A harpoon reaction model employing multiple crossings based on the formalism of Bauer et al. [J. Chem. Phys. 51, 4173 (1969)] and Gislason and Sachs [J. Chem. Phys. 62, 2678 (1975)] is developed to explain the large cross sections (σ∼330-975 Å2) measured for the reaction Xe*(5p5np,np′, n = 6,7) + Cl2. The model calculates the Landau-Zener transition probability for each intermediate ionic crossing with the covalent surface. The transition matrix elements are represented as a product of the electronic interaction (modeled by the empirical result of Olson et al. [Appl. Opt. 10, (1971)]) and a Franck-Condon factor for the Cl2-Cl2-transition. The model predicts near unit probability for a transition to the ionic surface for impact parameters less than 20 Bohr. Once transfer occurs, the pair is captured by dissociation of Cl2- to form XeCl*. The large temperature dependence observed qualitatively in the experiments is explained by the increased cross section for vibrationally excited Cl2. A simple model for orbiting collisions is used to estimate the effect of termolecular collisions. © 1990 American Institute of Physics.