OVERLAPPING-RESONANCE SCATTERING AND STATISTICAL-THEORY OF UNIMOLECULAR DECOMPOSITION

A random matrix model of unimolecular decomposition is investigated ba sed on the Feshbach theory of resonant scattering. Energies of zero-th order quasi-bound states are randomly distributed, and coupling matri x elements between these quasi-bound states and continua are generated by Gaussian random numbers. The average decay rate of the quasi-bound states exhibits systematic behavior as a function of density of quasi -bound states, average magnitude of the coupling and number of continu a. The average decay rate coincides with the one predicted by the stat istical theory of unimolecular decomposition (RRKM theory) when the me an spacing of the quasi-bound states is comparable with the average re sonance width. Under this condition, the spectrum of the quasi-bound s tates is most diffuse, and we can neither resolve each quasi-bound sta te nor even distinguish resonant collision from direct one clearly.