Charge transfer in neutral atom-multiply charged ion collisions

The electron transfer in neutral atom-multiply charged ion collisions 

The cross-section of electron transfer to a multiply charged ion can be calculated by solving a set of coupled equations which take into account the probability of electron transfer on to different levels. Such calculations are extremely tedious (for a review, see ref. 21). At the same time, the presence of transitions into a large number of states makes it possible to describe the charge transfer in terms of the formalism, based on the idea of electron tunneling from one potential well to another. Using such an approach, Chibisov [22] has obtained an analytical expression for the charge transfer cross-section. 

During slow collisions, the main contribution to the charge transfer cross-section is made by the impact parameters which exceed the size of a neutral atom. In this case, the potential barrier for tunneling is mainly formed by the electric field of the multiply charged ion in the vicinity of the neutral atom (Fig. 8). This field is equal to F = zjR2. The probability of 

From this equation we can see that, in the problem considered, the characteristic size (in atomic units) is of the order of yfz consequently, the time of collision has the order of y/z/v, where v is the relative velocity of the colliding particles. The probability of charge transfer during the collision with the impact parameter p can be estimated if we multiply the probability of tunneling per unit time by the time of collision 

Equating P(p) to unity, we obtain the characteristic impact parameter, p0, of charge transfer 

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