We present the results of calculations determining the cross sections for indirect dissociative recombination of LiH$_2^+$ + $e^-$. These calculations employ multichannel quantum defect theory and Fano's rovibrational frame transformation technique to obtain the indirect DR cross section in the manner described by Ref.\cite{hamilton}. We use \textit{ab initio} electron-molecule scattering codes to calculate quantum defects. In contrast to H$_3^+$, the LiH$_2^+$ molecule exhibits considerable mixing between rotation and vibration; however, by incorporating an exact treatment of the rovibrational dynamics of the LiH$_2^+$, we show that this mixing has only a small effect on the observed DR rate. We calculate a large DR rate for this cation, 4.0 $\times$ 10$^{-7}$ cm$^{3}$ s$^{-1}$ at 1 meV incident electron energy.
The LiH$^{+}$ molecule is prototypical of the indirect dissociative recombination (DR) process, in which a colliding electron destroys the molecule through Rydberg capture pathways. This Letter develops the first quantitative test of the Siegert state multichannel quantum defect theory description of indirect DR for a diatomic molecular ion. The R-matrix approach is adopted to calculate ab-initio quantum defects, functions of the internuclear distance that characterize both Rydberg states and the zero-energy collisions of electrons with LiH$^{+}$ ions. The calculated DR rate coefficient agrees…
The article presents an improved theoretical description of dissociative recombination of HCO$^+$ and DCO$^+$ ions with a low energy electron. In the previous theoretical study (Phys. Rev. A {\bf 74}, 032707) on HCO$^+$, the vibrational motion along the CO coordinate was neglected. Here, all vibrational degrees of freedom, including the CO stretch coordinate, are taken into account. The theoretical dissociative recombination cross-section obtained is similar to the previous theoretical result at low collision energies ($<$0.1 eV) but somewhat larger at higher ($>$0.1 eV) energies. Therefore, t…
The HeH$^+$ cation is the simplest molecular prototype of the indirect dissociative recombination (DR) process that proceeds through electron capture into Rydberg states of the corresponding neutral molecule. This Letter develops the first application of our recently developed energy-dependent frame transformation theory to the indirect DR processes. The theoretical model is based on the multichannel quantum-defect theory with the vibrational basis states computed using exterior complex scaling (ECS) of the nuclear Hamiltonian. The ab initio electronic R-matrix theory is adopted to compute qua…
The energy-dependent frame transformation theory of Gao and Greene 1990 [Phys. Rev. A {\bf 42}, 6946 (1990)] is extended to yield quantitatively accurate description of the dissociative recombination process. Evidence is presented to show that direct application of the original theory leads to inaccurate cross sections. A major revision, based on an interaction-free back-propagation of the Born-Oppenheimer solutions, markedly improves the frame transformation theory, reducing its average error by orders of magnitude. The original theory and its extension are tested on the previously explored 2…
The HeH$^+$ cation undergoes dissociative recombination with a free electron to produce neutral He and H fragments. We present calculations using ab initio quantum defects and Fano's rovibrational frame transformation technique, along with the methodology of PRL 89, 263003 (2002), to obtain the recombination rate both in the low-energy (1-300 meV) and high-energy (ca. 0.6 hartree) regions. We obtain very good agreement with experimental results, demonstrating that this relatively simple method is able to reproduce observed rates for both indirect dissociative recombination, driven by rovibrati…
An alternative method is introduced to solve a simple two-dimensional models describing vibrational excitation and dissociation processes during the electron-molecule collisions. The model works with one electronic and one nuclear degree of freedom. The two-dimensional $R$-matrix can be constructed simultaneously on the electronic and nuclear surfaces using all three forms developed previously for electron-atom and electron-molecule collisions. These are the eigenchannel $R$-matrix form, inversion technique of Nesbet and Robicheaux, and the Wigner-Eisenbud-type form using expansion over the po…
We experimentally investigate laser-induced dissociative recombination of CO$_2$ in linearly polarized strong laser fields with coincidence measurements. Our results show laser-induced dissociation processes originate from an electron recombination process after laser-induced double ionization. After double ionization of CO$_2$, one electron is recaptured by the CO$_2^{2+}$ and localized to O$^+$ or CO$^+$ in the following dissociation process. We found that the probability of electron localization to O$^{+}$ is much higher than that to CO$^+$. Further, our measurements reveal that the recombi…
We present a simple two-dimensional model of the indirect dissociative recombination process. The model has one electronic and one nuclear degree of freedom and it can be solved to high precision, without making any physically motivated approximations, by employing the exterior complex scaling method together with the finite-elements method and discrete variable representation. The approach is applied to solve a model for dissociative recombination of H$_2^+$ and the results serve as a benchmark to test validity of several physical approximations commonly used in the computational modeling of …
