Transition states near rank-two saddles: Correlated electron dynamics of helium |
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Authors: | George Haller, T. Uzer, Jesú s Palaci n, Patricia Yanguas,Charles Jaff |
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Affiliation: | aDepartment of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA;bCenter for Nonlinear Sciences, School of Physics, Georgia Institute of Technology, Atlanta, GA 30332-0430, USA;cDepartamento de Ingeniería Matemática e Informática, Universidad Pública de Navarra, 31006 Pamplona, Spain;dDepartment of Chemistry, West Virginia University, Morgantown, WV 26506-6045, USA |
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Abstract: | The phase space structure in the vicinity of a rank-two saddle is explored both analytically and numerically. In particular, the geometry of electron dynamics in the neighborhood of the rank-two saddle associated with the nonsequentual double ionization of helium is analyzed. As in the rank-one saddle case, codimension-one normally hyperbolic invariant manifolds turn out to control the rates of the correlated electron dynamics within each energy surface. The construction of these manifolds, however, is more involved here and requires the use of pseudo-hyperbolic invariant manifold theory. Two distinct correlated motions occur, the nonsequential double ionization and the nonsequential exchange of electrons. The relative rates of crossing the barrier are related to the Lyapunov exponents. The dynamics associated with the larger of the two Lyapunov exponents predominates. |
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Keywords: | Transition state theory Saddles in energy landscapes Correlated motion Double ionization Nonsequential ionization |
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