Approximation method for molecular collisions in the turning point region

The second order system of coupled differential equations in the close coupling approximation is approximately reduced to a first order unitary system. The procedure is illustrated numerically for a simple system in the vicinity of its turning points. The present work supplements some previous work. Taken together these works provide a fairly simple approximate means of reducing the second order close coupling equation to a unitary first order system over almost all of the range of the collision. The remaining portion of the problem, deep in the forbidden region, can be handled perturbatively