Use of the Optical Potential for Elastic Scattering of Electrons by Atoms

The use of the optical potential for elastic scattering of electrons by atoms is examined. The optical potential is related to the self-energy of the single-particle Green's function and is represented by a perturbation expansion. The optical potential is applied to the elastic triplet-state scattering of S-wave electrons from hydrogen. The Hartree-Fock potential is used to calculate the single-particle states of the perturbation expansion. It is found that the second-order optical-potential terms calculated with the Hartree-Fock potential are not sufficient to give good agreement with accurate results obtained by the variational calculations of Schwartz. The higher-order terms for the optical potential are evaluated by methods used in previous atomic many-body calculations, and good agreement with the variational results is then obtained.