Doubly excited states of the helium atom: statistical properties
(by Benoît Grémaud)


After a short review of the general properties of the doubly excited states of the helium atom and the way they are computed using the complex rotation method, we will focus on their statistical properties. From this analysis, we will show a transition toward a chaotic regime when approaching the double ionization threshold. However, the full chaotic regime is beyond computers capacities, so that the transition is emphasized with help of the stretched helium (i.e. 1D collinear eZe configuration). For this purpose, we have developed a new approach in which the matrix representation of the Hamiltonian is sparse and banded. I will discuss why this point represents a significant improvement over previous methods. Especially, I will show that the transition to the Ericson regime (strongly overlapping resonances) in the 1D helium appears much closer to the double ionization threshold than it is usually thought.