We consider the influence of long range forces on the total cross section for a twohyphen;state curve crossing process. If the upper potential curveV22(R) is attractive and behaves asRminus;nforRbeyond the crossing point, a centrifugal barrier will arise which affects the cross section. Using the Landaundash;Zener approximation, we derive cross sections accounting for this which can be expressed in terms of a simple dimensionless integral for both radial and rotational coupling. Results for suitably reduced cross sections are presented in a form which facilitates comparison with experiments forn=4, 5, and 6. Analytic expressions for the threshold behavior are also presented. We show that the low energy behavior of the cross section is very sensitive to the type of coupling, the value ofn, and the potential at the crossing point.
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