Inelastic multiple

The third equation is the kinetic equation, which describes the evolution of the one-particle density matrix p(r, r, E) of the electron in the process of multiple elastic and inelastic scattering in a solid... 

In summary, the movement of a high-energy electron in a solid may be described by a set of three Equations (1), (4) and (6). From these equations we may conclude that for high-energy electron diffraction the problem of multiple elastic and inelastic scattering by a solid is entirely determined by two functions, i.e. (1) the Coulomb interaction potential averaged over the motion of the crystal particles (V(r)> and (2) the mixed dynamic form factor S(r, r, E) of inelastic excitations of the solid. 

Kirtley J, Soven P (1979) Multiple-scattering theory of intensities in inelastic-electron-tunneling spectroscopy. Phys Rev B 19 1812-1817... 

The chemisorption process has its maximum cross section at 11 eV in contrast with cross sections for the radiolysis of bulk ice. This difference was understood as being dependent on the selective quenching of dissociative electronic states of water due to the resonant charge exchange between the substrate and adsorbate and the absence of multiple inelastic scattering in the H2O bilayer on Si(lll). 

The shifts in vibrational frequencies between the LS and HS species are responsible for the major parts of the entropy changes AS in spin transitions [13]. This has been repeatedly confirmed by infrared [13-15], Raman [14-17], and inelastic neutron scattering spectroscopies [18]. Since the observed entropy change 13.8 J K-1 mol-1 [12] in the present compound is not explained adequately solely by the entropy of the spin multiplicity (R ln(5/3) = 4.25 J K-1 mol-1). However, we cannot assign the extra entropy change to a vibrational origin, since the Raman spectra of the two phases differ only in intensities. 

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