The resonance charge exchange in ion-atom collisions

On the basis of qualitative reasoning we might think that the probability of charge exchange per unit time, W(p), is proportional to the probability of electron transition through the potential barrier (Fig. 5), i.e. 

This formula, obtained by Sena [17], correctly describes the dependence of the resonance charge exchange cross-section on the velocity of the colliding 

The quantitative theory of resonance charge exchange has been developed by Firsov [18]. The basis for calculations was the fact that, when the energies of the colliding particles relative motion are small, the solution of the time-dependent Schrodinger equation appears to be the wave function  

From eqns. (11) and (12), it follows that the probability of charge exchange is 

The charge exchange cross-section is determined by large impact parameters. This is why, in the course of the calculation of the integral in eqn. (13), it is possible to use the approximation of rectilinear trajectories. Taking into account also the exponential dependence of AW on the interatomic distance, Ml exp( - yR), we have 

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