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arXiv:physics/0011054 · Physical Review A

Pickoff and spin conversion of orthopositronium in oxygen

N. Shinohara, Naoki Suzuki, T. Chang, Toshio Hyodo

Published Sep 10, 2001• 33 citations
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Abstract

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 ${\mathrm{O}}_{2}$ 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 ${}^{1}{Z}_{\mathrm{eff}},$ the effective number of the electrons per molecule that contribute to the pickoff quenching, for ${\mathrm{O}}_{2}$ 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 $(1.16\ifmmode\pm\else\textpm\fi{}0.01)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}19} {\mathrm{cm}}^{2}.$

DOI
10.1103/physreva.64.042702

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arXiv:1803.03026•Physical Review A•Sep 3, 2019•18 citations
The quenching processes of the thermalized orthopositronium (o\ensuremath−Ps)(o\ensuremath{-}\mathrm{Ps})(o\ensuremath−Ps) on an oxygen molecule have been studied by the positron annihilation age-momentum correlation technique. The Doppler-broadening spectrum of the 511-kev \ensuremathγ\ensuremath{\gamma}\ensuremathγ rays from the 2\ensuremathγ2\ensuremath{\gamma}2\ensuremathγ annihilation of o\ensuremath−Pso\ensuremath{-}\mathrm{Ps}o\ensuremath−Ps in O2{\mathrm{O}}_{2}O2​ has been measured as a function of the o\ensuremath−Pso\ensuremath{-}\mathrm{Ps}o\ensuremath−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 \ensuremathγ\ensuremath{\gamma}\ensuremathγ rays from the annihilation of the o\ensuremath−Ps.o\ensuremath{-}\mathrm{Ps}.o\ensuremath−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±\else\textpm\fi0.4.0.6\ifmmode\pm\else\textpm\fi{}0.4.0.6\ifmmode±\else\textpm\fi0.4. The cross section for the elastic spin-conversion quenching is determined to be (1.16\ifmmode±\else\textpm\fi0.01)\ifmmode×\else\texttimes\fi10\ensuremath−19cm2.(1.16\ifmmode\pm\else\textpm\fi{}0.01)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}19} {\mathrm{cm}}^{2}.(1.16\ifmmode±\else\textpm\fi0.01)\ifmmode×\else\texttimes\fi10\ensuremath−19cm2.
When positrons are injected into a gas, 75% of the positronium (Ps) is likely to be formed as long-lived ortho-Ps. The main decay mechanisms for the ortho-Ps have been assumed to be natural decay of ortho-Ps and pickoff annihilation of the positron during Ps-atom collisions. A third possibility for annihilation is $\mathrm{o}\mathrm{r}\mathrm{t}\mathrm{h}\mathrm{o}\mathrm{\text{\ensuremath{-}}}\mathrm{P}\mathrm{s}\ensuremath{\rightarrow}\mathrm{p}\mathrm{a}\mathrm{r}\mathrm{a}\mathrm{\text{\ensuremath{-}}}\mathrm{P}\mathrm{s}$ conversion due to the spin-orbit interaction between the atom and colliding Ps. This extra quenching mechanism may explain a number of phenomena observed in the annihilation spectrum of Kr and Xe, including the very small Ps fraction of 3% seen for Xe.
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.
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.
Electron-positron annihilation rates calculated directly from the electron and positron densities are known to underestimate the true annihilation rate. A correction factor, known as the enhancement factor, allows for the local increase of the electron density around the positron caused by the attractive electron-positron interaction. Enhancement factors are given for positrons annihilating with the 1s1s1s electron in H, He+{\mathrm{He}}^{+}He+, He, Li2+{\mathrm{Li}}^{2+}Li2+, and Li+{\mathrm{Li}}^{+}Li+. The enhancement factor for a free positron annihilating with He+{\mathrm{He}}^{+}He+ and He is found to be close to that of ortho-positronium (i.e., Ps in its triplet state) annihilating with these atoms. The enhancement factor for Ps-He scattering is used in conjunction with the known annihilation rate for pickoff annihilation to derive a scattering length of 1.47a01.47{a}_{0}1.47a0​ for Ps-He scattering. Further, enhancement factors for e+{e}^{+}e+-Ne and e+{e}^{+}e+-Ar annihilation are used in conjunction with the pickoff annihilation rate to estimate scattering lengths of 1.46a01.46{a}_{0}1.46a0​ for Ps-Ne scattering and 1.75a01.75{a}_{0}1.75a0​ for Ps-Ar scattering.
The confined variational method is applied to investigate the low-energy elastic scattering of orthopositronium from H2{\text{H}}_{2}H2​ by first-principles quantum mechanics. Describing the correlations with explicitly correlated Gaussians, we obtain accurate sss-wave phase shifts and pickoff annihilation parameters for different incident momenta. By a least-squares fit of the data to the effective-range theory, we determine the sss-wave scattering length AS=2.02a0{A}_{S}=2.02{a}_{0}AS​=2.02a0​ and the zero-energy value of the pickoff annihilation parameter, 1Zeff=0.1839{}^{1}{Z}_{\text{eff}}=0.18391Zeff​=0.1839. The obtained 1Zeff{}^{1}{Z}_{\text{eff}}1Zeff​ agrees well with the precise experimental value of 0.186(1) [G. L. Wright et al., J. Phys. B 16, 4065 (1983)] and the obtained AS{A}_{S}AS​ agrees well with the value of 2.1(2)a02.1(2){a}_{0}2.1(2)a0​ estimated from the average experimental momentum-transfer cross section for positronium energy below 0.3 eV [F. Saito et al., J. Phys. B 36, 4191 (2003)].