Electron-vibration scattering

After some typical time, r, the electron will scatter off a lattice imperfection. This imperfection might be a lattice vibration or an impurity atom. If one assumes that no memory of the event resides after the scattering... 

Figure Bl.25.12. Excitation mechanisms in electron energy loss spectroscopy for a simple adsorbate system Dipole scattering excites only the vibration perpendicular to the surface (v ) in which a dipole moment nonnal to the surface changes the electron wave is reflected by the surface into the specular direction. Impact scattering excites also the bending mode v- in which the atom moves parallel to the surface electrons are scattered over a wide range of angles. The EELS spectra show the higlily intense elastic peak and the relatively weak loss peaks. Off-specular loss peaks are in general one to two orders of magnitude weaker than specular loss peaks.

Electronic, vibrational and rotational transitions may be involved in Raman scattering but, in this chapter, we consider only rotational transitions. 

Molecules initially in the J = 0 state encounter intense, monochromatic radiation of wavenumber v. Provided the energy hcv does not correspond to the difference in energy between J = 0 and any other state (electronic, vibrational or rotational) of the molecule it is not absorbed but produces an induced dipole in the molecule, as expressed by Equation (5.43). The molecule is said to be in a virtual state which, in the case shown in Figure 5.16, is Vq. When scattering occurs the molecule may return, according to the selection mles, to J = 0 (Rayleigh) or J = 2 (Stokes). Similarly a molecule initially in the J = 2 state goes to... 

The use of molecular and atomic beams is especially useful in studying chemiluminescence because the results of single molecular interactions can be observed without the complications that arise from preceding or subsequent energy-transfer coUisions. Such techniques permit determination of active vibrational states in reactants, the population distributions of electronic, vibrational, and rotational excited products, energy thresholds, reaction probabihties, and scattering angles of the products (181). 

The nature of the intemuclear distance, r, is the object of interest in this chapter. In Eq. (5.1) it has the meaning of an instantaneous distance i.e., at the instant when a single electron is scattered by a particular molecule, r is the value that is evoked by the measurement in accordance with the probability density of the molecular state. Thus, when electrons are scattered by an ensemble of molecules in a given vibrational state v, characterized by the wave function r /v(r), the molecular intensities, Iv(s), are obtained by averaging the electron diffraction operator over the vibrational probability density. 

Alhassid, Y., and Shao, B. (1992b), Algebraic Eikonal Approach to Electron-Molecule Scattering. II. Rotational-Vibrational Excitations, Phys. Rev. A 46, 3991. 

Figure 7 Incident electron energy dependence of the X v = 0, 1, 2, 3 vibrational and the a Ag (v = 0) electronic loss scattered intensities from a 10-layer film of O2 condensed on Pt(lll). was set at 10° with 6 at 45° and the azimuth at 10°. Also shown is the energy dependence of the inelastic background intensity located just before the v = 1 loss peak onset at Aif = 0.16 eV along with that contributing to each energy-loss profile (dashed lines). (From Ref. 118.)...

The conductivity of metallic conductors decreases with temperature. As the temperature rises the phonons gain energy the lattice vibrations have larger amplitudes. The displacement of the ionic cores from their lattice sites is thus greater and the electrons are scattered more, reducing the net current by reducing the mobility, //, of the electrons. 

An elementary treatment of the free-electron motion (see, e.g., Kittel, 1962, pp. 107-109) shows that the damping constant is related to the average time t between collisions by y = 1 /t. Collision times may be determined by impurities and imperfections at low temperatures but at ordinary temperatures are usually dominated by interaction of the electrons with lattice vibrations electron-phonon scattering. For most metals at room temperature y is much less than oip. Plasma frequencies of metals are in the visible and ultraviolet hu>p ranges from about 3 to 20 eV. Therefore, a good approximation to the Drude dielectric functions at visible and ultraviolet frequencies is... 

Le Roy, R.J. (1984). Vibrational predissociation of small van der Waals molecules, in Resonances in Electron-Molecule Scattering, van der Waals Molecules, and Reactive Chemical Dynamics, ed. D.G. Truhlar (American Chemical Society, Washington, D.C.). 

A third type of resonance may result from the two dimensional structure of the organized organic films. In this case the electron is delocalized in two dimensions but localized in the third one (see Fig. 6C).40 Hence, the structure in the transmission probability is not a result of complete delocalization of the electron (as in the case of band structure) nor to complete localization of the electron on a single molecule (as in a typical trap ). As expected, also in this process strong electron-vibration coupling occurs and evidence for inelastic scattering is observed. 

Nesbet, R.K. (1996). Nonadiabatic phase-matrix method for vibrational excitation and dissociative attachment in electron-molecule scattering, Phys. Rev. A 54,... 

Domcke, W. and Cederbaum, L.S. (1977). Theory of the vibrational structure of resonances in electron-atom scattering, Phys. Rev. A 16, 1465-1482. 

Mazevet, S., Morrison, M.A., Boydstun, O. and Nesbet, R.K. (1999). Adiabatic treatments of vibrational dynamics in low-energy electron-molecule scattering,... 

Miindel, C. and Domcke, W. (1984). Nuclear dynamics in resonant electron-molecule scattering beyond the local approximation model calculations on dissociative attachment and vibrational excitation, J. Phys. B 17, 3593-3616. 

---