Theory of vibrational relaxation processes in resonant collisions of low-energy electrons with large molecules

Abstract

The effect of intramolecular vibrational relaxation in resonant collisions of low-energy electrons with large molecules is investigated. The vibrational relaxation results from the coupling of a few active modes, which are strongly coupled to the electronic degrees of freedom and therefore coherently excited during the formation of the collision complex, to a large number of inactive bath modes. The theory is formulated within the framework of the projection-operator formalism. Starting from a model Hamiltonian which includes all vibrational modes, the bath degrees of freedom are eliminated, using perturbation theory in the system-bath coupling and projection techniques within the bath Hilbert space. The result is an effective-Hamiltonian description of inelastic electron scattering and electron attachment which incorporates vibrational dissipation. In addition, the time-dependent description of resonant electron-molecule scattering is extended to include the possibility of vibrational relaxation in the resonance state. This time-dependent formulation, which is based on the Markovian master equation for the reduced density operator, provides more direct insight into the dynamics of the collision complex. Calculations for simple model systems are performed which yield insight into the characteristic effects of vibrational relaxation on electron scattering and attachment cross sections, as well as on the time-dependent dynamics of shape resonances. In particular, the competition between autodetachment and vibrational relaxation in shape resonances close to threshold is studied in some detail. The inclusion of vibrational relaxation allows us to develop a microscopic dynamical description of the nondissociative capture of low-energy electrons by large molecules.