Long-lives resonances

Mowrey R C and Kouri D J 1987 Application of the close coupling wave packet method to long lived resonance states in molecule-surface scattering J. Chem. Phys. 86 6140... 

Consider next the limit of weak dipole coupling of the initial state with the continuum and/or long-lived resonances, where the direct amplitudes are small as compared to the resonance-mediated ones in the vicinity of a resonance. Returning to Eq. (43) and neglecting the direct-direct and direct-resonant interferences as compared to the resonant-resonant interference at E E j., we have... 

Many bimolecular and unimolecular reactions are dominated by long-lived resonances. As a result, having knowledge about the positions and lifetimes of such resonance states is highly desired. Recursive calculations of resonance states have been reported for many molecular systems, including... 

When a positron encounters normal matter it eventually annihilates with an electron after a lifetime which is inversely proportional to the local electron density. In condensed matter lifetimes are typically less than 500 ps, whilst in gases this figure can be considered as a lower limit, found either at very high gas densities or when the positron forms a bound state or long-lived resonance with an atom or molecule. 

Periodic orbits also explain the long-lived resonances in the photodissociation of CH.30N0(S i), for example, which we amply discussed in Chapter 7. But the existence of periodic orbits in such cases really does not come as a surprise because the potential barrier, independent of its height, stabilizes the periodic motion. If the adiabatic approximation is reasonably trustworthy the periodic orbits do not reveal any additional or new information. Finally, it is important to realize that, in general, the periodic orbits do not provide an assignment in the usual sense, i.e., labeling each peak in the spectrum by a set of quantum numbers. Because of the short lifetime of the excited complex, the stationary wavefunctions do not exhibit a distinct nodal structure as they do in truly indirect processes (see Figure 7.11 for examples). 

As in Chapter 9 we discuss first the elastic limit (no exit channel excitation) in Section 10.1 and subsequently the more interesting inelastic case in Section 10.2. In Section 10.3 we consider the decay of long-lived resonance states and the impact of exit channel dynamics on the product distributions. A simple approximation, the so-called impulsive model, which is frequently employed to analyze experimental distributions in the absence of a PES, is discussed critically in Section 10.4. The chapter ends with a more qualitative assessment of thermal broadening of rotational state distributions in Section 10.5... 

Schinke, R., Untch, A., Suter, H.U., and Huber, J.R. (1991). Mapping of transition-state wave functions I. Rotational state distributions following the decay of long-lived resonances in the photodissociation of HONO(Si), J. Chem. Phys. 94, 7929-7936. 

These times are only a factor of 2-3 greater than the time for an electron with 5 eV of kinetic energy to travel a distance equal to the "size" of the naphthalene molecule. Hence the wavefunctions associated with these very short-lived resonances have much less localization of charge in the molecular region than do those associated with long-lived resonances. As a result, the short-lived resonances undergo less electronic relaxation of the charge density associated with the neutral molecule. 

It is interesting to investigate the lineshape behavior of a long-living resonance near the phase separation critical point in a binary mixture. In binary mixtures, the differing molecules push out the coordinate sphere of the... 

To treat real molecules the theory must be extended to typical unbounded Hamiltonian systems, for which we expect there to be long-lived resonances associated with the quasi periodic islands in the classical description. 

Moreover, ffiso is predicted to peak at E,r) 10 K while decaying exponentially onwards, thus manifesting a non-capture behavior. Such a behavior has been attributed to isomerization, since most trajectories form a H-bond complex while transiting to the covalent minima at low energies (see Figure 17.10). It may also lead one to expect long-lived resonances, since some intramolecular... 

From this discussion it becomes quite clear that the fundamental expression of statistical unimolecular rate theory in equation (46) is an average quantity. When considered as an energy average over many isolated long-lived resonance scattering states in the interval A , one has the inequality (48) ... 

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