Generalization of the Rosen-Zener model of noncrossing interactions. I. Total cross sections

Abstract

The formalism developed previously to study electronic transitions by the curve-crossing mechanism is used to obtain a general model for transitions which take place due to the strong coupling of curves which do not cross. This exactly solvable model is a generalization of a model developed by Rosen and Zener. The model is shown to give respectable agreement with exact calculations at low velocities, and to go to the correct resonant-charge-exchange limit at high velocities. Predictions of the model are shown to give good agreement with the measured total cross sections for charge exchange in the sytem ${\mathrm{Li}}^{+}$ + Na\ensuremath{\rightleftarrows}Li+${\mathrm{Na}}^{+}$.