Cross sections for excitation of thenD1states of helium by electron impact and polarization of the resulting radiation in Glauber theory

Recently developed analytic methods, which reduce the Glauber amplitude for charged-particle-neutral-atom collisions to a one-dimensional integral representation involving modified Lommel functions, are used to evaluate the cross sections for the direct excitation of $3{}_{}{}^1{}_{}{}^{}D$ and $4{}_{}{}^1{}_{}{}^{}D$ states of helium by electron impact with incident energies from 40 to 1000 eV. It is shown that the Glauber amplitudes can be written in terms of three generating functions: One of these has already been derived by Thomas and Chan; the detailed reduction of the other two is given in this paper. Comparison is made with the Born, Ochkur, and Woollings-McDowell approximations. The polarization fraction of the 6678-Å helium line emitted in $e^{-}$+He collisions is also calculated in the Glauber approximation. The agreement between theory and experiment is less than satisfactory in the entire energy region.