Shape resonances electron-molecule scattering

M. Berman, H. Estrada, L.S. Cederbaum, W. Domcke, Nuclear dynamics in resonant electron-molecule scattering beyond the local approximation The 2.3-eV shape resonance in N2, Phys. Rev. A 28 (1983) 1363. 

This beautiful empirical evidence had a strong stimulating effect In the study of shape resonances In molecular photolon-Izatlon, Just as early observations of the Xg shape resonance In elastic e-No scattering did In the electron-molecule scattering field (3,17). 

Finally, note that we have Illustrated the vibrational effects of shape resonances In the context of molecular photolonlzatlon however, a rather analogous mechanism makes shape resonances extremely efficient In Inducing vibrational excitation In electronlcally-elastlc electron-molecule scattering (3,17,41). 

Connections Between Shape Resonances In Electron-Molecule Scattering And In Molecular Photolonlzatlon And Related Connections... 

One may classify the various proposed models in several ways. One way is to differentiate between models that focus on the role of the electric field E and the emission G terms (these two are related), on the one hand, and those that emphasize the role of changes in the Raman polarizability tensor, on the other. The former discuss the enhancement in terms of amplified fields, due to the presence of the surface, which act on the scattering molecule and its emission being further amplified by the surface. These are the local field and emission enhancement models (LFE). The difference between the various models which belong to this group is in the identification of the specific excitation in the solid which is responsible for the amplification plasmon polaritons, shape resonances, electron holes, etc. 

The same two shape resonances are also observed in electron-molecule scattering. Here, they are shifted to higher kinetic energy. This is due to the added electron, iidiich produces more repulsive potential, in fact pushing the resonance well into... 

The resonances in scattering of electrons off diatomic molecules have a long history /16/ and the initial application of the dilated electron propagator to the 2ng shape resonance in e-N2 and 2II shape resonance in e-CO scattering is due to their appeal as representative homo and hetero-nuclear diatomic systems which are also isoelectronic and therefore lend themselves to a comparative study /18,19/. 

Second, being quasibound Inside a potential barrier on the perimeter of the molecule, such resonances are localized, have enhanced electron density In the molecular core, and are uncoupled from the external environment of the molecule. This localization often produces Intense, easily studied spectral features, while suppressing non-resonant and/or Rydberg structure and, as discussed more fully below, has a marked Influence on vibrational motion. In addition, localization causes much of the conceptual framework developed for shape resonances In free molecules to apply equally well to photolonlzatlon and electron scattering and to other states of matter such as adsorbed molecules, molecular crystals, and Ionic solids. 

No doubt, the present author has his own private consensus which, in spite of his efforts, may inject itself into the review. In order to offset such an undesirable bias, as much as possible, and perhaps putting the cart before the horse, the author will state here his own conclusions and beliefs I am convinced that electric field amplification and enhanced emission near SERS-active surfaces due to resonating metal excitations (surface-plasmon polaritons, plasmonlike modes, shape resonances, or electron-hole pairs) is an active mechanism in most of the systems studied. However, in most systems, this contribution, though an important one, is minor compared to the total enhancement possible in SERS. The major mechanism, in my opinion, must be a resonance mechanism, in the sense of a resonance Raman process, i.e., a mechanism by which a part of the system (molecule, molecule-metal atoms, metal surface) becomes a strong scatterer by virtue of its large resonance polarizability and not as a result of strong fields exerted by the other parts of the system . 

At certain periods of the development and application of resonance scattering theory to atoms and molecules, the notions of "Feshbach" and "shape" resonances have occasionally been elevated to the level of an important issue. Characteristic discussions as to the relative merits of theoretical methods and as to the relevance of this issue can be found in the literature on doubly and triply excited resonances of the prototypical three-electron system. He , e.g.. Refs. [4a,4b,5b, llb,56,73,77]. For example, normally, if the... 

As discussed above, continuum resonance occurs when the excitation laser energy is higher than the dissociation limit of an excited, bound electronic state or directly with purely repulsive states. Continuum resonance Raman spectra of gaseous molecules are very sensitive to the position and shape of the potential functions involved in this type of light scattering as well as to the electronic transition moments between ground and excited states. Since it is possible to calculate the relevant spectra using both the KHD... 

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