Inelastic channel

Fig. 3 Energy diagram for an M-A-M diode showing elastic and inelastic tunneling processes (top). The HOMO (n) and LUMO (71 ) orbital energies and a few vibrational levels are indicated. Applied bias energy (eV) is just sufficient to allow inelastic tunneling with excitation of the first vibrational level, eV = hv. Also shown (bottom) are the I(V) curve, conductance- / curve, and the IETS spectrum that would result from both elastic processes and the first inelastic channel. (Reproduced by permission of the American Chemical Society from [19])...

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.)...

The oscillatory structure just mentioned has been clearly demonstrated to result from quantum-mechanical phase-interference phenomena. The necessary condition264,265 for the occurrence of oscillatory structure in the total cross section is the existence in the internuclear potentials of an inner pseudocrossing, at short internuclear distance, as well as an outer pseudo-crossing, at long internuclear distance. A schematic illustration of this dual-interaction model, proposed by Rosenthal and Foley,264 is shown in Fig. 37. The interaction can be considered to involve three separate phases, as discussed by Tolk and et al. 279 (1) the primary excitation mechanism, in which, as the collision partners approach, a transition is made from the ground UQ state to at least two inelastic channels U, and U2 (the transition occurs at the internuclear separation 7 , the inner pseudocrossing, in Fig. 37), (2) development of a phase difference between the inelastic channels,... 

As a general rule, when Pgl is energetically possible, it is overwhelmingly preferred to other electronically inelastic channels. Thus He ... 

The energy analysis of these inelastically scattered electrons is carried out by a cylindrical sector identical to the monochromator. The electrons are finally detected by a channeltron electron multiplier and the signal is amplified, counted and recorded outside of the vacuum chamber. A typical specularly reflected beam has an intensity of 10 to 10 electrons per second in the elastic channel and a full width at half maximum between 7 and 10 meV (60-80 cm l 1 meV = 8.065 cm-- -). Scattering into inelastic channels is between 10 and 1000 electrons per second. In our case the spectrometer is rotatable so that possible angular effects can also be studied. This becomes important for the study of vibrational excitation by short range "impact" scattering (8, 9, 10). 

As the positron energy is raised above the positronium formation threshold, EPs, the total cross section undergoes a conspicuous increase. Subsequent experimentation (see Chapter 4) has confirmed that much of this increase can be attributed to positronium formation via the reaction (1.12). Significant contributions also arise from target excitation and, more importantly, ionization above the respective thresholds (see Chapter 5). In marked contrast to the structure in aT(e+) associated with the opening of inelastic channels, the electron total cross section has a much smoother energy dependence, which can be attributed to the dominance of the elastic scattering cross section for this projectile. 

Vibrational spectroscopy is based on two fundamental processes excitation and detection. As we shall see later in this chapter, they are not equivalent, and indeed both have to be treated to understand the origin of active modes in the spectra. The excitation is based on inelastic scattering processes, thus connecting initial and final states with different energy. The detection relies on the effect of the new inelastic channel on experimentally observable magnitudes, i.e. the junction conductance. 

The inelastic channel A current is created when two electron reservoirs are connected. In equilibrium no-electron flow takes place the chemical potential (i.e. the Fermi energy at T = 0) is well defined. When a bias... 

When the bias voltage corresponds to chemical potential shifts smaller than the quantum of vibration the electron cannot yield its energy to the vibration because there is no final state at the surface electrode available (Fig. 1(a)). At T = 0, the excitation happens suddenly when the bias voltage energy is larger than the quantum of vibration. The inelastic electron can continue its propagation into an empty electronic state now available above the sample Fermi level. In this case, a new channel for electronic transport has been open this is called the inelastic channel (Fig. 1(b)). 

V. The molecular vibrator is represented by a harmonic oscillator located in the vacuum gap. When the electron energy eV is smaller than the vibrator eigenenergy, the final state of an inelastic transition would be a sample filled state (a) the inelastic channel is closed. Hence electrons tunnel without interaction with the oscillator. When eV reaches the mode energy hoj, empty final states at the sample s Fermi energy become accessible the inelastic channel is open. The opening of the inelastic channel causes (c) a sharp increase AG in the tunneling differential conductance d//dV or (d) peaks in the second derivative d2//dV 2. The activation of the inelastic channel takes place indistinguishably of the bias polarity. 

Thus in the case of a nonreactive (i.e., elastic or inelastic) channel the reactant and product asymptotes coincide an elastic channel is characterized, in addition, by the identity of the product and reactant internal states. 

Figure 19-20. Decay channels of a transient anion of a fundamental DNA unit (SU) formed at electron energy E0. Pathway 1, 2 and 3 represent the elastic, DEA and electronically inelastic channels, respectively. In channels 1 and 3, the additional electron can be emitted in a continuum of states (e ) or transferred to other DNA subunits (ep)...

In the case of inelastic processes, the asymptotic form of Ri(kr) given in Eq. (5) no longer holds. This is because the amplitude of the outgoing spherical wave must necessarily be less than that of the incoming wave. These amplitudes however refer only to the elastic component of the scattering amplitude. The breakdown of the radial standing wave pattern in Ri(kr) results in a nett inward flux towards the origin. In fact these are the waves which go into various inelastic channels. This is taken into accmmt by... 

The analysis and experimental procedures are very demanding in obtaining accurate cross-section data and there are particular problems in obtaining unique cross sections (see Huxley and Crompton (1974) and Kumar (1984) for details). If only the elastic channel is open the momentum-transfer cross section can be obtained reliably and accurately in some cases (e.g. He, 2%). With the addition of inelastic channels the uncertainty in the derived cross sections due to lack of uniqueness increases. 

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