Screened Coulomb scattering in the eikonal approximation

Abstract

Scattering amplitudes and cross sections for screened Coulomb potentials are examined using the eikonal approximation. We use the method of $h$ transforms to show that if the screening function is sufficiently smooth, then the screened cross section ${\ensuremath{\sigma}}_{\ensuremath{\rho}}$ approaches the Coulomb cross section ${\ensuremath{\sigma}}_{C}$ as the screening radius $\ensuremath{\rho}\ensuremath{\rightarrow}\ensuremath{\infty}$. On the other hand, for a sharply cut-off Coulomb potential ${\ensuremath{\sigma}}_{\ensuremath{\rho}}$ does not approach ${\ensuremath{\sigma}}_{C}$ as $\ensuremath{\rho}\ensuremath{\rightarrow}\ensuremath{\infty}$. These results agree with results obtained earlier using the Born approximation.