Abstract
The coupled equations of the semi-classical two-state approximation (with velocity of relative motion treated as constant) are considered. It is shown that the probability of a transition occurring for given impact parameter may be expressed in terms of the solutions to these equations at the point where the colliding atoms are closest. The formula obtained is rather similar to, but has revealing differences from, the corresponding formula of the Landau-Zener approximation. The significance of the differences is discussed. Detailed calculations are carried out on H + Be2+ -> H+ + Be+ and on H + Mg2+ -> H+ + Mg+. The cross-section-energy curve for the first has a single peak, the magnitude of which is almost twice that given by the Landau-Zener approximation; that for the second has two widely separated peaks.
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