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Physical Review A

Partial-wave analysis for positronium-xenon collisions in the ultralow-energy region

Kengo Shibuya, Haruo Saito

Published May 3, 2018• 5 citations
Publisher

Abstract

We propose a method to convert measured positronium annihilation rates in gaseous xenon into total and differential cross sections of positronium-xenon collisions in an ultralow-energy region of less than 80 meV where their experimental determinations as functions of the positronium kinetic energy are extremely difficult. This method makes it possible to determine not only the $s$-wave collisional parameters but also the $p$-wave and $d$-wave parameters. We have found a small positive value of the scattering length, ${A}_{0}=2.06\ifmmode\pm\else\textpm\fi{}0.10\phantom{\rule{0.16em}{0ex}}{a}_{0}$, which indicates that the positronium-xenon interaction in this energy region is repulsive and suggests that it is dominated by the scattering amplitude of the positron rather than that of the electron. An extrapolation of the analytical result into the experimentally inaccessible energy regions from 80 meV to 1.0 eV indicates that there should not be a Ramsauer-Townsend minimum but rather a peak in the total cross section at an energy of approximately 0.4 eV.

DOI
10.1103/physreva.97.052702

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We propose a method to convert measured positronium annihilation rates in gaseous xenon into total and differential cross sections of positronium-xenon collisions in an ultralow-energy region of less than 80 meV where their experimental determinations as functions of the positronium kinetic energy are extremely difficult. This method makes it possible to determine not only the sss-wave collisional parameters but also the ppp-wave and ddd-wave parameters. We have found a small positive value of the scattering length, A0=2.06\ifmmode±\else\textpm\fi0.10a0{A}_{0}=2.06\ifmmode\pm\else\textpm\fi{}0.10\phantom{\rule{0.16em}{0ex}}{a}_{0}A0​=2.06\ifmmode±\else\textpm\fi0.10a0​, which indicates that the positronium-xenon interaction in this energy region is repulsive and suggests that it is dominated by the scattering amplitude of the positron rather than that of the electron. An extrapolation of the analytical result into the experimentally inaccessible energy regions from 80 meV to 1.0 eV indicates that there should not be a Ramsauer-Townsend minimum but rather a peak in the total cross section at an energy of approximately 0.4 eV.
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 report total cross-section (TCS) results for low-energy positron scattering from the noble gas xenon. A comparison with previous measurements shows a good level of accord with the recent results of the ANU group (2011 New J. Phys. 13 125004). Very good qualitative agreement is also found with the convergent close-coupling (CCC) calculation of Fursa and Bray (2012 New J. Phys. 14 035002) over most of the common energies. By using the shape of the CCC results as a guide, we also extrapolate our measured cross sections to very low energy. With the aid of the CCC theory, we therefore derive the first experimental estimate for the positron–xenon scattering length of a = −99.2 ± 18.4 au. This value is found to be consistent with the CCC-based estimate and also with those of some other theories. This result supports the existence of a positron–xenon virtual state at a positron energy ε = (1.4 ± 0.6) × 10 −3 eV.
Total cross sections for the scattering of low-energy electrons and positrons by atomic beryllium in the energy range below the first inelastic thresholds are calculated. A Ramsauer–Townsend minimum is seen in the electron scattering cross sections, while no such effect is found in the case of positron scattering. A minimum total cross section of 0.016 a 0 2 at 0.0029 eV is observed for the electron case. In the limit of zero energy, the cross sections yield a scattering length of −0.61 a 0 for electron and a 0 for positron scattering.
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.
Low-energy properties of spin-polarized electron-helium (23S)(2\phantom{\rule{0.16em}{0ex}}^{3}S)(23S) and spin-polarized positronium-helium (23S)(2\phantom{\rule{0.16em}{0ex}}^{3}S)(23S) scattering are calculated using the modified confined variational method. To take the van der Waals interaction into consideration, the van der Waals coefficient between positronium and helium (23S)(2\phantom{\rule{0.16em}{0ex}}^{3}S)(23S) is calculated using the explicitly correlated Gaussian basis. Compared with the ground state noble gases, the larger scattering length and zero pickoff annihilation rate indicates that He(23S)\mathrm{He}(2\phantom{\rule{0.16em}{0ex}}^{3}S)He(23S) may be a more suitable cooling gas. In the energy range we considered, no similarity is found for the SSS-wave cross sections between these two scatterings. A Ramsauer-Townsend minimum is observed in spin-polarized electron-helium(23S)(2\phantom{\rule{0.16em}{0ex}}^{3}S)(23S) scattering due to the large polarization of metastable helium. This may open a new way to find and study the Ramsauer-Townsend effect.
We have calculated cross sections for elastic and spin-flip scattering processes of electrons on positronium atoms in the para and ortho states in the energy region scrE\ensuremath{\le}0.05 eV; elastic and symmetric charge-exchange cross sections for the same system were calculated without spin interactions for the scattering energies scrE\ensuremath{\le}4 eV. This energy region has been treated for the first time. The calculations have been done by the adiabatic method, where this three-body problem reduces to the multichannel-scattering problem. Very high scattering cross sections were obtained, expecially near the threshold for spin-flip processes.