Jahn-Teller Interactions in the Dissociative Recombination of H$_{3}^{+}$

A simple analytical approach is presented to describe the dissociative recombination (DR) of an electron with H$_{3}^{+}$ and its isotopomers. The principal assumption is that resonant capture mediated by the Jahn-Teller interaction dominates the cross section. The only input required comes from spectroscopic data on the 3pE' Rydberg state of H$_{3}$ and the $\nu _{2}$ vibrational frequencies of H$_{3}^{+}$ and its isotopomers. The approach provides an independent prediction of the low-energy DR cross sections and rates, and is in good agreement with the latest experimental$^{1}$ and theoretical$^{2}$ determinations. Work at Argonne was supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, Division of Chemical Sciences, Geosciences, and Biosciences under contract No. DE-AC02-06CH11357. 1. K. Kreckel et al., Phys. Rev. Lett. \textbf{95}, 263201 (2005); see also, B. J. McCall et al., Nature \textbf{422}, 500 (2003), and B. J. McCall et al., Phys. Rev. A \textbf{70}, 052716 (2004). 2. S. Fonseca dos Santos, V. Kokoouline, and C. H. Greene, J. Chem. Phys. \textbf{127}, 124309 (2007).