Eikonal analysis of Coulomb distortion in quasi-elastic electron scattering

TL;DR

This paper develops a systematic eikonal expansion to correct Coulomb distortion effects in quasi-elastic electron scattering, providing a more accurate approximation method that aligns well with full wave function calculations.

Contribution

It introduces an order $1/k^2$ eikonal correction for Coulomb distortion and derives an effective-momentum approximation that simplifies calculations while maintaining accuracy.

Findings

EMA agrees well with full calculations

Eikonal expansion improves correction accuracy

Effective-momentum approximation is validated

Abstract

An eikonal expansion is used to provide systematic corrections to the eikonal approximation through order $1/k^2$, where $k$ is the wave number. Electron wave functions are obtained for the Dirac equation with a Coulomb potential. They are used to investigate distorted-wave matrix elements for quasi-elastic electron scattering from a nucleus. A form of effective-momentum approximation is obtained using trajectory-dependent eikonal phases and focusing factors. Fixing the Coulomb distortion effects at the center of the nucleus, the often-used ema approximation is recovered. Comparisons of these approximations are made with full calculations using the electron eikonal wave functions. The ema results are found to agree well with the full calculations.