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arXiv:1706.01434 · Physical Review Letters

Positron Cooling and Annihilation in Noble Gases

Dermot G. Green

Published Nov 16, 2017• 12 citations
arXivHTMLPDF

Abstract

Positron cooling and annihilation in room temperature noble gases is simulated using accurate scattering and annihilation cross sections calculated with many-body theory, enabling the first simultaneous probing of the energy dependence of the scattering and annihilation cross sections. A strikingly small fraction of positrons is shown to survive to thermalization: ∼0.1 in He, ∼0 in Ne, ∼0.15 in Ar, ∼0.05 in Kr, and ∼0.01 in Xe. For Xe, the time-varying annihilation rate Z[over ¯]_{eff}(τ) is shown to be highly sensitive to the depletion of the momentum distribution due to annihilation, conclusively explaining the long-standing discrepancy between gas-cell and trap-based measurements. Overall, the use of the accurate atomic data gives Z[over ¯]_{eff}(τ) in close agreement with experiment for all noble gases except Ne, the experiment for which is proffered to have suffered from incomplete knowledge of the fraction of positrons surviving to thermalization and/or the presence of impurities.

DOI
10.1103/physrevlett.119.203403

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Positron cooling and annihilation in room temperature noble gases is simulated using accurate scattering and annihilation cross sections calculated with many-body theory, enabling the first simultaneous probing of the energy dependence of the scattering and annihilation cross sections. A strikingly small fraction of positrons is shown to survive to thermalization: ∼0.1 in He, ∼0 in Ne, ∼0.15 in Ar, ∼0.05 in Kr, and ∼0.01 in Xe. For Xe, the time-varying annihilation rate Z[over ¯]{eff}(τ) is shown to be highly sensitive to the depletion of the momentum distribution due to annihilation, conclusively explaining the long-standing discrepancy between gas-cell and trap-based measurements. Overall, the use of the accurate atomic data gives Z[over ¯]{eff}(τ) in close agreement with experiment for all noble gases except Ne, the experiment for which is proffered to have suffered from incomplete knowledge of the fraction of positrons surviving to thermalization and/or the presence of impurities.
Positronium (Ps) scattering by noble-gas atoms (He, Ne, Ar, Kr, and Xe) is studied in the frozen-target approximation and with inclusion of the van der Waals interaction. Single-particle electron and positron states in the field of the target atom are calculated, with the system enclosed by a hard spherical wall. The two-particle Ps wave function is expanded in these states, and the Hamiltonian matrix is diagonalized, giving the Ps energy levels in the cavity. Scattering phase shifts, scattering lengths, and cross sections are extracted from these energies and compared with existing calculations and experimental data. Analysis of the effect of the van der Waals interaction shows that it cannot explain the recent experimental data of Brawley et al. for Ar and Xe [Phys. Rev. Lett. 115, 223201 (2015)].
A two-parameter semiempirical theory of positron scattering and annihilation is developed and used to investigate the behavior of positrons interacting with the rare gases and metal vapors. The two-parameter theory is able to do a reasonable job of reproducing existing cross section and annihilation data for the rare gases. A model-potential calculation that correctly predicts the behavior of the phase shifts will also predict the energy dependence of Zeff(k){Z}_{\mathrm{eff}}(k)Zeff​(k) even if the magnitude is incorrect. Analysis of the Zeff{Z}_{\mathrm{eff}}Zeff​ versus temperature data of Kurz et al. [Phys. Rev. Lett. 77, 2929 (1996)] suggests scattering lengths of $\ensuremath{-}5.6\ifmmode\pm\else\textpm\fi{}{1.0a}_{0},$ $\ensuremath{-}10.3\ifmmode\pm\else\textpm\fi{}{2.0a}_{0},$ and $\ensuremath{-}56\ifmmode\pm\else\textpm\fi{}{15a}_{0}$ for Ar, Kr, and Xe, respectively. Existing bound-state calculations can be used to fix the values of the semi-empirical parameters for a number of metal vapors, resulting in predicted Zeff{Z}_{\mathrm{eff}}Zeff​ of 119, 36, and 94 for Be, Mg, and Cu at threshold. In addition to the calculations, expressions relating the threshold form of Zeff(k){Z}_{\mathrm{eff}}(k)Zeff​(k) to the complex scattering length are presented.
