Path-integral approach to resonant electron-molecule scattering

Journal Article · Thu Apr 01 04:00:00 EST 1993 · Physical Review A; (United States)

DOI:https://doi.org/10.1103/PhysRevA.47.2838· OSTI ID:6653409

Winterstetter, M; Domcke, W ^[1]

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1. Institute of Physical and Theoretical Chemistry, Technical University of Munich, D-8046 Garching (Germany)

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 vibrational degrees of freedom. The path-integral method is thus well suited to treat electron collisions with polyatomic molecules and molecular aggregates.

• OSTI ID: 6653409
• Journal Information: Physical Review A; (United States), Journal Name: Physical Review A; (United States) Vol. 47:4; ISSN 1050-2947; ISSN PLRAAN
• Country of Publication: United States
• Language: English

Related Subjects

664300* -- Atomic & Molecular Physics-- Collision Phenomena-- (1992-)
74 ATOMIC AND MOLECULAR PHYSICS
COLLISIONS
ELECTRON COLLISIONS
ELECTRON-MOLECULE COLLISIONS
ENERGY LEVELS
EXCITED STATES
FEYNMAN PATH INTEGRAL
HARMONIC OSCILLATOR MODELS
INELASTIC SCATTERING
INTEGRALS
MATHEMATICAL MODELS
MATHEMATICAL OPERATORS
MATHEMATICS
MOLECULE COLLISIONS
NUMERICAL ANALYSIS
PROJECTION OPERATORS
RESONANCE SCATTERING
SCATTERING
TUNNEL EFFECT
VIBRATIONAL STATES