Vibrational excitation elastic case

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). 

Hence the outcome of the vibration excitation on the conductance is too complicated to predict. This is particularly true when there is a strong mixing of molecular states with metallic states. In this case, the interplay between the elastic contribution (exchange effects) and the purely inelastic one (increase of tunneling probability) is difficult to assess except after complete electronic structure calculations. 

The interaction of an electron with a molecule is described as a collision or impact, although the electron is so small that there is no collision in the usual sense of the word. The collision process may be termed elastic (the electron is merely deflected), inelastic (energy is transferred from the electron to the molecule), and superelastic (energy is transferred from the molecule to the electron). Electron-impact ionization is an example of an inelastic collision. The energy imparted to a molecule during an inelastic collision can lead to rotational, electronic, and vibrational excitation with or separate from ionization. Further, multiple-electron excitation can occur followed by autoionization, and the latter process has been shown to lead to a substantial fraction of total ionized species in many cases (S. Meyerson et al., 1963). Thus, an electron of energy 20 eV may lead to any of the above excitations of a molecule. The gas pressures used in a mass spectrometer and the density of electrons in the electron-beam are such that multiple electron-molecule interactions leading to ionization are improbable. 

Similar problems are encountered in a description of elastic or rotationally inelastic collisions of the electrons with molecules that have permanent dipole moment. However in this case K is never zero because k0 and ki have different norms due to an energy transfer to the vibrational excitation. 

In the e + M case, a very sensitive Indicator of shape resonance behavior Is the vibrational excitation channel. Vibrational excitation Is enhanced by shape resonances (3,17), and Is typically very weak for non-resonant scattering. Hence, a shape resonance, particularly at Intermediate energy (10-40 eV) (41,50), may be barely visible In the vlbratlonally and electronically elastic scattering cross section, and yet be displayed prominently In the vlbratlonally Inelastic, electronically elastic cross section. 

The evolution of the mean total power loss by collisions /" / and by the various collision processes in the nitrogen plasma is also displayed in Fig. 5. It can be seen (right) that at almost all field strengths considered, the mean loss by vibrational excitation P"/n is the dominant power loss channel. Only at field strengths below about 0.2 V/cm, where the power loss by elastic collisions F /n becomes dominant, and above about 60 V/cm, where the power loss by the triplet excitation P /n becomes dominant, is this not the case. 

Quasi-elastic neutron scattering (QENS) is related to stochastic particle motions. Because the displacements are random, the diffusive motion of particles in liquids caimot be quantized, and the energies are continuously distributed. Unlike the case of cooperative motions like phonons in solids or molecular vibrational excitations, in the dynamic scattering function S(Q,(o), there are no 5-functions at finite momentum and energy transfers. Instead, the dynamic scattering function is centered at zero-energy transfer with a characteristic quasielastic line width proportional to the diffusivity of the particles. 

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