Coulomb corrections in quasi-elastic scattering based on the eikonal expansion for electron wave functions

Abstract

An eikonal expansion is developed in order to provide systematic corrections to 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 and for the Dirac equation with a Coulomb potential. Convergence is rapid at energies above about 250 MeV. Analytical results for the eikonal wave functions are obtained for a simple analytical form of the Coulomb potential of a nucleus. They are used to investigate distorted-wave matrix elements for quasi-elastic electron scattering from a nucleus. Focusing factors are shown to arise from the corrections to the eikonal approximation. A precise form of the effective-momentum approximation is developed by use of a momentum shift that depends on the electron's energy loss.

17 pages, 8 figure

References in corpus (3)

• Approximate treatment of electron Coulomb distortion in quasielastic (e,e') reactions
• Extraction of Structure Functions from Quasielastic Electron Scattering (e,e') from Medium and Heavy Nuclei
• Improved effective momentum approximation for quasielastic (e,e') scattering off highly charged nuclei

Cited by in corpus (5)

• Inclusive quasi-elastic electron-nucleus scattering
• Second-Order Eikonal Corrections for A(e,e'p)
• Coulomb corrections in quasi-elastic scattering: tests of the effective-momentum approximation
• Small-angle scattering and quasiclassical approximation beyond leading order
• Eikonal analysis of Coulomb distortion in quasi-elastic electron scattering