Two-electron atoms: From resonances to fragmentation

Semiclassical initial value calculations of the collinear helium atom

“…[6,7] These and subsequent works have enabled the quantization of a large number of bound and resonance states of the atom. [1,6,7,8,9] Although other restricted-configuration coplanar studies have been carried out, [10] most recent semiclassical treatments are based on a collinear model for the classical motion of the electrons, with corrections added for stable motion in the remaining degrees of freedom. [1] Collinear helium can exist in two configurations:…”

“…Semiclassical quantization in this case was performed by a periodic orbit cycle expansion technique. [6,7,8] • The Zee configuration, characterized by the two electrons on the same side of the nucleus. This configuration is implicated in the quantization of certain resonance states with maximal negative values of K. In strong contrast to the eZe case, the classical behavior for the Zee configuration is nearly integrable, with invariant tori centered about a stable periodic orbit describing the so-called "frozen planet" motion.…”

The interelectronic angle in doubly excited states: towards higherN

“…The dynamics in the neighborhood of the collinear subspaces is thus essentially decoupled from the rest of the full phase space. The coupling between all coordinates in the equation of motion increases when θ 12 approaches π/2 and the dynamics becomes ergodic and chaotic on the full five-dimensional energy manifold (Rost and Tanner 1997). A closer inspection of the collinear configurations themselves shows that the Z-e-e phase space is dominated by one stable island, whereas the dynamics of the e-Z-e configuration is completely chaotic (Richter et al 1993).…”

“…The stable periodic orbit which is connected to the collinear Z-e-e configuration plays a central role in the current understanding of the He atom (Richter and Wintgen 1991, Rost and Tanner 1997, Grémaud and Gaspard 1998. It was earlier identified with the quantum (N, K) A = (N, −N + 1) + states through their energies (Richter et al 1992) and through a scaled power spectroscopy using the 'exact' quantum mechanical solutions as input (Qui et al 1996).…”