Asymptotic behavior of charge-exchange amplitude

The eikonal approximation in the distorted wave formalism is modified for application to three-particle scattering with rearrangement in the region in which neither the Born nor the adiabatic approximation is valid. The long-range effects due to Coulomb interaction between the particles in both the entrance and exit reaction channels are investigated. The leading asymptotic term (in the large impact parameter) of the eikonal charge exchange amplitude is calculated for transitions between $s$ states of atoms. It is shown that the general expression for the amplitude correctly describes both limiting eases $v\ll v_0$ and $v\gg v_0$.