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.