4. Thomas A. Heim, A. R. P. Rau, Pair‐Rydberg Description of Doubly Excited States and the Six‐Dimensional Coulomb Problem

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Volume 13: Pages 358-366, 2000

PairRydberg Description of Doubly Excited States and the SixDimensional Coulomb Problem

Thomas A. Heim 1, A. R. P. Rau 2

1Institute of Physics, University of Basel, CH4056 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 wavefunctions for doubly excited twoelectron 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 sixdimensional 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