Collisions between negative and positive atomic ions are investigated. The
ionic wave function is expressed in terms of the Coulomb Green's function.
Normalizing this function allows the system of two ions to be described com
pletely. The exchange matrix elements turn out to be the sums of products o
f the Coulomb wave functions over degenerate states. These sums are express
ed in terms of the quadratic form of the wave function for a state with zer
o angular quantum numbers, l = m = 0. The nonadiabatic coupling of quasi-cr
ossing terms with other terms of the system is analyzed; this effect signif
icantly increases the cross section for single-electron capture. (C) 2001 M
AIK "Nauka/Interperiodica".