Shape resonances physical effects

Though many of the features of molecular PE cross sections can be attributed to atomic effects, some features, such as shape resonances, are critically dependent on the form of the molecular potential. This itself is determined in part by the physical shape of the molecule, from which the name of the effect derives. Shape resonances manifest themselves as increases in cross section, which are frequently sharp and generally at relatively low PE kinetic energies. They are generally viewed as attributable to momentary trapping of the electron in a quasi-bound continuum orbital created by an effective potential of the molecular ion, or, excitation into antibonding orbitals located in the continuum. ... 

The Lewis-type (L) contribution is considered the easy part of chemical wavefunction analysis, because it corresponds closely to the elementary Lewis structure model of freshman chemistry. Nevertheless, controversy often arises over the magnitude of steric or electrostatic effects that are associated with the Lewis model itself [i.e., distinct from the resonance-type effects contained in (NL)]. The NBO program offers useful tools for quantifying both steric and electrostatic interactions in terms of the space-filling (size and shape) and dielectric properties (charge, dipole moment, etc.) of the electron pair bonds and lone pairs that comprise the Lewis structure model. This chapter discusses the physical nature and numerical quantitation of these important chemical effects, which are often invoked in a hand-waving manner that reflects (and promotes) significant misconceptions. 

Theoretically, ESR lines should be infinitely narrow, experimentally, they are broadened by various mechanisms, both intrinsic (determined by sample properties and the physics of the resonance experiment) and extrinsic (dependent on spectrometer operating conditions) Line shapes of ESR signals of peroxy radicals in lignin are often asymmetric because of the solid-state or power spectrum effects of the vanous anisotropic interactions... 

The preparation and the crystal structures of single crystals of alkali aromatic ion pairs are discussed. A close relationship was found between the ion-pair structures in solution and in the solid state. The physical properties of the pseudo-two-dimensional magnetic alkali biphenyl crystals are reviewed. The effect of spin diffusion manifests itself clearly in the line width and line shape of the exchange-narrowed electron spin resonance (ESR) line. The monoanions of cycloocta-tetraene, produced by X-ray irradiation, rotate rapidly about their eightfold axes. At 20 K this rotation is frozen, and an alternating spin density distribution is found around the ring. The equilibrium position of the monoanion is rotated by 22.5 compared with the equilibrium position of the dianion. 

The calculated enhancement of this purely physical EM effect as function of the distance of the molecule from the spere, reflects the long range nature of this model The enhancement depends strongly upon the particle shape and the dielectric constants and 3 For small spheres, in resonance with the localized surface plasmons,... 

Two main types of heterogeneity effects are associated with fast criticals loaded in plate geometry fast and resonance. The fast effect depends on the physical shape of the fissile materials, i.e., thicknesses and tenths of columns, and on the physical separation between the fissile and fertile plates. It gives a positive contribution to the reactivity of the system. 

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