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arXiv:0811.4377 · Physical Review A

Formation of molecular oxygen in ultracold O+OH collisions

Goulven Quéméner, N. Balakrishnan, Brian K. Kendrick

Published Feb 5, 2009• 33 citations
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Abstract

We discuss the formation of molecular oxygen in ultracold collisions between hydroxyl radicals and atomic oxygen. A time-independent quantum formalism based on hyperspherical coordinates is employed for the calculations. Elastic, inelastic, and reactive cross sections as well as the vibrational and rotational populations of the product ${\mathrm{O}}_{2}$ molecules are reported. A $J$-shifting approximation is used to compute the rate coefficients. At temperatures $T=10--100\phantom{\rule{0.3em}{0ex}}\mathrm{mK}$ for which the OH molecules have been cooled and trapped experimentally, the elastic and reactive rate coefficients are of comparable magnitude, while at colder temperatures, $T<1\phantom{\rule{0.3em}{0ex}}\mathrm{mK}$, the formation of molecular oxygen becomes the dominant pathway. The validity of a classical capture model to describe cold collisions of OH and O is also discussed. While very good agreement is found between classical and quantum results at $T=0.3\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, at higher temperatures, the quantum calculations predict a larger rate coefficient than the classical model, in agreement with experimental data for the $\mathrm{O}+\mathrm{O}\mathrm{H}$ reaction. The zero-temperature limiting value of the rate coefficient is predicted to be about $6\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{3}\phantom{\rule{0.2em}{0ex}}{\text{molecule}}^{\ensuremath{-}1}\phantom{\rule{0.2em}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}$, a value comparable to that of barrierless alkali-metal atom-dimer systems and about a factor of five larger than that of the tunneling dominated $\mathrm{F}+{\mathrm{H}}_{2}$ reaction.

