Eikonal model for projectile-electron excitation and loss in relativistic collisions

We present an eikonal model for electron excitation and loss from highly charged ionic projectiles colliding with atomic targets at relativistic collision energies. In this model the distortion of the target transition four-current by the strong field of the projectile nucleus is taken into account using the symmetric eikonal approximation. General expressions are derived for the eikonal transition amplitude in the case of collisions with one- and two-electron targets. The correspondence between the eikonal and first-order transition amplitudes is discussed. Relativistic features and the nonrelativistic limit of the eikonal transition amplitude are considered. It is shown that the higher-order terms in the projectile-target interaction, which are not accounted for by the first-order amplitude, may be of importance even for quite small values of ν=Z_p∕v, where Z_p is the charge of the projectile nucleus and v the collision velocity.