We consider the influence of long range forces on the total cross section for a two-state curve crossing process. If the upper potential curve V 22(R) is attractive and behaves as R -n for R beyond the crossing point, a centrifugal barrier will arise which affects the cross section. Using the Landau-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 for n = 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 of n, and the potential at the crossing point. © 1979 American Institute of Physics.