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arXiv:physics/0703136 · The Journal of Chemical Physics

Interactions and dynamics in Li+Li2 ultracold collisions

Marko T. Cvitaš, Pavel Soldán, Jeremy M. Hutson, Pascal Honvault, Jean–Michel Launay

Published Aug 20, 2007• 71 citations
arXivHTMLPDF

Abstract

A potential energy surface for the lowest quartet electronic state ((4)A(')) of lithium trimer is developed and used to study spin-polarized Li+Li(2) collisions at ultralow kinetic energies. The potential energy surface allows barrierless atom exchange reactions. Elastic and inelastic cross sections are calculated for collisions involving a variety of rovibrational states of Li(2). Inelastic collisions are responsible for trap loss in molecule production experiments. Isotope effects and the sensitivity of the results to details of the potential energy surface are investigated. It is found that for vibrationally excited states, the cross sections are only quite weakly dependent on details of the potential energy surface.

DOI
10.1063/1.2752162

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A potential energy surface for the lowest quartet electronic state ((4)A(')) of lithium trimer is developed and used to study spin-polarized Li+Li(2) collisions at ultralow kinetic energies. The potential energy surface allows barrierless atom exchange reactions. Elastic and inelastic cross sections are calculated for collisions involving a variety of rovibrational states of Li(2). Inelastic collisions are responsible for trap loss in molecule production experiments. Isotope effects and the sensitivity of the results to details of the potential energy surface are investigated. It is found that for vibrationally excited states, the cross sections are only quite weakly dependent on details of the potential energy surface.
There is at present great interest in the properties of ultracold molecules. Molecules are created in traps in excited rovibrational states and any vibrational relaxation results in the trap loss. This thesis provides a theoretical study of interactions and collisions in the spin-polarized lithium -b lithium dimer system at ultralow energies. Potential energy surface of the electronic quartet ground state of lithium trimer is generated ab initio using the CCSD(T) method and represented by an IMLS/Shepard fit. Long-range nonadditive interactions are modelled using a symmetric global form with coefficients taken from a fit to the atom-molecule dispersion coefficients. The surface allows barrierless atom-exchange reactions. It has a global minimum of ≈ 4000 cm(^-1) at equilateral geometries with r(_e) = 3.1 Å. The nonadditive interactions are very strong near equilibrium. They increase the well depth by a factor of 4 and reduce the interatomic distance by ≈ 1 Å. Another surface of À symmetry in C(_s) meets the ground state surface at linear geometries at short range. Part of the seam, near D(_ooh) geometries, is in an energetically accessible region for cold collisions. Inside the seam, the lowest À surface correlates with (^4)II rather than (^4)Σ state. Inelastic and reactive collisions are investigated using a quantum mechanical coupled channel method in hyperspherical coordinates. Bosonic and fermionic systems in the spin-stretched states are considered. The inelastic rate coefficients from the rovibrationally excited states of dimer at ultralow collision energies are large, often above 10-(^-10) cm(^3)s(^-1) The elastic cross sections are ≈ 3 orders of magnitude lower at 1 nK. Atom-molecule mixtures, at the densities found in Bose-Einstein condensates of alkali metal atoms that were recently produced, would last only a fraction of a second. Classical Langevin model describes semi-quantitatively the energy dependence of inelastic cross sections above ≈ 50 mK. No systematic differences between the bosonic and fermionic systems were found. Sensitivity of the results on potential was investigated. Reactions in isotopic mixtures of lithium may be exothermic even from the molecular ground state. The reactive rate coefficients are 1 - 2 orders of magnitude smaller than those in systems involving an initially vibrationally excited dimer.
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).
