Hyperspherical coordinate theory of two electron atomic processes. Progress report, 1 August 1983-31 July 1984

Electron correlations are studied in two-electron atoms using theoretical methods employing hyperspherical coordinates. The doubly differential cross section for detachment of H- by impact with He is studied using adiabatic hyperspherical coordinate initial and final state wavefunctions to compute the H- form factors. The detached electron's angular distribution is highly sensitive to electron correlations. A pseudo-state method is developed to correct the gross inaccuracies of adiabatic hyperspherical wavefunctions at large radial distances. This procedure yields significantly improved 1S elastic phase shifts for electron scattering on atomic hydrogen. The Fock series expansion for two electron wavefunctions has been successfully implemented numerically. When matched to single channel adiabatic functions for some radius R0, the Fock wavefunctions for He and H- differ little (for O < R < R0) from the adiabatic wavefunctions, at least for the lowest adiabatic channels. This confirms recent results of Christensen-Dalsgaard. The R-matrix for sytems of coupled differential equations containing first derivative coupling matrix elements is found to be asymmetric. An alternative matrix (equal to the sum of the inverse R-matrix and the first derivative coupling matrix) is found to be symmetric. The Wannier threshold energy dependence of cross sections and angular distributions is derived quantum mechanically by J.M. Feagin for the Coulomb breakup of three-particle systems with arbitrary angular momentum. 8 references, 3 figures