Differential cross sections for high-energy electron capture in the impulse approximation

The eikonal form of the exact impulse approximation to electron capture in heavy-ion collisions has been evaluated. Comparison has been made to the peaked form of the impulse approximation, and the exact and peaked second Born expressions. It is found that there are two prominent features of the differential cross section, which all these approximations reproduce with greater or lesser success; the Thomas peak at scattering angle √3 m/2M (m, electron mass; M, projectile mass), and a minimum in the differential cross section at scattering angle m/2M. The peaked second Born amplitude is further analysed to show that whereas the Thomas peak is classical in origin, the minimum is produced by quantum mechanical interference between the first and second Born amplitudes. Finally the effect of an internuclear Coulomb interaction is considered, and it is shown that though the position of the Thomas peak is shifted by the Coulomb interaction, the peak itself will not be destroyed. (author)