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Proceedings of the Physical Society

The pick-off quenching of orthopositronium in helium

P A Fraser, M Kraidy

Published Nov 1, 1966• 45 citations
Publisher

Abstract

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.

DOI
10.1088/0370-1328/89/3/309

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The scattering and pick-off quenching of orthopositronium in helium

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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.

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Electron-spin amplitudes in the exchange quenching of orthopositronium

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Positronium-hydrogen elastic scattering: The electronic S=1 state

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We have continued our investigation into the elastic scattering of positronium atoms by hydrogen atoms, extending the work to include the spin-one (triplet) state of the two electrons. Once again we have extracted the $S$-wave phase shifts from normalizable trial functions by examining the spatial behavior of the center-of-mass wave functions. An effective-range expansion linear in the positronium energy fits the results very well and leads to a scattering length ${a}^{(\ensuremath{-})}\ensuremath{\simeq}2.36{a}_{0}$, compared with the static result ${a}^{(\ensuremath{-})}=2.476{a}_{0}$ of Hara and Fraser. The $S$-wave total and ortho-para conversion cross sections are calculated by making use of both $^{1}S$ and $^{3}S$ results. In the $^{3}S$ case, we see no indication of any resonances below the excitation threshold at 5.1 eV.

Physical Review A•Aug 1, 1976•61 citations
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.
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 $(1.16\ifmmode\pm\else\textpm\fi{}0.01)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}19} {\mathrm{cm}}^{2}.$
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.
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.
The cross sections and rates for quenching of thermalized antiprotonic helium atoms in binary collisions with ordinary helium atoms are calculated in perturbation theory and in the coupled-channel formalism at the temperature and the number density of the helium gas, T=6KT=6\phantom{\rule{0.3em}{0ex}}\mathrm{K}T=6K and $N={10}^{21}\phantom{\rule{0.3em}{0ex}}{\text{cm}}^{\ensuremath{-}3}$, respectively. It is shown that quenching is unlikely to be relevant for the metastable states of the antiprotonic helium atom with $32\ensuremath{\leqslant}n\ensuremath{\leqslant}40$. Comparison with experiment shows a good quantitative agreement for the (n,l)=(39,35)(n,l)=(39,35)(n,l)=(39,35) state of antiprotonic helium and a large disagreement for the (37,34)(37,34)(37,34) state. As a byproduct of this work, the existence of a series of bound states of the He−−p‾4He+\mathrm{He}--\overline{p}\phantom{\rule{0.2em}{0ex}}^{4}\mathrm{He}^{+}He−−p​4He+ dimer is demonstrated numerically for $n\ensuremath{\geqslant}38$.
We have continued our investigation into the elastic scattering of positronium atoms by hydrogen atoms, extending the work to include the spin-one (triplet) state of the two electrons. Once again we have extracted the SSS-wave phase shifts from normalizable trial functions by examining the spatial behavior of the center-of-mass wave functions. An effective-range expansion linear in the positronium energy fits the results very well and leads to a scattering length ${a}^{(\ensuremath{-})}\ensuremath{\simeq}2.36{a}_{0}$, compared with the static result ${a}^{(\ensuremath{-})}=2.476{a}_{0}$ of Hara and Fraser. The SSS-wave total and ortho-para conversion cross sections are calculated by making use of both 1S^{1}S1S and 3S^{3}S3S results. In the 3S^{3}S3S case, we see no indication of any resonances below the excitation threshold at 5.1 eV.