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.