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arXiv:physics/0105085 · Physical Review A

Ultracold collisions of oxygen molecules

А. V. Avdeenkov, John L. Bohn

Published Oct 2, 2001• 66 citations
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Abstract

Collision cross sections and rate constants between two ground-state oxygen molecules are investigated theoretically at translational energies below $\ensuremath{\sim}1$ K and in zero magnetic field. We present calculations for elastic and spin-changing inelastic collision rates for different isotopic combinations of oxygen atoms as a prelude to understanding their collisional stability in ultracold magnetic traps. A numerical analysis has been made in the framework of a rigid-rotor model that accounts fully for the singlet, triplet, and quintet potential-energy surfaces in this system. The results offer insights into the effectiveness of evaporative cooling and the properties of molecular Bose-Einstein condensates, as well as estimates of collisional lifetimes in magnetic traps. Specifically, ${}^{17}{\mathrm{O}}_{2}$ looks like a good candidate for ultracold studies, while ${}^{16}{\mathrm{O}}_{2}$ is unlikely to survive evaporative cooling. Since ${}^{17}{\mathrm{O}}_{2}$ is representative of a wide class of molecules that are paramagnetic in their ground state we conclude that many molecules can be successfully magnetically trapped at ultralow temperatures.

DOI
10.1103/physreva.64.052703

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•Jan 1, 2011•0 citations
Collision cross sections and rate constants between two ground-state oxygen molecules are investigated theoretically at translational energies below \ensuremath∼1\ensuremath{\sim}1\ensuremath∼1 K and in zero magnetic field. We present calculations for elastic and spin-changing inelastic collision rates for different isotopic combinations of oxygen atoms as a prelude to understanding their collisional stability in ultracold magnetic traps. A numerical analysis has been made in the framework of a rigid-rotor model that accounts fully for the singlet, triplet, and quintet potential-energy surfaces in this system. The results offer insights into the effectiveness of evaporative cooling and the properties of molecular Bose-Einstein condensates, as well as estimates of collisional lifetimes in magnetic traps. Specifically, 17O2{}^{17}{\mathrm{O}}_{2}17O2​ looks like a good candidate for ultracold studies, while 16O2{}^{16}{\mathrm{O}}_{2}16O2​ is unlikely to survive evaporative cooling. Since 17O2{}^{17}{\mathrm{O}}_{2}17O2​ is representative of a wide class of molecules that are paramagnetic in their ground state we conclude that many molecules can be successfully magnetically trapped at ultralow temperatures.
We investigate the collisional stability of magnetically trapped ultracold molecules, taking into account the influence of magnetic fields. We compute elastic and spin-state-changing inelastic rate constants for collisions of the prototype molecule 17O2{}^{17}{\mathrm{O}}_{2}17O2​ with a 3He{}^{3}\mathrm{He}3He buffer gas as a function of the magnetic field and the translational collision energy. We find that spin-state-changing collisions are suppressed by Wigner's threshold laws as long as the asymptotic Zeeman splitting between incident and final states does not exceed the height of the centrifugal barrier in the exit channel. In addition, we propose a useful one-parameter fitting formula that describes the threshold behavior of the inelastic rates as a function of the field and collision energy. Results show a semiquantitative agreement of this formula with the full quantum calculations, and suggest useful applications also to different systems. As an example, we predict the low-energy rate constants relevant to evaporative cooling of molecular oxygen.
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 $6\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{3}\phantom{\rule{0.2em}{0ex}}{\text{molecule}}^{\ensuremath{-}1}\phantom{\rule{0.2em}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}$, 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 F+H2\mathrm{F}+{\mathrm{H}}_{2}F+H2​ reaction.
Collision cross sections between oxygen molecules and helium atoms are computed at translational energies between 0.1 K and 10.0 K, motivated by the recently demonstrated cooling of molecules by a helium buffer gas. Detailed calculations based on a rigid-rotor model demonstrate the differences among various isotopic combinations of oxygen atoms and also serve to illustrate resonant features unique to cold molecules. Comparisons of elastic versus spin-changing inelastic collision rates suggest that buffer-gas cooling is likely to be a widely applicable tool for producing cold molecular samples.
Cold collisions of ground-state oxygen molecules with helium have been investigated in a wide range of cold-collision energies (from $1\ensuremath{\mu}\mathrm{K}$ up to 10 K) treating the oxygen molecule first as a rigid rotor and then introducing the vibrational degree of freedom. The comparison between the two models shows that at low energies the rigid-rotor approximation is very accurate and able to describe all the dynamical features of the system. The comparison between the two models has also been extended to cases where the interaction potential $\mathrm{He}\ensuremath{-}{\mathrm{O}}_{2}$ is made artificially stronger. In this case vibration can perturb rate constants, but fine tuning the rigid-rotor potential can alleviate the discrepancies between the two models.
In this work we investigate the potential of controlling cold (O(K)−mK) and ultracold (mK-μK) atom-molecule collisions by tuning scattering states across Feshbach resonances using magnetic fields. We are interested in particular in the prospect of suppressing the often undesirable inelastic collisions. The He-O_2 system provides the vehicle for our study. We calculate bound and quasi-bound states of several isotopic combinations, including their Zeeman structure, to reveal the underlaying pattern for easier characterization of quasi-bound states in terms of rigorous and approximately good quantum numbers. These calculations also help us locate the fields at which zero-energy resonances will occur. Scattering calculations are then performed for collisions of 3^He and 4^He with {16}^O_2 at fixed (1 μK) energy but varying magnetic field. The field is varied to sweep the scattering state across resonance. At low and ultralow energies we enter the Wigner threshold regime where the S-partial wave dominates the wavefunction. The cross sections, and the real and imaginary parts of the scattering length, vary dramatically across resonance. Their profiles are used to analyze the resonances. In a highlight of our results we show that dramatic suppression of inelastic cross sections occur for 4^He-{16}^O_2 . The resonances are relatively wide (of order 100 Gauss), with suppression of inelastic scattering over a similarly wide range of fields and for temperatures ranging from 10 mK down to 1 μK. We conclude that under certain conditions it is possible to almost completely eliminate inelastic collisions. This is potentially very important for cooling techniques, such as evaporative and sympathetic cooling, that require efficient elastic cross sections. Suppression of inelastic collisions can not only increase thermalization efficiency but it can also result in longer trap-lifetimes by reducing transitions to untrapable states.