Relativistic eikonal phase factors for electron capture

Abstract

The relativistic Born series for the transition amplitude for electron capture is summed using approximations which permit the closure relation to be used, thus producing the relativistic symmetric eikonal approximation. Two different forms of the prior eikonal phase factor are obtained. One form includes the operator which transforms the interaction potential from the projectile frame to the target frame while the other form does not. It is demonstrated that both forms provide legitimate and closely equivalent expressions for the transition amplitude for electron capture assuming that 'soft' elastic collisions occur before and after electron capture takes place.