Theory of asymmetric electron capture collisions

The current status of the theory of electron exchange between two nuclei in collision is reviewed. Special attention is given to the case where the projectile nuclear charge Zsub(p) is much smaller than the target nuclear charge Zsub(T). It is shown that fundamental difficulties arise from an expansion of the T-matrix element for electron exchange in powers of the small quantity Zsub(p)/Zsub(T). However, the expansion of the T operator itself may be so arranged as to collect all terms of a given order in Zsub(p)/Zsub(T). The outstanding problem of the theory of electron exchange in the case Zsub(p) approx. = Zsub(T) is discussed briefly. (author)