Scattering processes

MSS Molecule surface scattering [159-161] Translational and rotational energy distribution of a scattered molecular beam Quantum mechanics of scattering processes... 

One of the most interesting features of the Raman spectmm is its dependence on tire incident light frequency, coj. When Wj is on resonance with the excited electronic state, the scattering process closely resembles a process of absorption followed by emission. However, as Uj is detuned from resonance there are no longer... 

In this section we present several numerical teclmiques that are conmronly used to solve the Sclirodinger equation for scattering processes. Because the potential energy fiinctions used in many chemical physics problems are complicated (but known to reasonable precision), new numerical methods have played an important role in extending the domain of application of scattering theory. Indeed, although much of the fomial development of the previous sections was known 30 years ago, the numerical methods (and computers) needed to put this fomialism to work have only been developed since then. 

Balint-Kurti G G, Dixon R N and Marston C C 1992 Grid methods for solving the Schrodinger equation and time-dependent quantum dynamics of molecular photofragmentation and reactive scattering processes/of. Rev. Phys. Chem. 11 317—44... 

Inelastic scattering processes are not used for structural studies in TEM and STEM. Instead, the signal from inelastic scattering is used to probe the electron-chemical environment by interpreting the specific excitation of core electrons or valence electrons. Therefore, inelastic excitation spectra are exploited for analytical EM. 

Perhaps the best known and most used optical spectroscopy which relies on the use of lasers is Raman spectroscopy. Because Raman spectroscopy is based on the inelastic scattering of photons, the signals are usually weak, and are often masked by fluorescence and/or Rayleigh scattering processes. The interest in usmg Raman for the vibrational characterization of surfaces arises from the fact that the teclmique can be used in situ under non-vacuum enviromnents, and also because it follows selection rules that complement those of IR spectroscopy. 

Figure Bl.24.4. Energy loss components for a projectile that scatters from depth t. The particle loses energy A E- via inelastic collisions with electrons along the inward path. There is energy loss A E in the elastic scattering process at depth t. There is energy lost to melastic collisions A along the outward path. For an incident energy Eq the energy of tlie exiting particle is = q - A iv - AE - A E. ...

Both conventions are identical only for direct collisions A (a) + B((3) A(a )+B(P ). This nonnalization is customary [5] for elastic and inelastic scattering processes. 

This book presents an extensive and detailed description of basic teclmiques for the generation and detection of atomic and molecular beams, as well as beam teclmiques for the study of molecular scattering processes. 

Baer R, Charutz D M, Kosloff R and Baer M 1996 A study of conical intersection effects on scattering processes—the validity of adiabatic single-surface approximations within a quasi-Jahn-Teller model J. Chem. Phys. 105 9141... 

At this point, we make two comments (a) Conditions (1) and (2) lead to a well-defined sub-Hilbert space that for any further treatments (in spectroscopy or scattering processes) has to be treated as a whole (and not on a state by state level), (b) Since all states in a given sub-Hilbert space are adiabatic states, stiong interactions of the Landau-Zener type can occur between two consecutive states only. However, Demkov-type interactions may exist between any two states. 

With this as background, we are finally in a good position to look at the scattering process itself. 

Figure 5.16 Raman and Rayleigh scattering processes involving virtual states Fq and Fj...

The mechanism for Stokes and anti-Stokes vibrational Raman transitions is analogous to that for rotational transitions, illustrated in Figure 5.16. As shown in Figure 6.3, intense monochromatic radiation may take the molecule from the u = 0 state to a virtual state Vq. Then it may return to u = 0 in a Rayleigh scattering process or to u = 1 in a Stokes Raman transition. Alternatively, it may go from the v = state to the virtual state Fj and return to V = (Rayleigh) or to u = 0 (Raman anti-Stokes). Flowever, in many molecules at normal... 

The similarity between a two-photon absorption and a Raman scattering process is even closer. Figure 9.27(a) shows that a Raman transition between states 1 and 2 is really a two-photon process. The first photon is absorbed at a wavenumber to take the molecule from state 1 to the virtual state V and the second photon is emitted at a wavenumber Vj,. 

Sample preparation is straightforward for a scattering process such as Raman spectroscopy. Sample containers can be of glass or quartz, which are weak Raman scatterers, and aqueous solutions pose no problems. Raman microprobes have a spatial resolution of - 1 //m, much better than the diffraction limit imposed on ir microscopes (213). Eiber-optic probes can be used in process monitoring (214). 

The X-ray and neutron scattering processes provide relatively direct spatial information on atomic motions via detennination of the wave vector transferred between the photon/neutron and the sample this is a Fourier transfonn relationship between wave vectors in reciprocal space and position vectors in real space. Neutrons, by virtue of the possibility of resolving their energy transfers, can also give infonnation on the time dependence of the motions involved. 

CO) may contain elastic (co = 0) and inelastic (co 0) parts. Elastic scattering probes correlations of atomic positions at long times, whereas the inelastic scattering process probes position correlations as a function of time. 

Light-scattering processes involve the interaction of light with gases or particles in such a manner that the direction or frequency of the light is altered. Absorption processes occur when the electromagnetic radiation interacts with gases or particles and is transferred internally to the gas or particle. 

Figure 1 Schematic of eiectron energy-loss scattering process for electrons of energy striking a Rh single-crystal surface with adsorbed CO molecules present. The actual energy-loss spectrum, due to excitation of CO vibrations, is shown also.

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