Energy transfer in radiation chemistry. I. Dynamics of the electron-oscillators system

Single-mode excitation events in radiation chemistry are investigated by considering a simple model: an electron (characterized by mass m and momentum ℏk) in interaction with a collection of harmonic oscillators. The Hamiltonian corresponding to this model is identified, and then used within the framework of a master equation constructed from the time-dependent Schrödinger equation. The usual long-wavelength approximation is employed, which, in the infinite-system limit, necessitates an upper bound on the frequency spectrum of the oscillator bath. Once these constraints have been imposed, however, the time evolution of the system is determined exactly (i.e., no ``weak-coupling'' approximation) in two limiting regimes-the case of a low-energy incident electron and that of a high-energy incident electron. Our results are compared with those obtained using a weak-coupling approximation, first within the framework of the master equation cited above and then in conjunction with the Prigogine-Résibois master equation, and it is pointed out that for the system under study, the use of a weak-coupling approximation in both equations leads to unphysical results. Our results are also compared with those obtained earlier by Van Hove and co-workers on the electron-random scatterers model, and an attempt is made to understand the role of the approximations introduced in both models. Finally, suggestions for future work are given; in particular, we discuss the generalization of our approach to deal with multiple-mode excitation events in radiation chemistry.