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Physical Review A

Antihydrogen-hydrogen elastic scattering at thermal energies using an atomic-orbital technique

Prabal K. Sinha, Puspitapallab Chaudhuri, Arnab Ghosh

Published May 29, 2003• 17 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.67.052509

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In view of the recent interest in the trapping of antihydrogen atom H\ifmmode\elseˉ\textasciimacron\fi,\mathrm{H}\ifmmode\bar\else\textasciimacron\fi{},H\ifmmode\elseˉ​\textasciimacron\fi, at very low temperatures, H\ifmmode\elseˉ\textasciimacron\fi\ensuremath−H\mathrm{H}\ifmmode\bar\else\textasciimacron\fi{}\ensuremath{-}\mathrm{H}H\ifmmode\elseˉ​\textasciimacron\fi\ensuremath−H scattering has been investigated at low incident energies using a close-coupling model with the basis set H\ifmmode\elseˉ\textasciimacron\fi(1s,2s,2p‾)+H(1s,2s,2p‾).\mathrm{H}\ifmmode\bar\else\textasciimacron\fi{}(1s,2s,2\overline{p})+\mathrm{H}(1s,2s,2\overline{p}).H\ifmmode\elseˉ​\textasciimacron\fi(1s,2s,2p​)+H(1s,2s,2p​). 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 H\ifmmode\elseˉ\textasciimacron\fi\ensuremath−H\mathrm{H}\ifmmode\bar\else\textasciimacron\fi{}\ensuremath{-}\mathrm{H}H\ifmmode\elseˉ​\textasciimacron\fi\ensuremath−H scattering at ultracold temperatures.
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.
In view of current interest in the trapping of antihydrogen ( ) atoms at very low temperatures, we have carried out a calculation of s-wave hydrogen–antihydrogen scattering at very low energies, using the Kohn variational method, taking into account rearrangement scattering into the three channels that contain positronium in its ground state and lie closest to threshold. We find that our values for the elastic cross section are in good agreement with the values obtained by Jonsell et al (Jonsell et al 2001 Phys. Rev. A 64 052712) using a distorted wave approximation. However, our values for the total rearrangement cross section are much larger than their values. In particular, the largest such cross section is for the N = 23 s-state of protonium and positronium in its ground state, a channel that was estimated to make a negligible contribution by Jonsell et al . As a consequence of our much larger values for the total rearrangement cross section, we predict that cooling of by cold H would be considerably less efficient than was found to be the case by Jonsell et al .
We have investigated the sss-wave elastic scattering of antihydrogen atoms off atomic alkali-metal targets (Li, Na, K, and Rb) at thermal energies $({10}^{\ensuremath{-}16}--{10}^{\ensuremath{-}4}\phantom{\rule{0.3em}{0ex}}\mathrm{a.u.})$ 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.
A non-adiabatic model is employed to investigate the H-H scattering at low temperatures. Unlike molecular-orbital calculation technique, no separate calculations are required to obtain the potential energies of electrons in the field of hadrons. This model generates the non-adiabatic effective potential automatically. The coefficients of van der Waals and higher-order potentials are estimated in the present model and are found to be in very good agreement with the corresponding standard values. The s -wave singlet and triplet scattering lengths and thermal-average total triplet cross-section at 2 K are reported and compared with the existing theoretical and experimental predictions.
In this work we report the results of calculation for quantum-mechanical rotational transitions in molecular hydrogen, H2{\mathrm{H}}_{2}H2​, induced by an ultracold ground-state antihydrogen atom H‾1s{\overline{\mathrm{H}}}_{1s}H1s​. The calculations are accomplished using a nonreactive close-coupling quantum-mechanical approach. The H2{\mathrm{H}}_{2}H2​ molecule is treated as a rigid rotor. The total elastic-scattering cross section ${\ensuremath{\sigma}}_{\mathrm{el}}(\ensuremath{\epsilon})$ at energy $\ensuremath{\epsilon}$, state-resolved rotational transition cross sections ${\ensuremath{\sigma}}_{{\mathit{jj}}^{'}}(\ensuremath{\epsilon})$ between states jjj and j′{j}^{'}j′, and corresponding thermal rate coefficients kjj′(T){k}_{{\mathit{jj}}^{'}}(T)kjj′​(T) are computed in the temperature range $0.004 \mathrm{K}\ensuremath{\lesssim}T\ensuremath{\lesssim}$ 4 K. Satisfactory agreement with other calculations (variational) has been obtained for ${\ensuremath{\sigma}}_{\mathrm{el}}(\ensuremath{\epsilon})$.
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)].