Path-integral approach to resonant electron-molecule scattering. II. Second-order cumulant approximation and multimode applications

The real-time path-integral formulation of resonant electron-molecule scattering presented previously [Winterstetter and Domcke, Phys. Rev. A 47, 2838 (1993)] is extended to the second order of the cumulant expansion and to the case of many vibrational modes within the harmonic-oscillator approximation. The performance of the path-integral method is demonstrated for several models of electron-molecule shape resonances including up to five vibrational degrees of freedom. The coupling of the electronic tunneling dynamics with many vibrational modes is shown to result in an additional damping of the time-dependent correlation functions. Nontrivial multimode effects in the inelastic electron-molecule scattering cross sections are demonstrated for a model example.