Electron-Pair Analysis for Doubly Excited Ridge States.

We study doubly excited states of atoms and negative ions by electron-pair analysis. The two-electron Schrodinger equation is analyzed in hyperspherical coordinates, with the electrons described throughout as a pair. In contrast to the current adiabatic hyperspherical method, which reverts at large distances to a description in terms of individual electrons, the pair aspect is preserved also asymptotically. Whereas the adiabatic potential wells converge to the single ionization limit, we develop potential wells converging to the double ionization limit of the system, and doubly excited states are then viewed as eigenstates of the pair in these wells. At the simplest level, we get series converging to the double ionization limit which are described analytically by a Pair-Rydberg formula, with an effective charge that increases logarithmically with the principal quantum number. In this dissertation, we present the results for $\sp1S,\ \sp{1,3}P\sp{e,o}$ states. Our method consists of first diagonalizing the interaction within degenerate manifolds-here, the three pairs of Coulomb interactions in degenerate manifolds of the so-called grand angular momentum in the hyperspherical space. Similar problems involving other interactions in degenerate atomic and nuclear manifolds have also been considered analogously and are presented in an Appendix. The numerical methods used to solve the Schrodinger equation are Neumann and 5$\sp{th}$ order Runge Kutta. The computers we used for this work are IBM 3090 and SUN workstation. The computing speed is fast compared with other large scale calculations. On an IBM 3090 it only takes a few minutes to get all the potential wells and a few seconds to get an eigenvalue in each potential well. Our method is simple and physically clear. The results are fairly accurate compared with other calculations