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arXiv:1012.0804 · The Journal of Chemical Physics

Cold and ultracold NH–NH collisions: The field-free case

Liesbeth M. C. Janssen, Piotr Szymon Żuchowski, Ad van der Avoird, Jeremy M. Hutson, Gerrit C. Groenenboom

Published Mar 28, 2011• 25 citations
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Abstract

We present elastic and inelastic spin-changing cross sections for cold and ultracold NH(X (3)Σ(-)) + NH(X (3)Σ(-)) collisions, obtained from full quantum scattering calculations on an accurate ab initio quintet potential-energy surface. Although we consider only collisions in zero field, we focus on the cross sections relevant for magnetic trapping experiments. It is shown that evaporative cooling of both fermionic (14)NH and bosonic (15)NH is likely to be successful for hyperfine states that allow s-wave collisions. The calculated cross sections are very sensitive to the details of the interaction potential, due to the presence of (quasi)bound state resonances. The remaining inaccuracy of the ab initio potential-energy surface therefore gives rise to an uncertainty in the numerical cross-section values. However, based on a sampling of the uncertainty range of the ab initio calculations, we conclude that the exact potential is likely to be such that the elastic-to-inelastic cross-section ratio is sufficiently large to achieve efficient evaporative cooling. This likelihood is only weakly dependent on the size of the channel basis set used in the scattering calculations.

DOI
10.1063/1.3570596

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We present elastic and inelastic spin-changing cross sections for cold and ultracold NH(X (3)Σ(-)) + NH(X (3)Σ(-)) collisions, obtained from full quantum scattering calculations on an accurate ab initio quintet potential-energy surface. Although we consider only collisions in zero field, we focus on the cross sections relevant for magnetic trapping experiments. It is shown that evaporative cooling of both fermionic (14)NH and bosonic (15)NH is likely to be successful for hyperfine states that allow s-wave collisions. The calculated cross sections are very sensitive to the details of the interaction potential, due to the presence of (quasi)bound state resonances. The remaining inaccuracy of the ab initio potential-energy surface therefore gives rise to an uncertainty in the numerical cross-section values. However, based on a sampling of the uncertainty range of the ab initio calculations, we conclude that the exact potential is likely to be such that the elastic-to-inelastic cross-section ratio is sufficiently large to achieve efficient evaporative cooling. This likelihood is only weakly dependent on the size of the channel basis set used in the scattering calculations.
Elastic and spin-changing inelastic collision cross sections are presented for cold and ultracold magnetically trapped NH. The cross sections are obtained from coupled-channel scattering calculations as a function of energy and magnetic field. We specifically investigate the influence of the intramolecular spin-spin, spin-rotation, and intermolecular magnetic dipole coupling on the collision dynamics. It is shown that 15N^{15}\mathrm{N}15NH is a very suitable candidate for evaporative cooling experiments. The dominant trap-loss mechanism in the ultracold regime originates from the intermolecular dipolar coupling term. At higher energies and fields, intramolecular spin-spin coupling becomes increasingly important. Our qualitative results and conclusions are fairly independent of the exact form of the potential and of the size of the channel basis set.
The binary collision dynamics of 2Dg,3/2{}^{2}{D}_{g,3/2}2Dg,3/2​ ground state scandium atoms is studied from first principles. We employ 30 coupled diabatic ab initio potentials in a coupled-channels study of the scattering dynamics of cold and ultracold scandium atoms in external magnetic fields. Due to the long-ranged magnetic dipolar interaction, the field dependence of the cross section does not follow the threshold laws derived by Volpi and Bohn [Phys. Rev. A 65, 052712 (2002)]. In the field-free case, the near-threshold cross section is independent of the collision energy, and hence the cross section does not follow the well-established Wigner threshold laws. The observed threshold behavior is explained in the Born approximation. For energies above $1\phantom{\rule{4pt}{0ex}}\ensuremath{\mu}\mathrm{K}$, inelastic collisions are driven by the anisotropic nonrelativistic electronic interaction. For energies below $100\phantom{\rule{4pt}{0ex}}\ensuremath{\mu}\mathrm{K}$, the ratio of elastic-to-inelastic collisions is likely to be favorable for evaporative cooling. Both anisotropy in the long-range interaction and in the short-range potential contribute to large cross sections for inelastic collisions at higher energies and lead to a small ratio of elastic-to-inelastic collisions. This is in agreement with the large rates for Zeeman relaxation of submerged-shell atoms observed experimentally. The effect of the uncertainty in the ab initio potential is sampled by scaling the reduced mass and is found to have little influence on the conclusions drawn from this work.
Abstract We explore the combined effect of the uncertainties due to the interaction potential and basis set convergence on low-temperature collisional properties of spin-polarized NH molecules in a magnetic field. We show that quantum scattering calculations with different rotational basis sets and λ -scaled interaction potentials produce qualitatively different ratios of elastic to inelastic cross sections for collision energies above 10 −3 cm −1 , leading to favorable (unfavorable) prospects for sympathetic cooling of NH molecules depending on the basis set cutoff parameter N max . The physical reason behind this effect is that the resonance widths, which determine the maximum variation of the scattering cross sections with λ , tend to depend strongly on N max . At ultralow collision energies, all basis sets produce highly uncertain (and statistically indistinguishable) elastic and inelastic cross sections; however, their ratio γ is much less sensitive to small variations of the interaction potential. Our results highlight the importance of basis set convergence in quantum scattering calculations and establish the existence of parameter regimes where unconverged calculations can still be used to make qualitatively accurate predictions of scattering observables.
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.
We calculate the interaction potential between N atoms and NH molecules and use it to investigate cold and ultracold collisions important for sympathetic cooling. The ratio of elastic to inelastic cross sections is large over a wide range of collision energy and magnetic field for most isotopic combinations, so that sympathetic cooling of NH molecules by N atoms is a good prospect. However, there are important effects due to a p-wave shape resonance that may inhibit cooling in some cases. We show that scaling the reduced mass used in the collision is approximately equivalent to scaling the interaction potential. We then explore the dependence of the scattering properties on the reduced mass and explain the resonant effects observed using angular-momentum-insensitive quantum defect theory.
We present a theoretical study of elastic and rotationally inelastic collisions of NH3 and ND3 with rare gas atoms (He, Ne, Ar, Kr, Xe) at low energy. Quantum close-coupling calculations have been performed for energies between 0.001 and 300 cm(-1). We focus on collisions in which NH3 is initially in the upper state of the inversion doublet with j = 1, k = 1, which is the most relevant in an experimental context as it can be trapped electrostatically and Stark-decelerated. We discuss the presence of resonances in the elastic and inelastic cross sections, as well as the trends in the inelastic cross sections along the rare gas series and the differences between NH3 and ND3 as a colliding partner. We also demonstrate the importance of explicitly taking into account the umbrella (inversion) motion of NH3 in order to obtain accurate scattering cross sections at low collision energy. Finally, we investigate the possibility of sympathetic cooling of ammonia using cold or ultracold rare gas atoms. We show that some systems exhibit a large ratio of elastic to inelastic cross sections in the cold regime, which is promising for sympathetic cooling experiments. The close-coupling calculations are based on previously reported ab initio potential energy surfaces for NH3-He and NH3-Ar, as well as on new, four-dimensional, potential energy surfaces for the interaction of ammonia with Ne, Kr, and Xe, which were computed using the coupled-cluster method and large basis sets. We compare the properties of the potential energy surfaces corresponding to the interaction of ammonia with the various rare gas atoms.