Ground state and elastic phase shift of the electron-hydrogen system studied in hyperspherical coordinates

Using hyperspherical coordinates and adiabatic expansion methods, we obtain the potential curves for the electron-hydrogen system in ${}_{}{}^1{}_{}{}^{}S$ states. From the lowest potential curve we compute the ground-state energy of ${\mathrm{H}}^{-}$ to be -1.0547 Ry. We also compute the elastic scattering phase shifts at low energies from the same potential curve. Results are very good at low energies. The variations of important correlation effects as the system expands are also investigated.