The method of hyperspherical coordinates is used in obtaining very highly excited two-electron adiabatic potential curves up to the n=12 hydrogenic threshold. The present numerical effort exploits the analytic nature of the solutions to the Schrödinger equation at small and large distances to diagonalize the hyperspherical Hamiltonian in the combined basis set. Numerical deficiencies resulting from a linear dependency of the total nonorthogonal basis set are overcome in an automatic fashion. A high degree of diabaticity is observed which limits the channel interaction to within a select set of hyperspherical channels. The validity of this quasiconstant of motion as reported by H. R. Sadeghpour and C. H. Greene (SG) [Phys. Rev. Lett. 65, 313 (1990)] for ${\mathrm{H}}^{\mathrm{-}}$ is investigated for the photoabsorption of He and higher-z members of the He isoelectronic sequence. A generalized two-electron Rydberg formula capable of predicting the positions of the dominant He (ridge and valley) resonances is given. A new feature of the very-highly-excited resonance structure for ${\mathrm{H}}^{\mathrm{-}}$ and He [observed only recently by Domke et al., Phys. Rev. Lett. 66, 1306 (1991)] is discussed. Semiempirical multichannel-quantum-defect fits are also made to the photodetachment spectra of ${\mathrm{H}}^{\mathrm{-}}$, supporting the conclusions reached in SG.

• Received 1 November 1990

DOI:https://doi.org/10.1103/PhysRevA.43.5821