A quantum ergodic theory approach to unimolecular fragmentation

Abstract

Projection operator techniques are used to separate the complete Hilbert space of a molecular system into parts corresponding to bound and continuum states. The equation of motion of the amplitude associated with an initial excitation of the molecule is then formulated; this equation of motion contains memory effects. Although formally exact, its utility lies in the approximations suggested by its structure. Drawing on recent studies of intramolecular relaxation, a Markovian approximation is formulated and the properties of the model so defined investigated by numerical solution. The decay rate for the model is found to depend strongly upon the nature of the initial excitation, and to correlate with the ergodicity or lack of ergodicity of the initial excitation. When the prepared state is nonergodic, or nearly so, there is a delay in the decay of the molecule. When the state initially prepared is ergodic, there is no such delay. Intermediate cases are also found. It is argued that the formal analysis permits the development of better models and of more sophisticated treatments of the competition between intramolecular relaxation and molecular fragmentation, but that the simple model discussed contains the qualitative elements of importance in such processes.