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

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.

Topics & Concepts