Scattering region

The basic assumption here is the existence over the inelastic scattering region of a connnon classical trajectory R(t) for the relative motion under an appropriately averaged central potential y[R(t)]. The interaction V r, / (t)] between A and B may then be considered as time-dependent. The system wavefiinction therefore satisfies... 

Figure 12. Rays from different scattering regions...

Figures 4e and 4f show OCT images of two control seeds after 60 minutes when turgescence has started. Similar to the GMF seeds, individual structural differences of the seeds are clearly visible here. However, after the same time period the heterogeneous absorption zones (Fig. 4f) are less expressed than in the GMF seeds (Fig. 4d). The bright area corresponding to highly scattering regions (Fig. 4d) is narrower (about 100 im) in the control than in GMF seeds (about 200 pm). Thus OCT imaging of barley seeds can distinctly visualize water absorption processes within the first hour, as well as, individual variations in different seeds. The variations reflect the phenomenon of biological variability of seeds at the tissue level.

Figure 9. Formation of circular scattering regions (rings) in the reciprocal lattice of a texture, and relationship between their shape and the structure of the specimen. Transition from a point to a ring (a) for an ideal texture without disorder (c), having a distribution function (e) (d), (f) - corresponding diagrams for a real texture with some disorder.

Figure 10. Distribution of reciprocal lattice points of a plate texture along straight lines parallel to the texture axis and perpendicular to the face lying on the support (a) and distribution of circular scattering regions of the reciprocal lattice of a texture on coaxial cylinders.

Figure 11. (a) formation of layer lines in the reciprocal lattice of a texture for a orthogonal unit cell, (b) the doubling of number of circular scattering regions in the reciprocal lattice of a texture and therefore the number of reflections on an ellipse of a pattern for a non-orthogonal unit cell, (c) measurement of a values of 2r and 2 D on a texture pattern. 

Fig. 20 Schematic representation of a two-terminal device. The scattering region (enclosed in the dashed-line frame) with transmission probability T(E) is connected to semi-infinite left (L) and right (R) leads which end in electronic reservoirs (not shown) at chemical potentials Eu and r, kept fixed at the same value p for linear transport. By applying a small potential difference electronic transport will occur. The scattering region or molecule may include in general parts of the leads (shaded areas) (adapted from [105] with permission Copyright 2002 by Springer)...

This independency is related to the fact that the semiclassical calculation of the scattering amplitudes involves classical orbits belonging to an invariant set that is complementary to the set of trapped orbits in phase space [56]. The trapped orbits form the so-called repeller in systems where all the orbits are unstable of saddle type. The scattering orbits, by contrast, stay for a finite time in the scattering region. Even though the scattering orbits are controlled... 

All other trajectories spend only a finite time in the scattering region. They are referred to as scattering orbits, and they constitute the vast majority... 

Safford and Naumann (128) have shown that the time-of-flight spectra for 4.6M solutions of KF, KC1, CsCl, NaCl, and LiCl show peaks in the inelastic scattering region which coincide both in frequency and shape with the ice-like (structured) frequencies of pure water. Also, solutions of KSCN, KI, KBr, and NaC104 have lattice frequencies where they are found for water although in these cases apparently with less resolution and less intensity. Even an 18.5-M solution of KSCN showed a similar behavior. We take this to suggest that elements of water structure remain in these solutions (as discussed elsewhere in this paper, where we noted that the thermal anomalies occur at approximately the same temperatures, even for relatively concentrated solutions, as where they occur in pure water see also Ref. 103). 

---