On the relation between unimolecular reaction rates and overlapping resonances

Abstract

Response to "Comment on 'On the relation between unimolecular reaction rates and overlapping resonances'" [Comment on "On the relation between unimolecular reaction rates and overlapping resonances" [J. Chem. Unimolecular decay processes are studied in the regime of overlapping resonances with the goal of elucidating how. unimolecular reaction rates depend on resonances widths (the imaginary part of the Siegert eigenvalues). As illustrated analytically for one-dimensional models and numerically for a more general random matrix version of Feshbach's optical model, transition state theory (TST, Rice-Ramsperger-Kassel-Marcus) provides the correct average unimolecular decay rate whether the resonances are overlapping or not. For all studied cases, the explicit "universal" dependence of the TST average rate on the average resonance width (for a given energy, or an energy interval) is that of a saturation curve: in the regime of nonoverlapping resonances (i.e., weak coupling) the standard relation "unimolecular decay rate=resonance width Iii" holds, but as the resonance overlap increases (strong coupling) the rate saturates, becoming practically independent of the average resonance width in the strong overlapping limit. On the basis of these conclusions, a discussion of what has been or can be measured in experiments of unimolecular decay that relates to the average decay rate and to the resonance widths is given.

Quantum dynamics of ArI2 vibrational predissociation including low total angular momenta: The role of intramolecular vibrational energy redistribution

“…Of course, as the statistical limit is approached the resonances become not only energetically denser, but their widths begin to overlap, leading to potentially interesting features. 28,29 Our current work is aimed at addressing such issues. 26 It is also possible that coupling VP with EP might also have a smoothing effect.…”

Statistical aspects of ultracold resonant scattering

“…In this energy-domain picture, the resonance widths are related, sometimes in a subtle way, to the Hamiltonian matrix elements W µa that couple a bound resonant state µ of the collision complex, to a scattering state a [26][27][28]. In the random matrix theory of nuclear scattering, these matrix elements are themselves random numbers, distributed about a mean resonance widthΓ.…”

Dynamic aspects of electronic predissociation

“…Work concerning the relation between exact rate expressions and statistical microcanonical expressions for the rate 23 is an interesting and active field of research. 24,25 …”