Further contributions of the Thomas double-scattering mechanism to electron capture in the second Born approximation

The double-scattering mechanism of Thomas represents the dominant means in an ion-atom collision at high velocities for the electron-projectile subsystem to rid itself of its large internal kinetic energy and thus allow the electron to be captured. The plane-wave second Born approximation to the single-electron capture amplitude calculated in a linearized-propagator approximation gives the lowest-order quantum estimate of the Thomas mechanism by employing initial and final bound-state momentum values around the center of these distributions along with a neglect of the electronic part of the momentum transfer in the two collisions of the mechanism. It is shown that additional contributions to the amplitude deriving from values of the bound-state momentum in the wings of the distributions are non-negligible and in fact explain the large differences found between exact and linearized-propagator approximation results. Consequently, the second Born approximation is seen to suffer from the same problem as does the first Born approximation, namely, too dominant a contribution of the large bound-state momentum components.