sections. The free-electron contribution to absorption in metals, which dominates other absorption bands, extends from radio to far-ultraviolet frequencies. Hence, extinction features in the transparent region of insulating particles, such as ripple and interference structure, are suppressed in metallic particles because of their inherent opacity. But extinction by metallic particles is not without its interesting aspects. 

Ripple structure, beginning with the sharpest at large size parameters, is the first to disappear as a is increased. As the distribution is further widened, the interference structure fades away. For the widest distribution the only remaining features are reddening at small size parameters, and, at the other extreme, an asymptotic approach to the limiting value 2. < if ( K /... 

A glance at the curves in Fig. 11.15 reveals extinction characteristics similar to those for spheres at small size parameters there is a Rayleigh-like increase of Q a with x followed by an approximately linear region broad-scale interference structure is evident as is finer ripple structure, particularly in the curves for the oblate spheroids. The interference structure can be explained... 

Mie theory does an admirable job of predicting extinction by spherical particles with known optical constants even the finest details it predicts—ripple structure—have been observed in extinction by single spheres. Several different causes—a distribution of sizes or shapes, and absorption—have the same effect of effacing the ripple structure or even the broader interference structure. 

Fig. 3.2. High-resolution photoelectron image recorded in a DC field of 615V/cm, with the laser polarization perpendicular to the detector axis, and parallel to the plane of the detector. The image shows an interference structure that can be understood in terms of the pathlength differences between classical trajectories that carry the electron from the atom to the detector...

Figure 2.8. Reflectivity spectra in the various vibronic regions, b-polarized (upper part) and a-polarized (low part), of the (001) face of the anthracene crystal at 5 K. The energies of the main structures are indicated in reciprocal centimeters. (The interference structures are discussed in Section III.)...

As discussed in Section III.B, quantum interference structure tends to be quenched by these sums, and if the transition is classically allowed, the semi-classical theory then effectively degenerates to a completely classical result. 

Fig. 15. Polar differential cross section calculated semi-classically for the charge transfer process Na + I - Na+ + I, (a) Calculation with the complete interference structure with omission of the primary rainbow. (b) Approximate semi-classical calculation taking into account only interferences from net repulsive and net attractive scattering, (c) The full bars indicate maxima observed experimentally for net attractive scattering, the dashed bars for net repulsive scattering. H12(RC) = 0-065 eV angular coupling was neglected. (Delvigne and Los, 1973.)...

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