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Physical Review A

s -wave elastic scattering of antihydrogen off atomic alkali-metal targets

Prabal K. Sinha, Arnab Ghosh

Published Mar 10, 2006• 5 citations
Publisher

Abstract

We have investigated the $s$-wave elastic scattering of antihydrogen atoms off atomic alkali-metal targets (Li, Na, K, and Rb) at thermal energies $({10}^{\ensuremath{-}16}--{10}^{\ensuremath{-}4}\phantom{\rule{0.3em}{0ex}}\mathrm{a.u.})$ using an atomic orbital expansion technique. The elastic cross sections of these systems at thermal energies are found to be very high compared to $\overline{\mathrm{H}}\text{\ensuremath{-}}\mathrm{H}$ and $\overline{\mathrm{H}}\text{\ensuremath{-}}\mathrm{He}$ systems. The theoretical models employed in this study are so chosen to consider long-range forces dynamically in the calculation. The mechanism of cooling suggests that Li may be considered to be a good candidate as a buffer gas for enhanced cooling of antihydrogen atoms to ultracold temperature.

DOI
10.1103/physreva.73.032711

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We have investigated the sss-wave elastic scattering of antihydrogen atoms off atomic alkali-metal targets (Li, Na, K, and Rb) at thermal energies (10\ensuremath−16−−10\ensuremath−4a.u.)({10}^{\ensuremath{-}16}--{10}^{\ensuremath{-}4}\phantom{\rule{0.3em}{0ex}}\mathrm{a.u.})(10\ensuremath−16−−10\ensuremath−4a.u.) using an atomic orbital expansion technique. The elastic cross sections of these systems at thermal energies are found to be very high compared to H‾\ensuremath-H\overline{\mathrm{H}}\text{\ensuremath{-}}\mathrm{H}H\ensuremath-H and H‾\ensuremath-He\overline{\mathrm{H}}\text{\ensuremath{-}}\mathrm{He}H\ensuremath-He systems. The theoretical models employed in this study are so chosen to consider long-range forces dynamically in the calculation. The mechanism of cooling suggests that Li may be considered to be a good candidate as a buffer gas for enhanced cooling of antihydrogen atoms to ultracold temperature.
Projectile-elastic, target-elastic, and full close-coupling approximation models have been employed to investigate scattering of ortho-positronium off Li and Na atoms at low energies. Nine different basis sets for each system have been used to find the relative importance of atomic (target and projectile) states on the elastic scattering parameters and the convergence of the predicted results with added eigen- and pseudostates. The sss-wave elastic phase shifts, scattering lengths and cross sections of both the systems are reported upto the incident energy k=0.5a.u.k=0.5\phantom{\rule{0.3em}{0ex}}\text{a.u.}k=0.5a.u. and compared with the corresponding existing theoretical predictions. It has been found that the van der Waals and higher order long-range interactions play a crucial role in predicting sss-wave elastic parameters for Ps--alkali-metal-atom systems at low energies.
In view of the recent interest in the trapping of antihydrogen atom $\mathrm{H}\ifmmode\bar\else\textasciimacron\fi{},$ at very low temperatures, $\mathrm{H}\ifmmode\bar\else\textasciimacron\fi{}\ensuremath{-}\mathrm{H}$ scattering has been investigated at low incident energies using a close-coupling model with the basis set $\mathrm{H}\ifmmode\bar\else\textasciimacron\fi{}(1s,2s,2\overline{p})+\mathrm{H}(1s,2s,2\overline{p}).$ The predicted s-wave elastic phase shifts, scattering length, and effective range are in a good agreement with the other recent predictions of Jonsell et al. and of Armour and Chamberlain. The results indicate that the atomic orbital expansion model is suitable to study the $\mathrm{H}\ifmmode\bar\else\textasciimacron\fi{}\ensuremath{-}\mathrm{H}$ scattering at ultracold temperatures.
We consider the possibility of enhanced cooling of hydrogen atoms by a buffer gas of alkali-metal atoms Na, K, Rb, and Cs. Ultracold elastic collision cross sections for the Na-H and Rb-H purely spin-polarized pairs are found to be 640 and 860 times larger than that for the H-H pair, respectively. From an analysis of the techniques of production of ultracold sodium and rubidium samples, it seems feasible that the critical conditions for Bose-Einstein condensation of hydrogen could be achieved already at the stage of optical cooling of the sodium or rubidium buffer gas.
Quantal calculations for scattering of ground-state antihydrogen by metastable (n=2S)(n=2S)(n=2S) helium atoms have been performed using the nonadiabatic, atomic orbital expansion technique at thermal energies. The zero-energy elastic cross sections of the present systems are much greater than the corresponding value for the ground-state helium target. The low-energy elastic cross section for the singlet metastable helium [He(21S)][\mathrm{He}(2\phantom{\rule{0.2em}{0ex}}^{1}S)][He(21S)] target is higher than the corresponding value when the target is in the metastable triplet state [He(23S)][\mathrm{He}(2\phantom{\rule{0.2em}{0ex}}^{3}S)][He(23S)].
The sss-wave elastic phase shifts and cross sections for the $\overline{\mathrm{H}}\text{\ensuremath{-}}\mathrm{Li}$ system are predicted using an ab initio and nonadiabatic quantal method at very low energies. The smooth and monotonic change of the phase shifts with added eigenstates indicates that the leptonic potential for the present system has no barrier as noticed in the case of the $\overline{\mathrm{H}}\text{\ensuremath{-}}\mathrm{He}$ system, or even a hump which is present in $\overline{\mathrm{H}}\text{\ensuremath{-}}\mathrm{H}$ interaction. The very high value of the sss-wave elastic cross section at zero or near zero energy implies that Li will be a more efficient buffer gas in cooling the antiatom to ultralow temperatures. This study may stimulate new experiments in thermalizing H‾\overline{\mathrm{H}}H atom.
In view of the current interest in trapping antihydrogen H‾\overline{\mathrm{H}}H atoms below 1 K, the s-wave elastic-scattering parameters for the antihydrogen scattering off atomic helium target are calculated in the energy range $1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}16}--1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}2}\mathrm{a}.\mathrm{u}.$ using close-coupling models. The predicted cross section will help to simulate the evolution of a realistic mixture of He and H2{\mathrm{H}}_{2}H2​ through the process involving ejection of H‾\overline{\mathrm{H}}H from the trap. The trend of the present results with different basis sets conclusively indicates the reliability of the predicted results.