Pair-rydberg description of doubly excited states and the six-dimensional coulomb problem

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 whet her the channel potentials are constructed diabatically or adiabatically. In particular, we show in the present work that cross sections far photo double excitation calculated within such an approach are found to be exponentially small, which contradicts experimental observation. An alternative description based on 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