Theoretical Method For Solving A 2-Level Collision System

Collisionally induced transitions between two electronic states during atom-atom collisions are described in the near-adiabatic formalism. The two-level system, in the semiclassical impact-parameter method, is represented by time-dependent coupled differential equations which have been studied by many workers. We present a method of solving the system of equations under the approximation of slow variation of the matrix elements responsible for the transition. A general formula for the transition probability is obtained with special reference to the problem of charge transfer, though the result is applicable to other two-level systems. The formula reduces under various special conditions to other well-known expressions, such as those found by Vainshtein and co-workers, the Landau-Zener formula, and that for resonance charge transfer.