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Volume 13: Pages 358-366, 2000
Pair‐Rydberg Description of Doubly Excited States and the Six‐Dimensional Coulomb Problem
Thomas A. Heim 1, A. R. P. Rau 2
1Institute of Physics, University of Basel, CH‐4056 Basel, Switzerland
2Department of Physics and Astronomy, Louisana State University, Baton Rouge, Louisiana 70803 U.S.A.
Despite considerable success in calculating energies, any approach attempting adiabatic separation in hyperspherical coordinates has severe limitations in the determination of wave‐functions for doubly excited two‐electron systems, irrespective of whether the channel potentials are constructed diabatically or adiabatically. In particular, we show in the present work that cross sections for photo double excitation calculated within such an approach are found to be exponentially small, which contradicts experimental observation. An alternative description basedon the characteristics of the six‐dimensional Coulomb problem is proposed. Here too, the two electrons are treated as a pair throughout, but in addition the familiar degeneracies in the Coulomb spectrum are exploited to explain why the adiabatic hyperspherical separation approach fails to reproduce the photoexcitation cross sections, and how to overcome this limitation.
Keywords: doubly excited states, photoexcitation, hyperspherical methods
Received: May 1, 2000; Published online: December 15, 2008