Electronically inelastic processes

When compared with DCSs calculated on the lowest adiabatic CI+H2 PES (the CWad PES), the multi-surface DCSs agree exceptionally well for transitions out of low H2 rotational levels. This confirms the accuracy of the multi-surface methodology and seattering eode. However, as the H2 rotational level increases, the multi-surface reactive DCSs beeome progressively smaller than the single-surface CWad predictions. This is likely an indication of loss of reactive flux through electronically inelastic processes, whieh are not possible in a single-surface model. Obviously, more work should be done on this aspect of the reaction. 

The Gelbart-Freed model is based on the assumption that this direct, electronically inelastic process is significantly less probable than the perturbation-facilitated one. This is a reasonable assumption in the case of electronic transitions involving a change of electron spin multiplicity (AS 0) or a small... 

Bondybey and Miller (1978) and Katayama, et al, (1979) proposed that the rates of electronically inelastic processes in the gas phase should follow a Franck-Condon rate law,... 

The energy transfer from kinematic (elastic) to electronic (inelastic) processes is inefficient, a fact partially attributable to the differing channels and time... 

Figure Bl.25.6. Energy spectrum of electrons coming off a surface irradiated with a primary electron beam. Electrons have lost energy to vibrations and electronic transitions (loss electrons), to collective excitations of the electron sea (plasmons) and to all kinds of inelastic process (secondary electrons). The element-specific Auger electrons appear as small peaks on an intense background and are more visible in a derivative spectrum.

A partial wave decomposition provides the frill close-coupling quantal method for treating A-B collisions, electron-atom, electron-ion or atom-molecule collisions. The method [15] is siumnarized here for the inelastic processes... 

The probability for a particular electron collision process to occur is expressed in tenns of the corresponding electron-impact cross section n which is a function of the energy of the colliding electron. All inelastic electron collision processes have a minimum energy (tlireshold) below which the process cannot occur for reasons of energy conservation. In plasmas, the electrons are not mono-energetic, but have an energy or velocity distribution,/(v). In those cases, it is often convenient to define a rate coefficient /cfor each two-body collision process ... 

The width of the peaks in LETS depends upon the sharpness of the onset of the inelastic process, which in turn depends upon the thermal distribution of electron energies about EP. Thus, the IETS line width depends strongly on temperature and as shown by (3) [75]. Because of this, vibrational IETS provides infrared-quality resolution only when performed below 5 K. Electronic transitions are usually much broader than vibrational transitions therefore, electronic IETS is usually performed at liquid nitrogen temperature and slightly above (>77 K). An example of a system showing both vibrational and electronic IETS is presented in Fig. 5 [19]. 

Thus far the discussion has centered on elastic tunneling, but consideration of inelastic processes may offer additional analytical opportunities. An energy scale of the relevant phenomena is presented in Table 2. Inelastic tunneling was first observed in metal-oxide-metal junctions. It was immediately developed as a technique for photon-free vibrational spectroscopy (lETS) where the tunneling electrons dissipate energy by coupling to vibra-... 

Figure 3 Inelastic and elastic cross sections for electron impact excitation of the water molecule the data are from the review by Mark et al. [19]. The total interaction cross section ctt was determined from the sum of cross sections for all elastic and inelastic processes. Inelastic channels include the vibrational modes Cvi (the bending mode with threshold 0.198 eV), cTv2 (the sum of two stretching modes with thresholds 0.453 and 0.466 eV), and CvS (a lump sum of other vibrational excitation modes including higher hormonics and combinational modes with an assigned threshold of 1 eV). The electronic excitations and <7 2 have threshold energies of 7.5 and 13.3 eV. Ionization cross sections are those of Djuric et al. (O), and Bolarizadah and Rudd ( ). (From Ref 19.)...

Eq. (11.30) is strictly applicable only to elastic collisions, in which a = a, and is thus of limited utility. However, it is physically appealing to assume that the cross section o(a, a, / ,/ ) for an inelastic process a = a and ft (i can be written as the integral of the electron scattering cross section oe(J3, f, q) over the velocity distribution of the Rydberg electron in the initial state a. Making this notion explicit, we write19... 

One of the major questions that remains to be answered is the detailed mechanism of charge transfer. For redox couples which lie in the gap of the semiconductor, isoenergetic electron transfer would require the existence of an appropriate surface state. While such states have been postulated, little direct evidence of their existence is available. An alternate possibility is an inelastic (non-isoenergetic) electron transfer process such as is commonly observed in solid state dev ices.(18)... 

Figure 1 illustrates different modes of electron transfer between electrolyte states and carriers in the bands at the semiconductor surface. If the overlap between the electrolyte levels and the semiconductor bands is insufficient to allow direct, isoenergetic electron transfer, then an inelastic, energy-dissipating process mustnbe used to explain experimentally observed electron transfer. Duke has argued that a complete theory for electron transfer includes terms that allow direct, inelastic processes. The probability of such processes, however, has not been treated quantitatively. 

When the energy of the electron is below 10 eV, the most probable process is elastic scattering. The cross sections of elastic scattering are usually much greater than those of inelastic processes (except for the resonance ones) and range from 10 15 to 10 14cm2. 

When deriving Eqs. (2) we neglected possible weak localization corrections that may originate from quantum interference of electron waves. This approximation is legitimate if a magnetic field is applied as in Ref. [1] or dephasing is strong due to inelastic processes. 

Here we report how the single electron transport in Andreev wires at low temperatures T weak disorder introduced by impurity scattering assuming that inelastic processes are negligible. The Andreev wire is clean in the sense that the mean free path is much longer than the wire diameter, 3> a. 

Fig. 2.1. Schematic illustration of the behaviour of the positron-helium and electron-helium total scattering cross sections. Notable are the large differences in magnitude of the cross sections at low energies, their merging at approximately 200 eV and the onset of inelastic processes at the positronium formation threshold EPS in the positron curve.

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