Overlapping Resonances, Multiple Time Regime Evolution Laws and the Sampling of Phase Space in Unimolecular Processes

Abstract

AbstractUnimolecular processes can be described as the decay of an ensemble of N excited resonances coupled to K decay channels. Resonances are metastable states characterized by a complex energy whose real part is the position of the state along the energy axis while the imaginary part gives the individual decay rate of the state. Resonances usually overlap in the RRKM regime. The degree of overlap is measured by the parameter R = <I>/dE where <I> is the average of the individual decay rates of the excited resonances and dE is the average spacing between their position. In the exact degeneracy limit, that is, for an infinite value of R, (N‐K) resonances have a zero width, so that a fraction of the initial excitation remains permanently trapped in the bound subspace. This trapping effect subsists in the non degenerate case but is not complete. We use a random coupling effective Hamiltonian model to discuss the effect of the degree of overlapping R, and of the number of resonances N and decay channels K, on the temporal evolution laws of the bound subspace and of the fragments. The decay law of the bound subspace and the temporal evolution of the yields in fragments exhibit several time regimes. This is due to the fact that after the diagonalization of the effective Hamiltonian, the decay widths of the resonances cluster into one group of K large widths and one group of (N‐K) small ones. The trapping effect is due to the (N‐K) small widths. The amount of trapping depends on the value of the degree of overlapping R, and for a given value of R, on the ratio N/K: large values of R and of N/K correspond to a large amount of trapping in the bound subspace for times long when compared to ħ/<I>. The temporal evolution laws of the yields in fragment are also strongly affected by the degree of overlapping and the value of the ratio N/K. Due to the reorganization of the partial widths which follows the diagonalization of the effective Hamiltonian, we show that the nature of the dominant product can change while increasing the value of R and N/K. We also discuss the time evolution of the sampling of phase space for a specific preparation in terms of these two parameters. The volume sampled is computed using an entropic measure. When the resonances overlap, there is not enough time to completely sample phase space prior to dissociation. The fraction sampled decreases as the amount of trapping in the bound phase space increases.