Signature of Quantum Chaos in Helium
Present status : Doubly excited states of He have been measured using 3rd generation synchrotron since 1990's. The highest resonances that have been reported so far were taken by Puttner et al [PRL 2001] for resonances below the N=9 region of He+. The data show strong perturbation from intruder states. There is still no clear evidence that the spectra beginning to show quantum chaos based on the level spacing statistic. Ab Initio calculations cannot go to much higher energies.
What we have done?: We have developed a new theoretical method which would allow us to calculate doubly excited states at much higher N, or closer to the double ionization threshold, say up to N=25 to 40. Our method begins with solving the helium atom using hyperspherical coordinates in the adiabatic approximation. We then introduce approximate diabatization of these curves, and then throw away most of the potential curves that do not interact with the curves of interest. This is possible because the bending motion of the two electrons provides good approximate quantum numbers. Using such truncated calculations we were able to calculate the energy levels to much higher N's. We then analyze the level spacing statistic and evaluate the degree of quantum chaos using the so-called Bredy parameter q. We showed that reaching the Wigner distribution of q=1 is very slow.
Here is a He-chaos.pdf file to show our preliminary results. By analyzing levels between N=15 to 20 thresholds, we showed that q=0.66 for the singlet S states.