Electron scattering processes

Vol. 35 Wavefunctions and Mechanisms from Electron Scattering Processes. Edited by F.A. Gianturco and G. Stefani. IX, 279 pages. 1984. 

H.S. Taylor, Models, interpretations, and calculations concerning resonant electron scattering processes in atoms and molecules, Adv. Chem. Phys. 18 (1970) 91. 

Equation 6.22 predicts that electronic conductivity is dependent on the electron relaxation time. However, it suggests no physical mechanisms responsible for controlling this parameter. Since electrons exhibit wave-particle duahty, scattering events could be suspected to play a part. In a perfect crystal, the atoms of the lattice scatter electrons coherently so that the mean-free path of an electron is infinite. However, in real crystals there exist different types of electron scattering processes that can limit the electron mean-free path and, hence, conductivity. These include the collision of an electron with other electrons (electron-electron scattering), lattice vibrations, or phonons (electron-phonon scattering), and impurities (electron-impurity scattering). 

Frohlich (10) showed how second order perturbation theory could be applied to derive an effective interaction between electrons from the direct electron-ion interactions. The physical idea is that as one electron scatters from a nuclear center it distorts the lattice, this distortion is felt by another electron, and thus the electrons experience an indirect interaction. The result is that we can think of the electrons as exchanging phonon momentum q in an electron-electron scattering process shown in Figure 2. The effective potential of interaction between the electrons for a scattering involving a change in momentum q is (11),... 

Figure 2. Two electrons with momenta k and 1 exchanging a phonon of momentum q in an electron-electron scattering process.

Bass, A.D. and L. Sanche. 1998. Absolute and effective cross sections for low-energy electron scattering processes within condensed matter. Radiat Environ Biophys 37 243-257. 

Alternatively the observed gas electron diffraction patterns may be interpreted in terms of an extremely flexible octahedral equilibrium structure in which the energy required to deform the molecule under Csv symmetry is so low compared to the thermal energy that a significant fraction of the molecules have instantaneous structures far from octahedral symmetry during the brief (< 10 s) electron scattering process. 

Point contact experiments were performed at 1.8 K by pressing a sharply etched Mo wire against a cleaved LaSe single crystal. The dynamic resistance R as a function of voltage U has a flat bottom as is expected when the electron scattering processes are dominated by the electron-phonon interaction R (0) = 2Q. The second derivative plot R" = f(U), which gives the structure of the phonon density of states, reveals a shoulder at 12 mV and a peak at 23 mV, Frankowski, Wachter [10]. 

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