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Physical Review A

Ultracold atom-ion collisions

Robin Côté, A. Dalgarno

Published Jun 14, 2000• 218 citations
Publisher

Abstract

Studies of charge transfer and total cross sections in elastic collisions of atom-ion alkali metals at ultralow temperatures are reported. Calculations for $\mathrm{Na}+{\mathrm{Na}}^{+}$ have been carried out with the best available ${}^{2}{\ensuremath{\Sigma}}_{g}^{+}$ and ${}^{2}{\ensuremath{\Sigma}}_{u}^{+}$ potential curves. As functions of energy, the cross sections show considerable structure and are large in the limit of low temperature. The scattering lengths were also computed, and the effective range expansion verified. For higher temperatures, we compare quantal and semiclassical results, and investigate the range of applicability of the Langevin formula. Even at temperatures of a few degrees kelvin, the charge-transfer cross sections are large, and could provide an efficient way to produce cold ions.

DOI
10.1103/physreva.62.012709

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Studies of charge transfer and total cross sections in elastic collisions of atom-ion alkali metals at ultralow temperatures are reported. Calculations for Na+Na+\mathrm{Na}+{\mathrm{Na}}^{+}Na+Na+ have been carried out with the best available 2\ensuremathΣg+{}^{2}{\ensuremath{\Sigma}}_{g}^{+}2\ensuremathΣg+​ and 2\ensuremathΣu+{}^{2}{\ensuremath{\Sigma}}_{u}^{+}2\ensuremathΣu+​ potential curves. As functions of energy, the cross sections show considerable structure and are large in the limit of low temperature. The scattering lengths were also computed, and the effective range expansion verified. For higher temperatures, we compare quantal and semiclassical results, and investigate the range of applicability of the Langevin formula. Even at temperatures of a few degrees kelvin, the charge-transfer cross sections are large, and could provide an efficient way to produce cold ions.
Abstract Elastic, momentum-transfer (diffusion), and non-radiative charge-transfer cross sections are calculated for collisions between ground-state He + ( 2 S) ions and neutral He( 1 S) atoms over an energy range spanning fourteen orders of magnitude, from 10 −12 to 1 atomic unit. In this ultralow-energy regime, quantum mechanical effects dominate and the indistinguishability of helium nuclei necessitates a rigorous treatment of exchange symmetry. Phase shifts are computed using highly accurate ab initio potential energy curves for the X 2 Σ u and A 2 Σ g molecular states. The resulting elastic σ el , diffusion σ d , and charge-transfer σ ct cross sections reveal three distinct regimes: at energies below 10 −9 a.u., cross sections exceed 10 5 a 0 2 and are dominated by long-range polarization forces; in the intermediate range (10 −8 –10 −4 a.u.), pronounced quantum interference structures appear; at higher energies, results converge to semiclassical E −1/3 behavior. The data provide benchmark cross sections for ultracold ion–atom collision modeling relevant to cold-ion physics and hybrid atom–ion trapping experiments.
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The elastic scattering properties for collisions between two 7 Li atoms are investigated in the cold and ultracold regimes separately. Based on recent theoretical and experimental results, we present the improved hybrid potentials for the singlet X 1 ∑ g + and triplet a 3 ∑ u + ground states of the Li 2 . Our calculated values for the scattering lengths a and the effective ranges r e are compared with previous ones and found them to be in good agreement. The scattering lengths are 34.6 a 0 for the singlet state and −27.6 a 0 for the triplet state. Shape resonances occur in the collisions at low energies. We also calculate the total cross sections and the energy positions of shape resonances for both X 1 ∑ g + and a 3 ∑ u + states.
Atom-molecule collisions in helium--helium--alkali-metal triatomic systems at cold energies are studied using the adiabatic hyperspherical representation. We consider the elastic collision processes $^{4}\mathrm{He}X+^{4}\mathrm{He}\phantom{\rule{0.16em}{0ex}}\ensuremath{\rightarrow}^{4}\mathrm{He}X+^{4}\mathrm{He}$ and $^{4}\mathrm{He}_{2}+X\phantom{\rule{0.16em}{0ex}}\ensuremath{\rightarrow}^{4}\mathrm{He}_{2}+X$, as well as the reactive collision processes $^{4}\mathrm{He}X+^{4}\mathrm{He}\phantom{\rule{0.16em}{0ex}}\ensuremath{\rightleftharpoons}^{4}\mathrm{He}_{2}+X$, where XXX is one of the bosonic alkali-metal atoms: 7Li^{7}\mathrm{Li}7Li, 23Na^{23}\mathrm{Na}23Na, 39K^{39}\mathrm{K}39K, 85Rb^{85}\mathrm{Rb}85Rb, or 133Cs^{133}\mathrm{Cs}133Cs. The elastic and reactive collision cross sections are calculated at nonzero collision energies by including not only zero atom-molecule relative angular momentum, L=0L=0L=0, processes but also L>0L>0L>0 processes. The total cross section for $^{4}\mathrm{He}X+^{4}\mathrm{He}\phantom{\rule{0.16em}{0ex}}\ensuremath{\rightarrow}^{4}\mathrm{He}X+^{4}\mathrm{He}$ is found to increase with the scattering length between 4He^{4}\mathrm{He}4He and XXX, while the other collision processes are not found to have any systematic dependence on the alkali-metal species XXX.
We calculate the isotope-independent Li+{\mathrm{Li}}^{+}Li+-Li potential energy curves for the electronic ground and first excited states. The scattering phase shifts and total scattering cross section for the $^{7}\mathrm{Li}^{+}\text{\ensuremath{-}}^{7}\mathrm{Li}$ collision are calculated, with an emphasis on the ultralow-energy domain down to the sss-wave regime. The effect of physically motivated alterations on the calculated potential energy curves is used to determine the bound of accuracy of the low-energy scattering parameters for the ion-atom system. It is found that the scattering length for the $A{\phantom{\rule{0.16em}{0ex}}}^{2}{\mathrm{\ensuremath{\Sigma}}}_{u}^{+}$ state, au=1325a0{a}_{u}=1325{a}_{0}au​=1325a0​, is positive and has well-constrained bounds. For the $X{\phantom{\rule{0.16em}{0ex}}}^{2}{\mathrm{\ensuremath{\Sigma}}}_{g}^{+}$ state, the scattering length, ag=20465a0{a}_{g}=20\phantom{\rule{0.16em}{0ex}}465{a}_{0}ag​=20465a0​, has a large magnitude, as it is sensitive to the restrained change of the potential, due to the presence of a vibrational state in the vicinity of the dissociation limit.
The elastic scattering properties in a mixture of sodium and cesium atoms are investigated at cold and ultracold temperatures. Based on the accurate interatomic potential for the NaCs mixture, the interspecies s-wave scattering lengths, the effective ranges and the p-wave scattering lengths are calculated by the quantal method and the semiclassical method, respectively. The s-wave scattering lengths are 512.7 a 0 for the singlet state and 33.4 a 0 for the triplet state. In addition, the spin-change and elastic cross sections are also calculated, and the g-wave shape resonance is found in the total elastic cross sections.