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Physical Review A

Collisions of room-temperature helium with ultracold lithium and the van der Waals bound state of HeLi

Constantinos Makrides, Daniel S. Barker, James A. Fedchak, Julia K. Scherschligt, Stephen Eckel, Eite Tiesinga

Published Jan 6, 2020• 22 citations
Publisher

Abstract

We have computed the thermally averaged total, elastic rate coefficient for the collision of a room-temperature helium atom with an ultracold lithium atom. This rate coefficient has been computed as part of the characterization of a cold-atom vacuum sensor based on laser-cooled $^{6}\mathrm{Li}$ or $^{7}\mathrm{Li}$ atoms that will operate in the ultrahigh-vacuum ($p<{10}^{\ensuremath{-}6}$ Pa) and extreme-high-vacuum ($p<{10}^{\ensuremath{-}10}$ Pa) regimes. The analysis involves computing the $X{\phantom{\rule{0.16em}{0ex}}}^{2}{\mathrm{\ensuremath{\Sigma}}}^{+}$ HeLi Born-Oppenheimer potential followed by the numerical solution of the relevant radial Schr\"odinger equation. The potential is computed using a single-reference-coupled-cluster electronic-structure method with basis sets of different completeness in order to characterize our uncertainty budget. We predict that the rate coefficient for a 300 K helium gas and a 1 $\ensuremath{\mu}\mathrm{K}$ Li gas is $1.467(13)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}9}$ ${\mathrm{cm}}^{3}$/s for $^{4}\mathrm{He}+\phantom{\rule{0.16em}{0ex}}^{6}\mathrm{Li}$ and $1.471(13)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}9}$ ${\mathrm{cm}}^{3}$/s for $^{4}\mathrm{He}+\phantom{\rule{0.16em}{0ex}}^{7}\mathrm{Li}$, where the numbers in parentheses are the one-standard-deviation uncertainties in the last two significant digits. We quantify the temperature dependence as well. Finally, we evaluate the $s$-wave scattering length and binding of the single van der Waals bound state of HeLi. We predict that this weakly bound level has a binding energy of $\ensuremath{-}0.0064(43)\ifmmode\times\else\texttimes\fi{}hc$ ${\mathrm{cm}}^{\ensuremath{-}1}$ and $\ensuremath{-}0.0122(67)\ifmmode\times\else\texttimes\fi{}hc$ ${\mathrm{cm}}^{\ensuremath{-}1}$ for $^{4}\mathrm{He}\phantom{\rule{0.16em}{0ex}}^{6}\mathrm{Li}$ and $^{4}\mathrm{He}^{7}\mathrm{Li}$, respectively. The calculated binding energy of $^{4}\mathrm{He}^{7}\mathrm{Li}$ is consistent with the sole experimental determination.

DOI
10.1103/physreva.101.012702

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Trapped ultracold alkali-metal atoms can be used to measure pressure in the ultra-high-vacuum and XHV pressure regimes, those with p < 10−6 Pa. This application for ultracold atoms relies on precise knowledge of collision rate coefficients of alkali-metal atoms with residual room-temperature atoms and molecules in the ambient vacuum or with deliberately introduced gasses. Here, we determine combined elastic and inelastic rate coefficients as well as glancing-angle rate coefficients for ultracold 7Li and 87Rb with room-temperature noble gas atoms as well as H2 and 14N2 molecules. Glancing collisions are those processes where only little momentum is transferred to the alkali-metal atom and this atom is not ejected from its trap. Rate coefficients are found by performing quantum close-coupling scattering calculations using ab initio ground-state electronic Born–Oppenheimer potential energy surfaces. The potentials for Li and Rb with noble gas atoms and also for Rb(2S)–H2(XΣg+) and Rb(2S)–N2(X1Σg+) systems are based on the non-relativistic spin-restricted coupled-cluster method with single, double, and noniterative triple excitations [RCCSD(T)]. For Li(2S)–N2(X1Σg+), the potential is computed at the explicitly correlated spin-restricted RCCSD(T)-F12 level. For Rb, Kr, and Xe atoms, scalar relativistic corrections to the core electrons have been included, while second-order spin–orbit corrections from the valence electrons have been estimated. Data for Li–H2 and Li–He were taken from the existing literature. We estimate standard uncertainties of the rate coefficients by comparing rate coefficients calculated using potentials found with electronic basis sets of increasing size, including estimates of relativistic spin–orbit corrections and the uncertainty of the van der Waals coefficients. The relative uncertainties of rate coefficients are 1%–2% with the exception of 7Li or 87Rb colliding with 20Ne. Those have relative uncertainties of 9% and 8%, respectively. We also show that a commonly used semiclassical approximation for the total elastic rate coefficient agrees with the quantum calculations to 10% with the exception of 7Li and 87Rb collisions with H2, where the semiclassical value underestimates the quantum value by 20%.
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Atoms constitute promising quantum sensors for a variety of scenarios including vacuum metrology. Key to this application is knowledge of the collision rate coefficient of the sensor atom with the particles being detected. Prior work demonstrated that, for room-temperature collisions, the total collision rate coefficient and the trap depth dependence of the sensor atom loss rate from shallow traps are both universal, independent of the interaction potential at short range. It was also shown that measurements of the energy transferred to the sensor atom by the collision can be used to estimate the total collision rate coefficient. However, discrepancies found when comparing the results of this and other methods of deducing the rate coefficient call into question its accuracy. Here the universality hypothesis is reexamined and an important correction is presented. We find that measurements of the postcollision recoil energy of sensor atoms held in shallow magnetic traps only provide information about the interaction potential at the very largest interatomic distances (e.g., the value of C6{C}_{6}C6​ for a leading order term of $\ensuremath{-}{C}_{6}/{r}^{6}$). As other non-negligible terms exist at medium and long ranges, the total collision rate coefficient, even if universal, can differ from that computed solely from the value of C6{C}_{6}C6​. By incorporating these other long-range terms into a simple semiclassical (SC) calculation, we find the SC prediction matches that of full, multichannel, quantum mechanical scattering calculations using the complete potential. This work resolves the discrepancies, demonstrates the simplicity of estimating the rate coefficients for universal collision partners, and provides guidance for using atoms as a self-calibrating primary quantum pressure standard.