Calculation of the relativistic rise in electron-impact-excitation cross sections for highly charged ions

Abstract

Exact relativistic plane-wave Born (RPWB) matrix elements of the Møller interaction are incorporated in the “analytic Born subtraction technique” and employed in the relativistic convergent close-coupling method. Application to the calculation of high-energy electron-impact-excitation cross sections of highly charged hydrogenlike ions demonstrates the “Bethe rise,” an effect that is manifest in Bethe's original 1932 work on relativistic high-energy, electron-impact excitation. The result represents an improvement over Bethe's relativistic high-energy theory developed in the 1930s in that (i) both target and projectile electrons are represented relativistically with Dirac spinor wave functions and (ii) the dipole approximation plus additional assumptions are not employed in the RPWB scattering amplitude of the Møller interaction.