Glaubere−+ He Elastic Scattering Amplitude: A Useful Integral Representation

New analytic methods for reducing the Glauber amplitude for charged particle-neutral atom collisions to a one-dimensional integral representation involving modified Lommel functions are proposed. To illustrate these new methods, the reduction of the Glauber amplitude for $e^{-}$ + He elastic scattering, using a simple Hylleraas wave function for the He ground state, is described in detail, and the resulting integral for the amplitude is evaluated numerically. The Glauber-approximation-predicted elastic scattering amplitude previously calculated by Franco from a three-dimensional integral representation, with a more complex Hartree-Fock wave function for the ground state, is also recalculated using these new procedures; these results are in good agreement with those obtained by Franco. Thus, the utility and practicality of these new techniques are demonstrated. The application of these procedures to more general charged particle-neutral atom collisions is discussed.