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Physical Review A

Collisions of NH(Σ3−) with Rb and Cs at ultralow energies: A quantum study of rotational cooling efficiency

M. Tacconi, Lola González‐Sánchez, Enrico Bodo, Franco Antonio Gianturco

Published Sep 5, 2007• 12 citations
Publisher

Abstract

Using ab initio calculations for the lowest, spin-stretched, quartet potential energy surfaces for Rb and Cs neutral atoms interacting with the $\text{NH}({^{3}\ensuremath{\Sigma}}^{\ensuremath{-}})$ polar target, the cold collision quantum dynamics is analyzed at ultralow energies to examine possible propensity rules existing for the relaxation of either spin or rotational target states (or both) via sympathetic cooling induced by the partner atoms. The specific coupling of Hund's case (b) is adopted for the dynamical treatment of spin and rotational angular momenta and the coupled channel approach is employed to solve the scattering equations. Both rotational and/or spin relaxation cross sections are obtained down to ${10}^{\ensuremath{-}6}\text{ }{\text{cm}}^{\ensuremath{-}1}$ of energy and corresponding cooling rates are analyzed and compared between the two systems.

DOI
10.1103/physreva.76.032702

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Using ab initio calculations for the lowest, spin-stretched, quartet potential energy surfaces for Rb and Cs neutral atoms interacting with the NH(3\ensuremathΣ\ensuremath−)\text{NH}({^{3}\ensuremath{\Sigma}}^{\ensuremath{-}})NH(3\ensuremathΣ\ensuremath−) polar target, the cold collision quantum dynamics is analyzed at ultralow energies to examine possible propensity rules existing for the relaxation of either spin or rotational target states (or both) via sympathetic cooling induced by the partner atoms. The specific coupling of Hund's case (b) is adopted for the dynamical treatment of spin and rotational angular momenta and the coupled channel approach is employed to solve the scattering equations. Both rotational and/or spin relaxation cross sections are obtained down to 10\ensuremath−6 cm\ensuremath−1{10}^{\ensuremath{-}6}\text{ }{\text{cm}}^{\ensuremath{-}1}10\ensuremath−6 cm\ensuremath−1 of energy and corresponding cooling rates are analyzed and compared between the two systems.
The relative size of the elastic cross sections between NH\mathrm{NH}NH molecules colliding with Cs and Rb atoms on the lowest potential energy surfaces of spin-stretched quartet symmetry are computed using the full quantum treatment and taking the target molecule to be in its ground rotational state. Results are compared between the two systems under similar dynamics and the Rb atom is found to yield larger cross sections at ultralow energies. The process is seen to be dominated by dispersion interaction and an analysis of the effects on the cross sections induced by changes on the C6{C}_{6}C6​ coefficients is carried out in detail for both systems.
Quantum-scattering calculations at ultralow (close to ${10}^{\ensuremath{-}6}$ cm${}^{\ensuremath{-}1}$) collision energies are carried out for the Cs dimer in its spin-stretched triplet state, interacting with helium. An ab initio potential energy surface is computed and employed, while the target molecule is kept in its ground vibrational state and several excitated initial rotational states are considered in the quantum dynamics. The highly anisotropic interaction is seen to cause, in spite of its weakness, internal energy quenching rates comparable with the efficiency of the collisional cooling of relative kinetic energies. The rates of spin-flip processes are also analyzed and compared with pure rotational quenching events.
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.
We explore the suitability of ultracold collisions between spin-polarized $\mathrm{SrF}(^{2}\mathrm{\ensuremath{\Sigma}}^{+})$ molecules and Rb(2S)\mathrm{Rb}(^{2}S)Rb(2S) atoms as elementary steps for the sympathetic cooling of $\mathrm{SrF}(^{2}\mathrm{\ensuremath{\Sigma}}^{+})$ molecules in a magnetic trap. To this end, we carry out quantum-mechanical scattering calculations on ultracold Rb + SrF collisions in a magnetic field based on an accurate potential-energy surface for the triplet electronic state of Rb-SrF developed ab initio using a spin-restricted coupled cluster method with single, double, and noniterative triple excitations [RCCSD(T)]. The Rb-SrF interaction has a global minimum with a well depth of 3444 ${\mathrm{cm}}^{\ensuremath{-}1}$ in a bent geometry and a shallow local minimum in the linear geometry. Despite such a strong and anisotropic interaction, we find that converged close-coupling scattering calculations on Rb + SrF collisions in a magnetic field are still possible using rotational basis sets including up to 125 closed rotational channels in the total angular momentum representation. Our calculations show that electronic spin relaxation in fully spin-polarized Rb-SrF collisions occurs much more slowly than elastic scattering over a wide range of magnetic fields (1--1000 G) and collision energies (${10}^{\ensuremath{-}5}--{10}^{\ensuremath{-}3}$ K), suggesting good prospects of sympathetic cooling into the microkelvin regime of laser-cooled $\mathrm{SrF}(^{2}\mathrm{\ensuremath{\Sigma}}^{+})$ molecules with spin-polarized Rb(2S)\mathrm{Rb}(^{2}S)Rb(2S) atoms in a magnetic trap. We show that incoming ppp-wave scattering plays a significant role in ultracold collisions due to the large reduced mass of the Rb-SrF collision pair. The calculated magnetic-field dependence of the inelastic cross sections at $1.4\phantom{\rule{0.28em}{0ex}}\ensuremath{\mu}\mathrm{K}$ displays a rich resonance structure including a low-field ppp-wave resonance, which suggests that external magnetic fields can be used to enhance the efficiency of sympathetic cooling in heavy atom-molecule mixtures.
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A new three-dimensional potential energy surface (PES), which describes the interaction between the OH(-)(X (1)Sigma(+)) anionic molecule and the Rb((2)S) atomic gas has been obtained by using a highly correlated ab initio model of the electronic structure and a large atomic basis set supplemented with a set of midbond Gaussian functions. This accurate PES is being employed to evaluate the OH(-)(X (1)Sigma(+)) vibrational quenching efficiency induced by collisions with Rb((2)S) at low and ultralow energies. Calculations employ the coupled-channel ansatz to describe the nuclear quantum dynamics and finally show a very marked dependence of the inelastic cross sections and rates, at vanishing collision energies, on the initial vibrational energy content of the partner molecules. The present findings allow us to make specific suggestions on the likely outcomes from energy interplay between the title species within a mixed MOT/Paul Trap environment.