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arXiv:1411.2666 · Physical Review A

Beyond universality: Parametrizing ultracold complex-mediated reactions using statistical assumptions

Manuel Lara, Pablo G. Jambrina, Jean–Michel Launay, F. Javier Aoiz

Published Mar 30, 2015• 10 citations
arXivHTMLPDF

Abstract

We have calculated accurate quantum reactive and elastic cross sections for the prototypical barrierless reaction ${\mathrm{D}}^{+}+{\mathrm{H}}_{2}(v=0,\phantom{\rule{0.28em}{0ex}}j=0)$ using a modified hyperspherical scattering method. The considered kinetic energy ranges from the ultracold to the Langevin regimes. A reaction rate coefficient practically constant in no less than eight orders of magnitude is obtained. The availability of accurate results for this system allows one to test the quantum theory by Jachymski et al. [K. Jachymski, M. Krych, P. S. Julienne, and Z. Idziaszek, Phys. Rev. Lett. 110, 213202 (2013)] in a nonuniversal case. The short-range reaction probability is rationalized using statistical model assumptions and related to a statistical factor. This provides a means to estimate one of the parameters that characterizes ultracold processes from first principles.

DOI
10.1103/physreva.91.030701

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We have calculated accurate quantum reactive and elastic cross sections for the prototypical barrierless reaction D++H2(v=0,j=0){\mathrm{D}}^{+}+{\mathrm{H}}_{2}(v=0,\phantom{\rule{0.28em}{0ex}}j=0)D++H2​(v=0,j=0) using a modified hyperspherical scattering method. The considered kinetic energy ranges from the ultracold to the Langevin regimes. A reaction rate coefficient practically constant in no less than eight orders of magnitude is obtained. The availability of accurate results for this system allows one to test the quantum theory by Jachymski et al. [K. Jachymski, M. Krych, P. S. Julienne, and Z. Idziaszek, Phys. Rev. Lett. 110, 213202 (2013)] in a nonuniversal case. The short-range reaction probability is rationalized using statistical model assumptions and related to a statistical factor. This provides a means to estimate one of the parameters that characterizes ultracold processes from first principles.
A fundamental question in the study of chemical reactions is how reactions proceed at a collision energy close to absolute zero. This question is no longer hypothetical: quantum degenerate gases of atoms and molecules can now be created at temperatures lower than a few tens of nanoKelvin. In this work we consider the benchmark ultracold reaction between, the most-celebrated ultracold molecule, KRb and K. For the first time we map out an accurate ab initio ground state potential energy surface of the KRbK complex in full dimensionality and report numerically exact quantum-mechanical reaction dynamics. The distribution of rotationally resolved rates is shown to be Poissonian. An analysis of the hyperspherical adiabatic potential curves explains this statistical character revealing a chaotic distribution for the short-range collision complex that plays a key role in governing the reaction outcome. We compare this with a lighter system with a smaller density of states (here the LiYbLi trimer) which displays random, and not chaotic, behavior.
A simple quantum-defect model gives analytic expressions for the complex scattering length and threshold collision rates of ultracold molecules. If the probability of reaction in the short-range part of the collision is high, the model gives universal rate constants for s- and p-wave collisions that are independent of short-range dynamics. This model explains the magnitudes of the recently measured rate constants for collisions of two ultracold 40K87Rb molecules, or an ultracold 40K atom with the 40K87Rb molecule [S. Ospelkaus et al., Science 327, 853 (2010).
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. ^
Abstract A fundamental question in the study of chemical reactions is how reactions proceed at a collision energy close to absolute zero. This question is no longer hypothetical: quantum degenerate gases of atoms and molecules can now be created at temperatures lower than a few tens of nanokelvin. Here we consider the benchmark ultracold reaction between, the most-celebrated ultracold molecule, KRb and K. We map out an accurate ab initio ground-state potential energy surface of the K 2 Rb complex in full dimensionality and report numerically-exact quantum-mechanical reaction dynamics. The distribution of rotationally resolved rates is shown to be Poissonian. An analysis of the hyperspherical adiabatic potential curves explains this statistical character revealing a chaotic distribution for the short-range collision complex that plays a key role in governing the reaction outcome.
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.
We consider a general problem of inelastic collision of particles interacting with power-law potentials. Using quantum-defect theory we derive an analytical formula for the energy-dependent complex scattering length, valid for arbitrary collision energy, and use it to analyze the elastic and reactive collision rates. Our theory is applicable for both universal and nonuniversal collisions. The former corresponds to the unit reaction probability at short range, while in the latter case the reaction probability is smaller than one. In the high-energy limit we present a method that allows us to incorporate quantum corrections to the classical reaction rate due to the shape resonances and the quantum tunneling.