Very Highly-Excited States of Two-Electron Systems
The delicate balance that exists between the forces mediating the interaction within multiply-excited electrons and the binding forces of these electrons to the nucleus is totally ignored in the independent particle model of electronic interactions. This dynamical "see-saw" is best described in the hyperspherical representation. We use this method to obtain hyperspherical potential curves, analogous to the Born-Oppenheimer curves of molecular species, for very highly-excited two-electron states of the hydrogen negative ion, helium, and calcium. The present numerical effort exploits the analytic nature of the solutions to the Schroedinger equation at small and large distances to diagonalize the hyperspherical Hamiltonian in the combined representative basis functions. Numerical deficiencies resulting from linear dependency of the total basis set are overcome in an automatic fashion. In the case of He and H^-, a high degree of diabaticity is observed which limits the channel interaction to within a select set of hyperspherical channels. These dominant channels relevant to photoionization experiments of H ^- and He are identified. Inelastic excitation probabilities to these channels are calculated with (a) coupled-hyperspherical channel method and (b) Landau-Zener method in which only nearest -neighbor coupling is considered. Transition probabilities obtained in the Landau-Zener approximation show monotonic behavior with energy. Correlation effects in H^- and He due to the interaction of an asymptotic electron with a permanent electric dipole moment caused by the orbital momentum degeneracy of hydrogenic levels, are studied in the independent-electron coordinate picture. The correlation between the bound electron and the escaping electron is built in through the long-range dipole operator. The polarization of the fluorescence from photofragments is calculated and is shown to violate propensity rules in certain instances. A preliminary investigation of the correlation effects in Ca is pursued by obtaining highly-excited hyperspherical potential curves for both ^1P ^circ and ^1S ^ e final-state symmetries.
- Pub Date:
- COUPLED CHANNEL INTEGRATION;
- ADIABATIC APPROXIMATION;
- Physics: Atomic