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Physical Review A

S -wave Ps-Li and Ps-Na scattering

Sumana Chakraborty, Prabal K. Sinha, Arnab Ghosh

Published May 17, 2004• 5 citations
Publisher

Abstract

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 $s$-wave elastic phase shifts, scattering lengths and cross sections of both the systems are reported upto the incident energy $k=0.5\phantom{\rule{0.3em}{0ex}}\text{a.u.}$ 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 $s$-wave elastic parameters for Ps--alkali-metal-atom systems at low energies.

DOI
10.1103/physreva.69.052506

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Resonances in positronium-rubidium and positronium-cesium scattering

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Scattering of ortho positronium (Ps) by cesium and rubidium atoms has been investigated employing a three-Ps-state coupled-channel model with Ps(1s,2s,2p) states using a time-reversal-symmetric regularized electronexchange model potential. We find a narrow S-wave singlet resonance at 5.057 eV of width 0.003 eV in the Ps-Rb system and at 5.067 eV of width 0.003 eV in the Ps-Cs system. Singlet P-wave resonances in both systems are found at 5.3 eV of width 0.4 eV. Singlet D-wave structures are found at 5.4 eV in both systems. The pronounced P- and D-wave resonances in these systems lead to easily detectable local minima in the low-energy elastic cross sections. We also report results for elastic and Ps-excitation cross sections for Ps scattering by Rb and Cs. PACS Number(s): 34.10.+x, 36.10.DrRecent measurements of ortho positronium (Ps) scattering cross section by H2, N2, He, Ne, Ar, C4H10, and C5H12 [1–7] have initiated new theoretical investigations [8–14] in this subject. We suggested [15–17] a regularized, symmetric, nonlocal electron-exchange model

•Jan 1, 2001•5 citations
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.
The scattering of orthopositronium off atomic lithium (Li) target has been investigated using the close-coupling approximation (CCA) with different basis sets. The predictions of different projectile-elastic and target-elastic CCA models have been presented along with static-exchange results. We report the scattering length, the effective range, and the zero-energy cross section for singlet and triplet scattering. The spin averaged zero-energy cross section is significantly improved over the static-exchange prediction by the inclusion of the virtual Ps excitation channels in the basis set. All the present models indicate a binding of lithium-positride (LiPs) in the attractive singlet channel. The low-energy (below first Li excitation threshold) and low order (up to l=2)l=2)l=2) phase shifts are also reported and are found to be variationally consistent. Except the s-wave singlet scattering, other phase shifts are influenced more by the target distortion effect than the projectile inelastic effect. Estimates of the different single-atom excitation cross sections have also been reported along with an estimate of the total cross section. The peak in the total cross-section curve for the present system is not prominent at energies around the Ps inelastic threshold, unlike the Ps-Na case. For incident energy 20 eV or more the Ps ionization is the dominant contributor to the total cross section.
A pseudopotential for positronium-atom interaction, based on electron-atom and positron-atom phase shifts, is constructed, and the phase shifts for Ps-Kr and Ps-Ar scattering are calculated. This approach allows us to extend the Ps-atom cross sections, obtained previously in the impulse approximation [I. I. Fabrikant and G. F. Gribakin, Phys. Rev. Lett. 112, 243201 (2014)], to energies below the Ps ionization threshold. Although experimental data are not available in this low-energy region, our results describe well the tendency of the measured cross sections to drop with decreasing velocity at v<1v<1v<1 a.u. Our results show that the effect of the Ps-atom van der Waals interaction is weak compared to the polarization interaction in electron-atom and positron-atom scattering. As a result, the Ps scattering length for both Ar and Kr is positive, and the Ramsauer-Townsend minimum is not observed for Ps scattering from these targets. This makes Ps scattering quite different from electron scattering in the low-energy region, in contrast to the intermediate energy range from the Ps ionization threshold up to $v\ensuremath{\sim}2$ a.u., where the two are similar.
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.
We investigate ortho-positronium--lithium-atom (Ps-Li) scattering using static-exchange and three-Ps-state coupled-channel calculations. The present three-Ps-state scheme, while closely agreeing with the resonance and binding energies in the Ps-H system, predicts $S\ensuremath{-},$ $P\ensuremath{-},$ and DDD-wave resonances at 4.25 eV, 4.9 eV, and 5.25 eV, respectively, in the electronic spin-singlet channel of Ps-Li scattering. The present calculation also yields a Ps-Li binding in this attractive singlet channel with an approximate binding energy of 0.218 eV, which is in adherence with the recent findings of a chemically stable PsLi system using stocastic variational and quantum Monte Carlo calculations. We further report elastic, $\mathrm{Ps}(2s)\ensuremath{-},$ and Ps(2p)\mathrm{Ps}(2p)Ps(2p)-excitation cross sections at low to medium energies (0.068--30 eV).
The elastic and annihilation cross sections for positron-cadmium scattering are reported up to the positronium-formation threshold (at 2.22.22.2 eV). The low-energy phase shifts for the elastic scattering of positrons from cadmium were derived from the bound and pseudostate energies of a very large basis configuration-interaction calculation of the e+{e}^{+}e+-Cd system. The sss-wave binding energy is estimated to be $126\ifmmode\pm\else\textpm\fi{}42$ meV, with a scattering length of ${A}_{\mathrm{scat}}=(14.2\ifmmode\pm\else\textpm\fi{}2.1)$a0{a}_{0}a0​, while the threshold annihilation parameter, Zeff{Z}_{\mathrm{eff}}Zeff​, was $93.9\ifmmode\pm\else\textpm\fi{}26.5$. The ppp-wave phase shift exhibits a weak shape resonance that results in a peak Zeff{Z}_{\mathrm{eff}}Zeff​ of $91\ifmmode\pm\else\textpm\fi{}17$ at a collision energy of about $490\ifmmode\pm\else\textpm\fi{}50$ meV.
Scattering of ortho positronium (Ps) by cesium and rubidium atoms has been investigated employing a three-Ps-state coupled-channel model with Ps(1s,2s,2p) states using a time-reversal-symmetric regularized electronexchange model potential. We find a narrow S-wave singlet resonance at 5.057 eV of width 0.003 eV in the Ps-Rb system and at 5.067 eV of width 0.003 eV in the Ps-Cs system. Singlet P-wave resonances in both systems are found at 5.3 eV of width 0.4 eV. Singlet D-wave structures are found at 5.4 eV in both systems. The pronounced P- and D-wave resonances in these systems lead to easily detectable local minima in the low-energy elastic cross sections. We also report results for elastic and Ps-excitation cross sections for Ps scattering by Rb and Cs. PACS Number(s): 34.10.+x, 36.10.DrRecent measurements of ortho positronium (Ps) scattering cross section by H2, N2, He, Ne, Ar, C4H10, and C5H12 [1–7] have initiated new theoretical investigations [8–14] in this subject. We suggested [15–17] a regularized, symmetric, nonlocal electron-exchange model