Scattering trajectory

Diffraction is based on wave interference, whether the wave is an electromagnetic wave (optical, x-ray, etc), or a quantum mechanical wave associated with a particle (electron, neutron, atom, etc), or any other kind of wave. To obtain infonnation about atomic positions, one exploits the interference between different scattering trajectories among atoms in a solid or at a surface, since this interference is very sensitive to differences in patii lengths and hence to relative atomic positions (see chapter B1.9). 

The calculation of backscatter coefficients via the approach outlined above is mathematically complex. Heidenreich 44) developed a simple empirical backscatter model which is applicable to resist exposure being based on the direct observation of chemical changes produced by backscat-tered electrons at different accelerating voltages on several substrates. The model is independent of scattering trajectory and energy dissipation calculations and is essentially a radial exponential decay of backscatter current density out to the backscatter radius determined by electron range. 

Fig. 2.11. The three-disk scattering system with three sample trajectories, (a) An exiting scattering trajectory, (b) a trapped periodic trajectory, (c) a trapped nonperiodic trajectory.

Since the set A of trapped orbits is not reachable from the outside, it repells scattering trajectories that eventually exit the system. Exiting scattering trajectories, which at some point in their time evolution may be close to a trapped trajectory, will eventually be repelled from the trapped trajectory and scatter off to infinity. This is the reason why the set A of unreachable trapped trajectories is also called a repeller. Repeller... 

Fig. 1. Illustration of scattering by three discs of radius a, whose centres are separated by the distance R. The solid line is the periodic trapped trajectory labelled 123. The dashed line is a scattering trajectory which escapes from the interaction region after six reflections by a disc...

Fig. 8. Phase space for the dynamics generated by the Hamiltonian (12) for = 2. The initial conditions of scattering trajectories are defined by the asymptotic incoming energy E, and a phase 27iT relative to the oscillating potential. Initial conditions leading to trajectories x t) with a total of two zeros are marked black. The white regions in between correspond to trajectories with three or more zeros (From [62])...

Figure Bl.23.7. Scattering intensity versus incident angle a scans for 2 keV Ne incident on (1 x 2)-Pt l 10 at 6 =149° along the (110), (001) and (112) azimuths. A top view of the (lx 2) missing-row Pt 110 surface along with atomic labels is shown. Cross-section diagrams along the three azimuths illustrating scattering trajectories for the peaks observed in the scans are shown on the right.

However, according to Mott and Massey [11], one can relate the phase shift to the scattering trajectories (deflection function) by means of the... 

Illustration of a damped (deep inelastic) collision. The projectile trajectory is shown by the heavy curve and the extension of the original Coulomb-scattering trajectory by dashed lines. During the rotation angle of the dinuclear complex, A0 = — exp/ a neck is formed between the reacting... 

Classical Trajectory Simulations Final Conditions Mixed Quantum-Classical Methods Rates of Chemical Reactions State to State Reactive Scattering Trajectory Simulations of Molecular Collisions Classical Treatment Transition State Theory Unimolecular Reaction Dynamics Wave Packets. 

Figure 5.11 Scattering trajectories (/[ = 0, Vj = 0, v = 1.32X10 cm sec ) represented as changes in interatomic distance with time (a) Non-reactive trajectory, (h) Reactive trajectory. The difference between the two trajectories appears to he due to a very small difference in the vibrational phase of the molecule BC. The crossing observed in (b) is due to the formation of rotationally excited products (/ x5) [2].

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