Validity of the Coulomb-Born approximation for (e,2e) reactions

The Coulomb-Born approximation (CBA) is tested against experiment and against the distorted-wave Born approximation (DWBA) for target inner-shell ionization by fast electrons. It is found that the CBA is fairly accurate in the binary region for the heavy systems when relativistic effects play a minor role. However, CBA underestimates the cross sections in the recoil region for the heavy targets, but also in the binary region for light targets. This is caused by an inappropriate representation of the electronic wave functions, and is neither a deficiency of a first-order theory nor due to lack of orthogonality in the present form of the CBA.