Unified theoretical treatment of dissociative recombination of $D_{3h}$ triatomic ions: Application to ${\mathrm{H}}_3^{+}$ and ${\mathrm{D}}_3^{+}$

The dissociative recombination of an ${\mathrm{H}}_3^{+}$ ion after it is struck by a low-energy electron is important for understanding observations of ${\mathrm{H}}_3^{+}$ in diffuse interstellar clouds. At the same time, it is the simplest triatomic ion and for this reason its theoretical description can serve as a prototype for other polyatomic ions. Meanwhile, experimental determinations of the recombination rate have varied widely, which has resulted in some controversy and confusion. Until recently, it seemed unlikely that this problem could be resolved by theoretical studies because the mechanism of ${\mathrm{H}}_3^{+}$ dissociative recombination remained unclear. A recent study, however [Kokoouline et al., Nature (London) 412, 891 (2001)], provided evidence that the inclusion of the Jahn-Teller coupling can produce a dissociative recombination rate that overlaps the range of experimental observations. Here, we propose a theoretical description of the coupling between nuclear and electronic degrees of freedom in a polyatomic molecule, which describes the competition between autoionization and predissociation of the Rydberg states formed after an incident electron is captured. The method treats the vibrational and rotational excitations of the ion, accounts for all symmetry restrictions imposed by the geometry of the molecule, including vibrational, rotational, and electronic and nuclear-spin symmetries. The framework combines the multichannel quantum-defect theory, the adiabatic hyperspherical approach, and the techniques of outgoing-wave Siegert pseudostates. The proposed method can be applied to studies of dissociative recombination of other triatomic ions, including all the degrees of freedom quantum mechanically. Our calculations of the cross section and the recombination rate confirm that the Jahn-Teller effect is responsible for the large rate in ${\mathrm{H}}_3^{+}.$ Theoretical results for dissociative recombination of ${\mathrm{H}}_3^{+}$ are in agreement with storage-ring experiments.