Determination of Non-adiabatic Scattering Wave Functions in a Born-Oppenheimer Model |
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Authors: | George A Hagedorn Alain Joye |
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Institution: | (1) Department of Mathematics and Center for Statistical Mechanics and Mathematical Physics, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061-0123, USA;(2) Institut Fourier, Unité Mixte de Recherche CNRS-UJF 5582, Université de Grenoble I, BP 74, F-38402 Saint Martin d’Hères Cedex, France |
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Abstract: | We study non-adiabatic transitions in scattering theory for the timedependent molecular Schr?dinger equation in the Born-Oppenheimer
limit. We assume the electron Hamiltonian has finitely many levels and consider the propagation of coherent states with high
enough total energy.
When two of the electronic levels are isolated from the rest of the electron Hamiltonian’s spectrum and display an avoided
crossing, we compute the component of the nuclear wave function associated with the non-adiabatic transition that is generated
by propagation through the avoided crossing. This component is shown to be exponentially small in the square of the Born-Oppenheimer
parameter, due to the Landau-Zener mechanism. It propagates asymptotically as a free Gaussian in the nuclear variables, and
its momentum is shifted. The total transition probability for this transition and the momentum shift are both larger than
what one would expect from a naive approximation and energy conservation.
Communicated by Yosi Avron
submitted 14/10/04, accepted 18/01/05
An erratum to this article is available at . |
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