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Physical Review A

Calculations of some weakly bound diatomic molecular negative ions

Yong Li, C. D. Lin

Published Sep 1, 1999• 41 citations
Publisher

Abstract

We examine the existence of stable bound states of some diatomic molecular ions where the neutral molecule itself is either unbound or barely bound. Two bound states have been found for the ${\mathrm{HeH}}^{\ensuremath{-}}$ ion even though HeH is known to be unbound. We have found no bound states for ${\mathrm{He}}_{2}^{\ensuremath{-}}$ even though ${}^{4}{\mathrm{He}}_{2}$ is known to have one bound state. The predicted binding energies for ${\mathrm{HeH}}^{\ensuremath{-}}$ are of the order of 1 K and depend sensitively on the isotope combinations. Other weakly bound negative ions such as ${\mathrm{NeH}}^{\ensuremath{-}}$ and ${\mathrm{ArH}}^{\ensuremath{-}}$ have also been investigated. These weakly bound molecular ions are good candidates for cold collision experiments.

DOI
10.1103/physreva.60.2009

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We examine the existence of stable bound states of some diatomic molecular ions where the neutral molecule itself is either unbound or barely bound. Two bound states have been found for the HeH\ensuremath−{\mathrm{HeH}}^{\ensuremath{-}}HeH\ensuremath− ion even though HeH is known to be unbound. We have found no bound states for He2\ensuremath−{\mathrm{He}}_{2}^{\ensuremath{-}}He2\ensuremath−​ even though 4He2{}^{4}{\mathrm{He}}_{2}4He2​ is known to have one bound state. The predicted binding energies for HeH\ensuremath−{\mathrm{HeH}}^{\ensuremath{-}}HeH\ensuremath− are of the order of 1 K and depend sensitively on the isotope combinations. Other weakly bound negative ions such as NeH\ensuremath−{\mathrm{NeH}}^{\ensuremath{-}}NeH\ensuremath− and ArH\ensuremath−{\mathrm{ArH}}^{\ensuremath{-}}ArH\ensuremath− have also been investigated. These weakly bound molecular ions are good candidates for cold collision experiments.
We searched for the existence of weakly bound He-He-H, He-He-H - and He-H-H molecules where the binding energies are expected to be of the order of degrees Kelvin. By employing the best empirical interaction between each pair of particles, we solved the Schrödinger equation for the triatomic systems using hyperspherical coordinates in the adiabatic approximation. We found no bound states for 4 He- 4 He- 1 H, three bound states for 4 He- 4 He- 1 H - and one bound state for 4 He- 1 H- 1 H. Bound states for other isotope combinations are also examined.
We study the existence of stable bound states of triatomic molecules containing two helium atoms and one alkali atom X (X = Li, Na) and examine the dependence of their binding energies on the mass of the constituent atoms. The three-body systems are solved within the adiabatic approximation in hyperspherical coordinates using the He - He and He - X pair van der Waals interactions that are available in the literature. The binding energies of these systems are shown to be of less than 1 K for some isotope combinations. For the lighter isotopes it is shown that no bound states exist. We found no evidence of the existence of halo states or Efimov states for these systems.
We predict sss-wave elastic cross-sections $\ensuremath{\sigma}$ for low-energy atom-molecule collisions with kinetic energies up to 40 mK for the 4He^{4}\mathrm{He}4He collision with weakly bound diatomic molecules formed by 4He^{4}\mathrm{He}4He with 7Li,6Li^{7}\mathrm{Li},\phantom{\rule{0.28em}{0ex}}^{6}\mathrm{Li}7Li,6Li, and 23Na^{23}\mathrm{Na}23Na. Our scattering calculations are performed by using diatomic and triatomic molecular binding energies obtained from several available realistic models as input in a renormalized zero-range model as well as a finite-range one-term separable potential in order to quantify the relevance of range corrections to our predictions. Of particular relevance for possible experimental realization, we show the occurrence of a zero in $\ensuremath{\sigma}$ for the collision of cold 4He^{4}\mathrm{He}4He on a 4He23Na^{4}\mathrm{He}\phantom{\rule{0.16em}{0ex}}^{23}\mathrm{Na}4He23Na molecule below 20 mK. Also our results for the elastic collision 4He^{4}\mathrm{He}4He on 4He6,7Li^{4}\mathrm{He}\phantom{\rule{0.16em}{0ex}}^{6,7}\mathrm{Li}4He6,7Li molecules suggest that $\ensuremath{\sigma}$ varies considerably for the realistic models studied. As the chosen molecules are weakly bound and the scattering energies are very low, our results are interpreted on the light of the Efimov physics, which explains the model independence and robustness of our predictions despite some sensitivity on the potential range.
