On the relation between unimolecular reaction rates and overlapping resonances

Abstract

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 /ℏ’’ 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.