DOI
10.1103/physreva.79.022703

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We discuss the formation of molecular oxygen in ultracold collisions between hydroxyl radicals and atomic oxygen. A time-independent quantum formalism based on hyperspherical coordinates is employed for the calculations. Elastic, inelastic, and reactive cross sections as well as the vibrational and rotational populations of the product O2{\mathrm{O}}_{2}O2​ molecules are reported. A JJJ-shifting approximation is used to compute the rate coefficients. At temperatures T=10−−100mKT=10--100\phantom{\rule{0.3em}{0ex}}\mathrm{mK}T=10−−100mK for which the OH molecules have been cooled and trapped experimentally, the elastic and reactive rate coefficients are of comparable magnitude, while at colder temperatures, T<1mKT<1\phantom{\rule{0.3em}{0ex}}\mathrm{mK}T<1mK, the formation of molecular oxygen becomes the dominant pathway. The validity of a classical capture model to describe cold collisions of OH and O is also discussed. While very good agreement is found between classical and quantum results at T=0.3KT=0.3\phantom{\rule{0.3em}{0ex}}\mathrm{K}T=0.3K, at higher temperatures, the quantum calculations predict a larger rate coefficient than the classical model, in agreement with experimental data for the O+OH\mathrm{O}+\mathrm{O}\mathrm{H}O+OH reaction. The zero-temperature limiting value of the rate coefficient is predicted to be about 6\ifmmode×\else\texttimes\fi10\ensuremath−12cm3molecule\ensuremath−1s\ensuremath−16\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{3}\phantom{\rule{0.2em}{0ex}}{\text{molecule}}^{\ensuremath{-}1}\phantom{\rule{0.2em}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}6\ifmmode×\else\texttimes\fi10\ensuremath−12cm3molecule\ensuremath−1s\ensuremath−1, a value comparable to that of barrierless alkali-metal atom-dimer systems and about a factor of five larger than that of the tunneling dominated F+H2\mathrm{F}+{\mathrm{H}}_{2}F+H2​ reaction.
We discuss the formation of molecular oxygen in ultracold collisions between hydroxyl radicals and atomic oxygen. A time-independent quantum formalism based on hyperspherical coordinates is employed for the calculations. Elastic, inelastic and reactive cross sections as well as the vibrational and rotational populations of the product O{sub 2} molecules are reported. A J-shifting approximation is used to compute the rate coefficients. At temperatures T = 10--100 mK for which the OH molecules have been cooled and trapped experimentally, the elastic and reactive rate coefficients are of comparable magnitude, while at colder temperatures, T < 1 mK, the formation of molecular oxygen becomes the dominant pathway. The validity of a classical capture model to describe cold collisions of OH and O is also discussed. While very good agreement is found between classical and quantum results at T = 0.3 K, at higher temperatures, the quantum calculations predict a higher rate coefficient than the classical model, in agreement with experimental data for the O + OH reaction. The zero-temperature limiting value of the rate coefficient is predicted to be about 6 x 10{sup -12} cm{sup 3} s{sup 01}, a value comparable to that of barrierless alkali metal atom-dimer systems and about a factor of five larger than that of the tunneling dominated F + H{sub 2} reaction.
It has recently become possible to form molecules in ultracold gases of trapped alkali metal atoms. Once formed, the molecules may undergo elastic, inelastic and reactive collisions. Inelastic and reactive collisions are particularly important because they release kinetic energy and eject atoms and molecules from the trap. The theory needed to handle such collisions is presented and recent quantum dynamics calculations on ultracold atom–diatom collisions of spin-polarized Li + Li2, Na + Na2 and K + K2 are described. All these systems have potential energy surfaces on which barrierless atom exchange reactions can occur, and both inelastic and reactive rates are very fast (typically k inel > 10-10 cm3 s−1 in the Wigner regime).
Theoretical results for ultracold atom-molecule collisions involving exoergic reactions are presented. Systems with a reaction barrier are considered; specifically, we report the results of extensive computations for D + H 2 and Cl + H2. We analyzed the extreme situation of translationally cold collisions between an atom and an internally hot molecule; namely, for D + H2 we explored the role played by the internal vibrational excitation of the diatomic target for initial states H2(υ) with υ = 0,1,2,…, 8. The υ-dependence of the zero-temperature limit of the reaction rate coefficient shows two distinct regimes: a barrier dominated regime for υ < 4, and a barrierless regime for υ > 4. Also, for highly excited initial states, the distribution over the final states of the products shows an approximate conservation of the internal vibrational energy. For Cl + H2 we studied in detail the isotopic effect by varying continuously the mass of H, which allowed us to find resonance effects in the threshold behavior of cross sections. These resonances are caused by long-lived van der Waals complexes (Cl···H2) which have vanishingly small binding energy, or by virtual states of the Cl···H 2 complex. ^
II. Inelastic atom -molecule collisions 2 A. Vibrational and rotational relaxation 2 1. Collisions at cold and ultracold temperatures 2 2. Shape resonances in molecular collisions 6 3. Feshbach resonances in molecular collisions 6 B. Quasi-resonant transitions 7 C. Atom -molecular ion collisions 8 III.Chemical Reactions at ultracold temperatures 9 A. Tunneling dominated reactions 9 1.Reactions at zero temperature 10 2. Feshbach resonances in reactive scattering 12 B. Barrierless reactions 14 1.Collision systems of three alkali metal atoms 14 2. Role of PES in determining ultracold reactions 16 3.Relaxation of vibrationally excited alkali metal dimers 18 4. Reactions of heteronuclear and isotopically substituted alkali-metal dimer systems 19 IV.Inelastic molecule -molecule collisions 20 A. Molecules in the ground vibrational state 20 B. Vibrationally inelastic transitions 22 V. Summary and outlook 24 References 24 I. A. Vibrational and rotational relaxation 1. Collisions at cold and ultracold temperatures
We have calculated elastic and state-resolved inelastic cross sections for cold and ultracold collisions in the $\mathrm{Rb}(^{1}S)+\mathrm{O}\mathrm{H}(^{2}\ensuremath{\Pi}_{3∕2})$ system, including fine-structure and hyperfine effects. We have developed a set of five potential energy surfaces for $\mathrm{Rb}\text{\ensuremath{-}}\mathrm{O}\mathrm{H}(^{2}\ensuremath{\Pi})$ from high-level ab initio electronic structure calculations, which exhibit conical intersections between covalent and ion-pair states. The surfaces are transformed to a quasidiabatic representation. The collision problem is expanded in a set of channels suitable for handling the system in the presence of electric and/or magnetic fields, although we consider the zero-field limit in this work. Because of the large number of scattering channels involved, we propose and make use of suitable approximations. To account for the hyperfine structure of both collision partners in the short-range region we develop a frame-transformation procedure which includes most of the hyperfine Hamiltonian. Scattering cross sections on the order of ${10}^{\ensuremath{-}13}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{2}$ are predicted for temperatures typical of Stark decelerators. We conclude that spin orientation of the partners is completely disrupted during the collision. Implications for both sympathetic cooling of OH molecules in an environment of ultracold Rb atoms and experimental observability of the collisions are discussed.