Resonances shape

Jolicard G, Leforestier C and Austin E J 1988 Resonance states using the optical potential model. Study of Feshbach resonances and broad shape resonances J. Chem. Phys. 88 1026... 

It is well known that the value of the p parameter, more than the cross-section a, often shows a strong response to resonant structure embedded in the continuum. Given the sensitivity exhibited by the parameter in the foregoing there must be an a priori expectation that it would also show a strong response to resonant behavior. Computational methods do not yet exist to deal with autoionization phenomena in the systems of interest here, but one electron shape resonances can, in principle, be examined. 

A possible role for shape resonances has been postulated in a number of the photoionization studies mentioned above [52, 53, 57, 60], although it has to be noted that except for camphor [57], the evidence for the existence of the shape resonance is not definitive. (It also then remains an open question how any such resonances, inferred from fixed geometry calculations, would manifest themselves in practice in large, and sometimes floppy, molecules, such as these chiral species.)... 

In general terms, it has been seen here that the parameter curves are almost always more stmctured than p parameter curves. The latter are known from years of study to broadly conform to a pattern (in the absence of resonances) that starts from a small value at threshold and over a span of a few tens of electronvolts approaches the positive limit (p = +2), essentially monotonically. Empirically, small distinctions between a and n orbital ionizations can be discussed, and of course there are many significant exceptions to such broad expectations. In contrast, there is clearly far more variability, and much less inmitive predictabihty in the detail of the curves we have seen. That being the case, while suggested shape resonant features in a and p parameter curves can sometimes apparently map onto features in the curves [55, 57, 60] these are no more prominent than other structure and seem unlikely, by themselves, to provide visual clues to the presence of a resonance. 

Since these formal bases, which are supposed to describe the true continuum background, will be represented upon finite sets, all the qnantities which must be interpolated from these representations (i.e. matrix elements and phaseshifts) must be smooth functions of the energy index this reqnires a snitable redefinition of the channel hamiltonian Hp if this supports narrow shape resonances. 

Prior knowledge allows to include fixed relations between some of the four parameters (amplitude, phase, frequency position, peak width) describing a symmetrical well-shaped resonance. Signal ratios, chemical shift difierences, linewidth relations and zero-order phase relations can be included. The reduction of the number of unknown parameters leads to a reduced calculation time, better convergence behaviour and improved results. However, the assumptions made to include the prior knowledge must be validated for each experiment. Differences between the parameter values set by the prior knowledge and the actual parameters could lead to systematic errors. 

By scattering within molecular solids and at their surfaces, LEE can excite with considerable cross sections not only phonon modes of the lattice [35,36,83,84,87,90,98,99], but also individual vibrational levels of the molecular constituents [36,90,98-119] of the solid. These modes can be excited either by nonresonant or by resonant scattering prevailing at specific energies, but as will be seen, resonances can enhance this energy-loss process by orders of magnitude. We provide in the next two subsections specific examples of vibrational excitation induced by LEE in molecular solid films. The HREEL spectra of solid N2 illustrate well the enhancement of vibrational excitation due to a shape resonance. The other example with solid O2 and 02-doped Ar further shows the effect of the density of states on vibrational excitation. 

The point at which the kinetic energy equals the well depth is indicated by e in Fig. 46. At lower energies the expected increase in the ionization cross section is observed. The sharp peaks superimposed on the gradual rise are the result of orbiting or shape resonances. They are caused by... 

Depending on the kind of the intermediate molecular ion, all resonance processes can be divided into two groups.116 The first group is the so-called shape resonances, where the electron is trapped in a potential well formed in the ground electron state of the molecule by centrifugal or polarization forces. The lifetime of such states is between 10 15 and 10 s. 

Feshbach shape resonance in the exchange-like off-diagonal interband pairing term, as predicted since 1993, appears to be the mechanism for evading temperature decoherence effects and enhancing the critical temperature. 

FESHBACH SHAPE RESONANCES IN MULTIBAND HIGH Tc SUPERCONDUCTORS... 

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