An improved version of the Glauber-eikonal amplitude for electron-molecule scattering, originally developed by Bhattacharyya and Ghosh, that includes the effects of nonspherical potential terms up to =6 is presented. Application is made to e-H2 scattering at intermediate energies to test a recently proposed, parameter-free, correlation-polarization potential. This potential is based, as suggested by OConnell and Lane, on the hybridization of local-electron-gas theory and the long-range polarization. Results obtained are found to be very encouraging. © 1985 The American Physical Society.