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Canadian Journal of Physics

Cross section for photoionization of the positronium negative ion at the lowest Feshbach resonance

Allen Paine Mills

Published Jul 29, 2013• 12 citations
Publisher

Abstract

The photoionization cross section for the positronium (Ps) negative ion, Ps−, at the lowest n = 2 Feshbach resonance, estimated by neglecting the influences of the weakly bound outer electron, is σF = 1.4 × 10−12 cm2, about 3 × 103 times the existing lower limit calculated by Igarashi and co-workers (New J. Phys. 2, 17 (2000)). Although the estimated cross section is 200 times smaller than the analogous cross section for photoexcitation of the Ps Lyman-α transition, including the effect of the broad line width of the resonance shows it will be feasible to observe this resonance to obtain precision information about the three body Ps− system.

DOI
10.1139/cjp-2013-0210

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The photoionization cross section for the positronium (Ps) negative ion, Ps−, at the lowest n = 2 Feshbach resonance, estimated by neglecting the influences of the weakly bound outer electron, is σF = 1.4 × 10−12 cm2, about 3 × 103 times the existing lower limit calculated by Igarashi and co-workers (New J. Phys. 2, 17 (2000)). Although the estimated cross section is 200 times smaller than the analogous cross section for photoexcitation of the Ps Lyman-α transition, including the effect of the broad line width of the resonance shows it will be feasible to observe this resonance to obtain precision information about the three body Ps− system.
A three-state and a six-state close-coupling approximation have been employed to investigate the e − -Ps scattering below the first excitation threshold of the Ps atom. Present s - and p -wave phase shifts and total cross-sections are compared with the corresponding predictions of Ward et al. ( J. Phys. B , 20 (1987) 127). All the Feshbach resonances below the n = 2 threshold, including 3 S e and 3 P e resonances as predicted by Ho ( Phys. Lett. A , 120 (1984) 348 and Phys. Rev. A , 60 (1999) 2834), have been obtained.
An adiabatic treatment in hyperspherical coordinates is used to predict the existence of resonant structures in ${\mathrm{Ps}}^{\ensuremath{-}}$ (Ps denotes positronium) photodetachment. This highly correlated system displays a weak series of narrow Feshbach resonances lying just below the Ps(n=2)\mathrm{Ps}(n=2)Ps(n=2) threshold, while a single strong shape resonance dominates the photodetachment spectrum above this threshold as in ${\mathrm{H}}^{\ensuremath{-}}$. Use of a "prediagonalized" representation of hyperspherical harmonics dramatically improves the convergence of the adiabatic calculation.
The total cross section of positronium scattering from a variety of atoms and molecules has been found to be unexpectedly close to that of a bare electron moving at the same velocity, despite Ps being neutral and having twice the mass [Science 330, 789 (2010)]. This behaviour appears to extend to velocities where effects such as the Ramsauer-Townsend minima and shape resonances occur for electrons. The latter has now been observed in collisions with CO 2 . Results are presented along with recent production efficiency measurements of Ps at high energies.
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.