This thesis explores the fundamental physical and chemical processes between molecular ions and neutral atoms in the gas phase at very low energies. At temperatures in the mK regime, these are dominated by long-range interactions and only a few partial waves. This study contributes to the understanding of the details of intermolecular interactions and provides valuable data for benchmarking theoretical models and quantum-chemical calculations. Although there is a wide range of previous atomic collision system studies, the investigations of cold collisions with molecular ions are limited. The experimental setup used in this work enabled the measurement of rate coefficients for molecular ion-neutral collisions. The development of a dynamic ion-neutral hybrid trap with improved control over collision energy led to new insights into charge-transfer rate coefficients for molecular ion-neutral atom collisions involving N2+^+_22+​+Rb, O2+^+_22+​+Rb and N2_22​H+^+++Rb. Two different experimental settings enable state-and collision-energy dependent measurements of rate coefficients for all systems revealing an intriguing interplay between long-and short-range effects for the homonuclear diatomics by comparison to theoretical calculations and surprising experimental results for the polyatomic study. A fit of a constant function to the measured CT rate coefficients in the state-dependent experiment of N2_22​H+^+++Rb yielded the similar result as for N2+^+_22+​+Rb(5s5s5s)(2S1/2^2S_{1/2}2S1/2​). In the collision-energy dependent experiment the CT rate coefficient for N2_22​H+^+++Rb(5s5s5s)(2S1/2^2S_{1/2}2S1/2​) and N2_22​H+^+++Rb(5p5p5p)(2P3/2^2P_{3/2}2P3/2​) are both similar to the results for N2+^+_22+​+Rb(5s5s5s)(2S1/2^2S_{1/2}2S1/2​), and also the rate coefficients increase as the collision-energy increases.
We present a theoretical description of the formation of weakly bound (${E}_{b}\ensuremath{\sim}0.1\text{--}10$ meV) negative ions in collisions of Rydberg atoms with neutral atoms or molecules. Using the adiabatic approximation for the collision, we obtain an analytical expression for the formation cross section. It is shown that the cross section has a sharp peak in its dependence on the principal quantum number of the Rydberg electron. This result is in agreement with the experimental studies. We obtain a simple analytical expression that relates the peak position and the binding energy of the negative ion. This expression generalizes the empirical law previously established by Desfran\ifmmode \mbox{\c{c}}\else \c{c}\fi{}ois [Phys. Rev. A 51, 3667 (1995)]. Comparison of our calculations with the experimental data on dipole-bound anion formation shows that the obtained formula can be used for determination of binding energies of weakly bound negative ions from Rydberg electron transfer reactions with good accuracy.
We describe two simple models for the determination of electron binding energies (Eb{\mathit{E}}_{\mathit{b}}Eb​) of several dipole-bound negative ions from field-detachment experiments and charge-transfer formation-rate-constant measurements in collisions between cold neutral molecules and Rydberg atoms. These models are able to correctly reproduce the experimental data, from which we deduce two compatible sets of Eb{\mathit{E}}_{\mathit{b}}Eb​ values. A curve-crossing model for calculating anion formation rate constants allows us to qualitatively understand the sharply peaked shapes of the experimental curves and to derive a simple quantitative law between Eb{\mathit{E}}_{\mathit{b}}Eb​ values and principal Rydberg quantum numbers at which anion formation rate constants are maximum.