Eikonal approximation for charge transfer from a multielectron atom to fast projectiles

The eikonal approach developed previously for calculating electron-capture cross sections for bare projectiles colliding with hydrogenic targets is extended here to allow for multielectron targets. Both the impact and wave pictures are employed and their equivalence is discussed. As a first approximation, each atomic orbital is specified by the three hydrogenic quantum numbers, an effective nuclear charge $Z_t$, and an energy eigen-value in the impact picture, or ionization potential in the wave picture. The $Z_t^{\prime }$ appearing in the eikonal phase factor is left undetermined because of incomplete information on the many-body target. However, analytic expressions are derived for the theoretical cross sections, and numerical values are calculated for simple choices of $Z_t^{\prime }$. Those results are compared with existing experimental data for C, Ne, Ar, ${\mathrm{N}}_2$, ${\mathrm{O}}_2$, and He targets.