Path-integral approach to resonant electron-molecule scattering.

Abstract

A path-integral formulation of resonant electron-molecule scattering is developed within the framework of the projection-operator formalism of scattering theory. The formation and decay of resonances is treated in real time as a quantum-mechanical electronic-tunneling process, modified by the coupling of the electronic motion with the nuclear degrees of freedom. It is shown that the electronic continuum can be summed over in the path-integral formulation, resulting formally in the path integral for an effective two-state system with coupling to vibrations. The harmonic-oscillator approximation is adopted for the vibrational motion in the present work. Approximation methods are introduced which render the numerical evaluation of the sum over paths feasible for up to [approx]10[sup 3] elementary time slices. The theory is numerically realized for simple but nontrivial models representing the [sup 2][Pi][sub [ital g]] [ital d]-wave shape resonance in [ital e][sup [minus]]+N[sub 2] collisions and the [sup 2][Sigma][sub [ital u]][sup +] [ital p]-wave shape resonance in [ital e][sup [minus]]+H[sub 2] collisions, respectively. The accuracy of the path-integral results is assessed by comparison with exact numerical reference data for these models. The essential virtue of the path-integral approach is the fact that the computational effort scales at most linearly with the number of vibrationalmore » degrees of freedom. The path-integral method is thus well suited to treat electron collisions with polyatomic molecules and molecular aggregates.« less