Inelastic scattering of electrons by helium

Bethe-Goldstone continuum equations for the scattering of electrons from helium are solved variationally in the energy range between the $n=2$ and $n=3$ thresholds. Polarization and correlation effects are included in the calculations by allowing for virtual excitation of the $2s$ electron. Shape resonances are found above the $2^{3}S$ threshold, in substantial agreement with close-coupling calculations of Burke, Cooper, and Ormonde. Structures observed immediately below the $3^{3}S$ threshold in experimental cross sections for metastable formation are attributed to several Feshbach resonances whose energies and widths are computed. Cross sections are presented for elastic and inelastic scattering involving the ground state and $n=2$ states of helium. Cusp behavior, expected at various inelastic thresholds and found in the variational calculations, accounts for several prominent structural features in the scattering cross sections. The present computed results are compared with previous theoretical studies and, wherever possible, with experimental data.