Application of Many-Body Green's Functions to the Scattering and Bound-State Properties of Helium

The approximation scheme suggested by Schneider, Taylor, and Yaris is applied to the scattering and the bound-state properties of the helium atom. Elastic scattering phase shifts for $s$, $p$, and $d$ partial waves, ionization potentials, one-electron ground-state properties (i.e., electron densities, the natural orbitals, and the ground-state energy), and excitation energies from the ground to the excited states of helium have been calculated simultaneously from the linear-response function and one-particle Green's function. This simultaneity is made possible by concentrating all computational effort on calculating the one- and two- particle amplitudes rather than on the ground- and excited-state wave functions. These amplitudes can be directly related to almost all the properties of physical interest in atomic and molecular systems. Our results for both the scattering- and stationary-state properties are in good agreement with experiment and other previous calculations.