Quantum-mechanical statistical theories for chemical reactivity: overlapping resonances

A unified analysis of the link between the statistical concept of microcanonical reaction rate constant and the collisional concepts of resonance width and resonance overlap is presented. It allows one to propose an interpretation to a recent controversy, according to which the transition state theory rate constant saturates, either when the discrete-continuum coupling terms increase and the transmission coefficients individually tend to one (Peskin, Reisler and Miller, J. Chem. Phys., 1997, 106, 4812), or when the increase of the discrete-continuum coupling terms induces the saturation of the mean resonance width because of the trapping effect (Rotter, J. Chem. Phys., 1997, 106, 4810). Both proposals may be true, depending on which definition of the resonance widths, energy gaps and resonance overlaps the discussion is referred to: either from the zero-order discrete states, whose widths are perturbationally estimated at the level of the golden rule, or from a set of narrow resonances appearing as a consequence of the trapping effect. In the unified interpretation, important roles are played by the penetration matrix of Satchler (Phys. Lett., 1963, 7, 55) and by the correlation width of Moldauer (Phys. Rev. C, 1974, 11, 426), two ingredients often used in nuclear physics literature.