Numerical calculations of vibrational levels of alkali dimers close to the dissociation limit are developed in the framework of a Fourier Grid Hamiltonian method. The aim is to interpret photoassociation experiments in cold atom samples. In order to avoid the implementation of very large grids we propose a mapping procedure adapted to the asymptotic $R^{\mathrm{-n}}$ behavior of the long-range potentials. On a single electronic potential, this allows us to determine vibrational wave functions extending up to ${\text{500a}}_0$ using a minimal number of grid points. Calculations with two electronic states, ${\mathrm{A }}^1{\Sigma }_u^{+}$ and ${\mathrm{b }}^3{\Pi }_u$ states, both correlated to the $\mathrm{Rb}\text{(5s)+}\mathrm{Rb}\text{(5p)}$ dissociation limit, coupled by fine structure are presented. We predict strong perturbation effects in the ${\mathrm{Rb}}_{\mathrm{2}}{\text{(0}}_u^{+}$ ) spectrum, manifested under the $\text{5s,}$ ${\text{5p\hspace{0.05em}}}^2{P}_{\text{1/2}}$ dissociation limit by an oscillatory behavior of the rotational constants.

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.

Astronomy & Astrophysics (A&A) is an international journal which publishes papers on all aspects of astronomy and astrophysics

The article presents calculated dissociative recombination (DR) rate coefficients for H3+. The previous theoretical work on H3+ was performed using the adiabatic hyperspherical approximation to calculate the target ion vibrational states and it considered just a limited number of ionic rotational states. In this study, we use accurate vibrational wave functions and a larger number of possible rotational states of the H3+ ground vibrational level. The DR rate coefficient obtained is found to agree better with the experimental data from storage ring experiments than the previous theoretical calculation. We present evidence that excited rotational states could be playing an important role in those experiments for collision energies above 10meV. The DR rate coefficients calculated separately for ortho- and para-H3+ are predicted to differ significantly at low energy, a result consistent with a recent experiment. We also present DR rate coefficients for vibrationally excited initial states of H3+, which are found to be somewhat larger than the rate coefficient for the ground vibrational level.

We propose a fully quantal description of ${\mathrm{H}}_3^{+}$ dissociative recombination. The new method combines multichannel quantum defect theory, the adiabatic hyperspherical approach, and the techniques of outgoing-wave Siegert pseudostates. The vibrational, rotational, nuclear spin degrees of freedom of the ion, in their full dimensionality, are all taken into account for the first time in any calculation of polyatomic dissociative recombination. Our calculation of the recombination rate confirms that the Jahn-Teller effect is responsible for the large rate in ${\mathrm{H}}_3^{+}$. The resulting theoretical rates for dissociative recombination of ${\mathrm{H}}_3^{+}$ are in good general agreement with experiment.