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Physical Review Letters

Quasiresonant Energy Transfer in Ultracold Atom-Diatom Collisions

Robert C. Forrey, N. Balakrishnan, A. Dalgarno, Michael R. Haggerty, Eric J. Heller

Published Mar 29, 1999• 97 citations
Publisher

Abstract

Quantum and classical quasiresonant vibration-rotation energy transfer is investigated for ultracold $\mathrm{He}\ensuremath{-}{\mathrm{H}}_{2}$ collisions. Classical trajectory computations show that extremely strong correlations between $\ensuremath{\Delta}j$ and $\ensuremath{\Delta}v$ persist at low energies, though the changes themselves are less than one quantum. Quantum computations show that quasiresonant transitions occur in the limit of zero collision energy but that threshold effects become important and that some quasiresonant channels close. The qualitative similarity between classical and quantum results suggests that they share a common mechanism.

DOI
10.1103/physrevlett.82.2657

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Quantum and classical quasiresonant vibration-rotation energy transfer is investigated for ultracold He\ensuremath−H2\mathrm{He}\ensuremath{-}{\mathrm{H}}_{2}He\ensuremath−H2​ collisions. Classical trajectory computations show that extremely strong correlations between \ensuremathΔj\ensuremath{\Delta}j\ensuremathΔj and \ensuremathΔv\ensuremath{\Delta}v\ensuremathΔv persist at low energies, though the changes themselves are less than one quantum. Quantum computations show that quasiresonant transitions occur in the limit of zero collision energy but that threshold effects become important and that some quasiresonant channels close. The qualitative similarity between classical and quantum results suggests that they share a common mechanism.
Highly efficient and specific energy transfer mechanisms that involve rotation-rotation, vibration-vibration, and vibration-rotation exchange in diatomic molecules are examined theoretically in ultracold H(2), D(2), and HD self-collisions as a function of initial vibrational level v. The three quasiresonant mechanisms are found to operate for all vibrational levels and yield complex scattering lengths which vary smoothly with v. Exceptions to this trend occur at select high values of v where the scattering lengths are modulated by orders of magnitude corresponding to the location of an s-wave zero-energy resonance in "vibration space." The quasiresonant mechanisms, which are not very sensitive to the details of the interaction potential, generally control the final distribution of molecular states for any given initial distribution. The zero-energy resonances are more sensitive to the potential and may be used to vibrationally "tune" the interaction strength, similar to methods which vary applied external fields.
We present a rigorous study of vibrational relaxation in $\text{para}\text{\ensuremath{-}}{\mathrm{H}}_{2}+\text{para}\text{\ensuremath{-}}{\mathrm{H}}_{2}$ collisions at cold and ultracold temperatures and identify an efficient mechanism of rovibrational energy transfer. If the colliding molecules are in different rotational and vibrational levels, the internal energy may be transferred between the molecules through an extremely state-selective process involving simultaneous conservation of internal energy and total rotational angular momentum. The same transition in collisions of distinguishable molecules corresponds to the rotational energy transfer from one vibrational state of the colliding molecules to another.
Cold and ultracold collisions involving rotationally hot CO\mathrm{CO}CO molecules are investigated using quantum mechanical coupled channel, coupled states, and effective potential scattering formulations. Quenching rate coefficients are given for initial rotational levels near the dissociation threshold. The stability of the CO\mathrm{CO}CO ``super rotors'' against collisional decay is compared to previous investigations involving homonuclear molecules. It is found that quasiresonant transitions provide a significantly stronger contribution to the total relaxation rate than in the comparable case of O2{\mathrm{O}}_{2}O2​. As in the case of H2{\mathrm{H}}_{2}H2​, sharp structures in the distribution of total quenching rate coefficients are found at rotational levels where quasiresonant scattering is not allowed.
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. ^
Cross sections for He+H2\mathrm{He}+{\mathrm{H}}_{2}He+H2​ collisions are reported for rovibrational states near dissociation at translational energies less than $1000\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$. In contrast to our previously reported cross sections for lower-lying initial rotational states, the excited rotational states near dissociation give rise to shape resonances for energies between 0.001 and $1\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$. The emergence of these resonances with increasing rotational level is opposite to the trend found for He+CO\mathrm{He}+\mathrm{C}\mathrm{O}He+CO where the shape resonance strength decreases with rotational level for low-lying states. Quasiresonant energy transfer and low energy excitation thresholds are also discussed and it is found that there are 11 rovibrationally excited states that are stable against collision at ultracold temperatures.
A close coupling quantum-mechanical calculation is performed for rotational energy transfer in a HD+HD collision at very low energy, down to the ultracold temperatures: $T\ensuremath{\sim}{10}^{\ensuremath{-}8}$ K. A global six-dimensional H2{}_{2}2​-H2{}_{2}2​ potential-energy surface is adopted from a previous work [Boothroyd et al., J. Chem. Phys. 116, 666 (2002)]. State-resolved integral cross sections ${\ensuremath{\sigma}}_{ij\ensuremath{\rightarrow}{i}^{\ensuremath{'}}{j}^{\ensuremath{'}}}({\ensuremath{\varepsilon}}_{\text{kin}})$ of different quantum-mechanical rotational transitions $ij\ensuremath{\rightarrow}{i}^{\ensuremath{'}}{j}^{\ensuremath{'}}$ in the HD molecules and corresponding state-resolved thermal rate coefficients ${k}_{ij\ensuremath{\rightarrow}{i}^{\ensuremath{'}}{j}^{\ensuremath{'}}}(T)$ have been computed. Additionally, for comparison, H2{}_{2}2​+H2{}_{2}2​ calculations for a few selected rotational transitions have also been performed. The hydrogen and deuterated hydrogen molecules are treated as rigid rotors in this work. A pronounced isotope effect is identified in the cross sections of these collisions at low and ultracold temperatures.