We calculate the isotope-independent Li+{\mathrm{Li}}^{+}Li+-Li potential energy curves for the electronic ground and first excited states. The scattering phase shifts and total scattering cross section for the $^{7}\mathrm{Li}^{+}\text{\ensuremath{-}}^{7}\mathrm{Li}$ collision are calculated, with an emphasis on the ultralow-energy domain down to the sss-wave regime. The effect of physically motivated alterations on the calculated potential energy curves is used to determine the bound of accuracy of the low-energy scattering parameters for the ion-atom system. It is found that the scattering length for the $A{\phantom{\rule{0.16em}{0ex}}}^{2}{\mathrm{\ensuremath{\Sigma}}}_{u}^{+}$ state, au=1325a0{a}_{u}=1325{a}_{0}au​=1325a0​, is positive and has well-constrained bounds. For the $X{\phantom{\rule{0.16em}{0ex}}}^{2}{\mathrm{\ensuremath{\Sigma}}}_{g}^{+}$ state, the scattering length, ag=20465a0{a}_{g}=20\phantom{\rule{0.16em}{0ex}}465{a}_{0}ag​=20465a0​, has a large magnitude, as it is sensitive to the restrained change of the potential, due to the presence of a vibrational state in the vicinity of the dissociation limit.
A first-principles based quantum dynamics study of the Li + LiNa(v = 0, j = 0) → Li2(v′, j′) + Na reaction is reported for collision energies spanning the ultracold (1 nK) to cold (1 K) regimes. A full-dimensional ab initio potential energy surface for the ground electronic state of Li2Na is utilized that includes an accurate treatment of the long-range interactions. The Li + LiNa reaction is barrierless and exoergic and exhibits a deep attractive potential well that supports complex formation. Thus, significant reactivity occurs even for collision temperatures approaching absolute zero. The reactive scattering calculations are based on a numerically exact time-independent quantum dynamics methodology in hyperspherical coordinates. Total and rotationally resolved rate coefficients are reported at 56 collision energies and include all contributing partial waves. Several shape resonances are observed in many of the rotationally resolved rate coefficients and a small resonance feature is also reported in the total rate coefficient near 50 mK. Of particular interest, the angular distributions or differential cross sections are reported as a function of both the collision energy and scattering angle. Unique quantum fingerprints (bumps, channels, and ripples) are observed in the angular distributions for each product rotational state due to quantum interference and shape resonance contributions. The Li + LiNa reaction is under active experimental investigation so that these intriguing features could be verified experimentally when sufficient product state resolution becomes feasible for collision energies below 1 K.
Ultracold collisions between spin-polarized Na atoms and vibrationally excited Na2{\mathrm{N}\mathrm{a}}_{2}Na2​ molecules are investigated theoretically, using a reactive scattering formalism (including atom exchange). Calculations are carried out on both pairwise additive and nonadditive potential energy surfaces for the quartet electronic state. The Wigner threshold laws are followed for energies below ${10}^{\ensuremath{-}5}\text{ }\mathrm{K}$. Vibrational relaxation processes dominate elastic processes for temperatures below ${10}^{\ensuremath{-}3}--{10}^{\ensuremath{-}4}\text{ }\mathrm{K}$. For temperatures below ${10}^{\ensuremath{-}5}\text{ }\mathrm{K}$, the rate coefficients for vibrational relaxation ($v=1\ensuremath{\rightarrow}0$) are $4.8\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}11}$ and $5.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}10}\text{ }{\mathrm{c}\mathrm{m}}^{3}\text{ }{\mathrm{s}}^{\ensuremath{-}1}$ for the additive and nonadditive potentials, respectively. The large difference emphasizes the importance of using accurate potential energy surfaces for such calculations.
Ultracold chemical reactions of weakly bound triplet-state alkali metal dimer molecules have recently attracted much experimental interest. We perform rigorous quantum scattering calculations with a new ab initio potential energy surface to explore the chemical reaction of spin-polarized NaLi( a 3 Σ + ) and Li( 2 S) to form Li 2 ( a 3 Σ u + ) and Na( 2 S). The reaction is exothermic and proceeds readily at ultralow temperatures. Significantly, we observe strong sensitivity of the total reaction rate to small variations of the three-body part of the Li 2 Na interaction at short range, which we attribute to a relatively small number of open Li 2 ( a 3 Σ u + ) product channels populated in the reaction. This provides the first signature of highly non-universal dynamics seen in rigorous quantum reactive scattering calculations of an ultracold exothermic insertion reaction involving a polar alkali dimer molecule, opening up the possibility of probing microscopic interactions in atom+molecule collision complexes via ultracold reactive scattering experiments.