Theory of Electronic Transitions in Slow Atomic Collisions

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Abstract
The near-adiabatic transition probability between a pair of pseudocrossing adiabatic (molecular) electronic states is studied be generalizing Zener's time-dependent treatment and describing the heavy-particle motion classically. This more rigorous formalism, based however on the simple Landau-Zener model, leads to the well-known Landau-Zener formula in a first approximation. From a reasonable definition of the width of the finite region over which the transitions take place on the trajectory, a precise condition which inherently limits the validity of the formula is derived. This condition may be compared with similar ones obtained in recent quite different derivations and removes some apparent difficulties which have been raised in connection with earlier treatments. The first correction to the Landau-Zener formula, associated with the finiteness of the transition region, is studied analytically and found to be important and to have interesting properties. This leads to further information about the validity of the simple Landau-Zener expression.

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