Inelastic low-energy (0--1 eV) collisions of electrons with HeH$^+$ cations are treated theoretically, with a focus on the rovibrational excitation and dissociative recombination (DR) channels. In an application of {\it ab initio} multichannel quantum defect theory (MQDT), the description of both processes is based on the Born-Oppenheimer quantum defects. The quantum defects were determined using the R-matrix approach in two different frames of reference: the center-of-charge and the center-of-mass frames. The results obtained in the two reference systems, after implementing the Fano-Jungen st…
The cross section for dissociative recombination of BeH^+ is calculated by solution of the time-dependent Schrodinger equation in the local complex potential approximation. The effects of couplings between resonant states and the Rydberg states converging to the ground state of the ion are studied. The relevant potentials, couplings and autoionization widths are extracted using ab initio electron scattering and structure calculations, followed by a diabatization procedure. The calculated cross sections shows a sizable magnitude at low energy, followed by a high-energy peak centered around 1 eV…
We estimate rates for the dissociative recombination (DR) of NO$_2^+$ + e$^-$. Although accurate excited state potential energy curves for the excited states of the neutral are not available, we estimate that the 1 $^2$Φ$_g$ and the 1 $^2$Π$_g$ states of the neutral may intersect the ground state cation potential energy surface near its equilibrium geometry. Using fixed nuclei scattering calculations we estimate the rate for direct DR via these states and find it to be significant. We also perform approximate calculations of DR triggered by the indirect mechanism, which suggest that the indire…
Direct dissociative recombination and resonant ion-pair formation reactions of $\mathrm{HeH^+}$ are theoretically studied using time-dependant wave-packets methods. The wave packets are propagated on potential energy curves that are in either the adiabatic representation or the diabatic representation. The reaction cross sections are computed for collisions of different isotopes of $\mathrm{He}$ and $\mathrm{H}$. The reactions are modeled in the collision energy range 0 eV to 50 eV. Final states distributions are also investigated for the $\mathrm{^4HeH^+}$ dissociative recombination reaction,…
We report on an energy-sensitive imaging detector for studying the fragmentation of polyatomic molecules in the dissociative recombination of fast molecular ions with electrons. The system is based on a large area (10 cm x 10 cm) position-sensitive, double-sided Si-strip detector with 128 horizontal and 128 vertical strips, whose pulse height information is read out individually. The setup allows to uniquely identify fragment masses and is thus capable of measuring branching ratios between different fragmentation channels, kinetic energy releases, as well as breakup geometries, as a function o…
On a dense energy grid reaching up to 75 meV electron collision energy the fragmentation angle and the kinetic energy release of neutral dissociative recombination fragments have been studied in a twin merged beam experiment. The anisotropy described by Legendre polynomials and the extracted rotational state contributions were found to vary on a likewise narrow energy scale as the rotationally averaged rate coefficient. For the first time angular dependences higher than 2$^{nd}$ order could be deduced. Moreover, a slight anisotropy at zero collision energy was observed which is caused by the f…
The collision-energy resolved rate coefficient for dissociative recombination of HD+ ions in the vibrational ground state is measured using the photocathode electron target at the heavy-ion storage ring TSR. Rydberg resonances associated with ro-vibrational excitation of the HD+ core are scanned as a function of the electron collision energy with an instrumental broadening below 1 meV in the low-energy limit. The measurement is compared to calculations using multichannel quantum defect theory, accounting for rotational structure and interactions and considering the six lowest rotational energy…
The dissociative recombination of the lowest rotational states of H3+ has been investigated at the storage ring TSR using a cryogenic 22-pole radiofrequency ion trap as injector. The H3+ was cooled with buffer gas at ~15 K to the lowest rotational levels, (J,G)=(1,0) and (1,1), which belong to the ortho and para proton-spin symmetry, respectively. The rate coefficients and dissociation dynamics of H3+(J,G) populations produced with normal- and para-H2 were measured and compared to the rate and dynamics of a hot H3+ beam from a Penning source. The production of cold H3+ rotational populations w…
New high-resolution dissociative recombination rate coefficients of rotationally cool and hot H3+ in the vibrational ground state have been measured with a 22-pole trap setup and a Penning ion source, respectively, at the ion storage ring TSR. The experimental results are compared with theoretical calculations to explore the dependence of the rate coefficient on ion temperature and to study the contributions of different symmetries to probe the rich predicted resonance spectrum. The break-up energy was investigated by fragment imaging to derive internal temperatures of the stored parent ions u…
We review the study of dissociative recombination and ro-vibrational excitation of diatomic and small polyatomic molecular ions initiating complex organic molecules formation. In particular, we show how Multichannel Quantum Defect Theory (MQDT) and R-matrix methods are used to compute cross sections and rate coefficients for cations in well defined ro-vibrational levels of the ground electronic state, from sub-meV up to few eV collision energies. The most recent MQDT results are compared with either other theoretical data, or with measured data obtained in storage-ring experiments.
