Electron capture in asymmetric collisions

A new theoretical approach to calculate electron-capture cross sections is developed to deal with asymmetric collisions. The method consists of introducing the correct Coulomb asymptotic conditions to the peaking impulse approximation. The approach is elaborated to be meaningful, not only at high projectile energies, but also in the intermediate region (i.e., when the ion velocity, in atomic units, is much larger than the smaller Coulomb charge, but about the same order of the larger charge). An integral expression of the $T$-matrix element is obtained after performing a peaking approximation. This element has a closed form for any transition. $K-K$ charge exchange total and differential cross sections are calculated and compared with experimental results. The approach seems to be more reliable than the continuum distorted wave and peaking impulse approximation.