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An eikonal expansion is developed in order to provide systematic correctionsto the eikonal approximation through order 1/k^2, where k is the wave number.The expansion is applied to wave functions for the Klein-Gordon equation andfor the Dirac equation with a Coulomb potential. Convergence is rapid atenergies above about 250 MeV. Analytical results for the eikonal wave functionsare obtained for a simple analytical form of the Coulomb potential of anucleus. They are used to investigate distorted-wave matrix elements forquasi-elastic electron scattering from a nucleus. Focusing factors are shown toarise from the corrections to the eikonal approximation. A precise form of theeffective-momentum approximation is developed by use of a momentum shift thatdepends on the electron's energy loss.Comment: 17 pages, 8 figur

Coulomb corrections in quasielastic scattering based on the eikonal expansion for electron wave functions