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Journal of Physics B Atomic and Molecular Physics

The scattering and pick-off quenching of orthopositronium in helium

P A Fraser

Published Sep 1, 1968• 41 citations
Publisher

Abstract

An error in some earlier reported work on orthopositronium collisions with helium and on the pick-off quenching of orthopositronium by helium is pointed out, and corrected results are presented. The scattering length is decreased by 13% to 1·88 a 0 , and the theoretical pick-off quenching rate is doubled. The revised quenching rate is still much smaller than experimental observations.

DOI
10.1088/0022-3700/1/5/135

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Physical Review A•Sep 21, 2012•1 citation
An error in some earlier reported work on orthopositronium collisions with helium and on the pick-off quenching of orthopositronium by helium is pointed out, and corrected results are presented. The scattering length is decreased by 13% to 1·88 a 0 , and the theoretical pick-off quenching rate is doubled. The revised quenching rate is still much smaller than experimental observations.
The measurement by Duff and Heymann in 1962 of the pressure-proportional pick-off quenching rate of orthopositronium in helium gas may be interpreted as giving an effective number of electrons per atom in a singlet state relative to the positron of 0 108 ± 0 010 for thermal orthopositronium kinetic energies. A trial wave function used in the study of collisions of orthopositronium with helium, arising from an extension of work by Fraser in 1962, is employed to calculate this effective number of electrons. The unsatisfactory result at low energies is 0.019. A possible improvement in the collision trial wave function is suggested.
When orthopositronium collides with a closed-shell atom or ion the ``pick-off'' process is the dominant process for positron annihilation. In pick-off annihilation the positron annihilates with electrons in the target but not with the electron that is part of the positronium atom. The rate for pick-off annihilation, expressed in terms of the dimensionless parameter 1Zeff,{}^{1}{Z}_{\mathrm{eff}},1Zeff​, for orthopositronium scattering from Li+,Na+,{\mathrm{Li}}^{+},{\mathrm{Na}}^{+},Li+,Na+, and K+{\mathrm{K}}^{+}K+ was computed with an L2{L}^{2}L2 variant of the fixed-core stochastic variational method. The threshold 1Zeff{}^{1}{Z}_{\mathrm{eff}}1Zeff​ for Li+{\mathrm{Li}}^{+}Li+ and Na+,{\mathrm{Na}}^{+},Na+, which can form a stable bound state with Ps were found to be 0.067 and 0.73, respectively, while that for K+,{\mathrm{K}}^{+},K+, which does not bind Ps, was 0.064.
The scattering of orthopositronium from Kr and Xe is investigated with the fixed core stochastic variational method. The scattering lengths for Ps-Kr and Ps-Xe scattering in the fixed core approximation are 3.18a0{3.18a}_{0}3.18a0​ and 3.82a0,{3.82a}_{0},3.82a0​, respectively. Inclusion of core-polarization potentials leads to a significant reduction in the scattering lengths. The Ps-Kr and Ps-Xe scattering lengths were 1.98a0{1.98a}_{0}1.98a0​ and 2.29a0{2.29a}_{0}2.29a0​ for polarization potentials that were tuned to an average of the model electron-atom and positron-atom scattering lengths for the respective atoms. Other choices of the polarization potential resulted in scattering lengths that could be larger by 0.3a0{0.3a}_{0}0.3a0​ or smaller by 0.8a0.{0.8a}_{0}.0.8a0​. The pick-off annihilation parameter 1Zeff{}_{1}{Z}_{\mathrm{eff}}1​Zeff​ has also been computed as part of the analysis. The present values of 1Zeff{}_{1}{Z}_{\mathrm{eff}}1​Zeff​ are about 3 to 10 times smaller than the accepted experimental values since short-range electron-positron correlations were ignored when the annihilation matrix element was evaluated.
The quenching processes of the thermalized orthopositronium $(o\ensuremath{-}\mathrm{Ps})$ on an oxygen molecule have been studied by the positron annihilation age-momentum correlation technique. The Doppler-broadening spectrum of the 511-kev $\ensuremath{\gamma}$ rays from the $2\ensuremath{\gamma}$ annihilation of $o\ensuremath{-}\mathrm{Ps}$ in O2{\mathrm{O}}_{2}O2​ has been measured as a function of the $o\ensuremath{-}\mathrm{Ps}$ age. The rate of the quenching, consisting of the pickoff and the spin conversion, is estimated from the positron lifetime spectrum. The ratio of the pickoff quenching rate to the spin-conversion rate is deduced from the Doppler broadening of the 511-kev $\ensuremath{\gamma}$ rays from the annihilation of the $o\ensuremath{-}\mathrm{Ps}.$ The pickoff parameter 1Zeff,{}^{1}{Z}_{\mathrm{eff}},1Zeff​, the effective number of the electrons per molecule that contribute to the pickoff quenching, for O2{\mathrm{O}}_{2}O2​ is determined to be $0.6\ifmmode\pm\else\textpm\fi{}0.4.$ The cross section for the elastic spin-conversion quenching is determined to be $(1.16\ifmmode\pm\else\textpm\fi{}0.01)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}19} {\mathrm{cm}}^{2}.$
We study single collisions between orthopositronium beams and targets with unpaired electrons, in which the conversion (quenching) of the long-lived orthopositronium into the short-lived parapositronium occurs as a result of electron exchange. We consider unpolarized and polarized targets with one and two unpaired electrons. Angular-momentum coupling and density-matrix techniques are used to calculate the probabilities of obtaining either para- or orthopositronium after the collisions. The probability of the initial orthopositronium being converted to parapositronium (quenching probability) is given in terms of complex scattering amplitudes labeled with total electron spin. Quenching probabilities are calculated for polarized and unpolarized targets, with and without detection of the spins of the targets after the collisions. Ratios of the probabilities of producing parapositronium to that of obtaining orthopositronium are given in terms of electron-spin amplitudes.