Measurements of positron temperature as a function of time are presented when a positron gas, confined in an electromagnetic trap at an elevated temperature ( K), is cooled by interactions with the molecular gases , or CO at 300 K. A simple model describing positron thermalization by coupling to vibrational and rotational modes is presented, with cooling-rate predictions calculated in the Born approximation. Comparisons to the measured positron cooling-rate curves permit estimates of the magnitudes of the relevant cross sections. The results are compared with experiment for the case of vibrational excitation, where direct measurements exist; and they provide estimates of the rotational excitation cross sections where direct measurements are not currently possible. Positron cooling rates are compared for these gases at 300 K, and estimates of their effectiveness in cooling positrons to cryogenic temperatures are discussed.
The scattering of orthopositronium from He, Ne, Ar, Li+,{\mathrm{Li}}^{+},Li+, Na+,{\mathrm{Na}}^{+},Na+, and K+{\mathrm{K}}^{+}K+ is investigated with the fixed-core stochastic variational method. The scattering length for $\mathrm{Ps}\ensuremath{-}\mathrm{He}$ scattering was 1.57a0,{1.57a}_{0},1.57a0​, a value consistent with the threshold cross sections derived from three positron lifetime experiments. The scattering lengths for the $\mathrm{P}\mathrm{s}\ensuremath{-}\mathrm{N}\mathrm{e}$ and $\mathrm{P}\mathrm{s}\ensuremath{-}\mathrm{A}\mathrm{r}$ systems were 1.55a0{1.55a}_{0}1.55a0​ and 1.79a0,{1.79a}_{0},1.79a0​, respectively. That there was only a 15% variation among the scattering lengths is compatible with the experiment of Coleman et al. [J. Phys. B 27, 981 (1994)], who found the low-energy cross sections for He, Ne, and Ar to be about the same size. The scattering lengths for Ps scattering from Li+,{\mathrm{Li}}^{+},Li+, Na+,{\mathrm{Na}}^{+},Na+, and K+{\mathrm{K}}^{+}K+ were 12.9a0,{12.9a}_{0},12.9a0​, 28.5a0,{28.5a}_{0},28.5a0​, and $\ensuremath{-}{1.9a}_{0}.$ The relatively small magnitude of the ${\mathrm{P}\mathrm{s}\ensuremath{-}\mathrm{K}}^{+}$ scattering length strongly supports previous suggestions that the ${\mathrm{P}\mathrm{s}\ensuremath{-}\mathrm{K}}^{+}$ system does not support a bound state. The annihilation parameter 1Zeff{}^{1}{Z}_{\mathrm{eff}}1Zeff​ has also been computed as part of the analysis. The present values of 1Zeff{}^{1}{Z}_{\mathrm{eff}}1Zeff​ are about 2.5--3 times smaller than the accepted experimental values since short-range electron-positron correlations were not taken into consideration when the annihilation matrix element was evaluated.
An overview is presented of recent studies of the interaction of low-energy positrons with atoms and molecules using a trap-based positron beam. The beam is tunable from ~100 meV to many electron volts, with a typical energy resolution of 25 meV (FWHM). A variety of scattering processes are investigated using the properties of positron orbits in a spatially varying magnetic field. Recent scattering measurements are reviewed, and new data for electronic excitation, ionization, and positronium formation in noble gases are presented. In a separate set of experiments, positron annihilation below the threshold for positronium formation is studied in molecules as a function of positron energy. The data show large Feshbach resonances in the range of energies of the molecular vibrations. Within the framework of this model, these results provide the first experimental evidence that positrons bind to hydrocarbon molecules.
Recent results for positron scattering from noble gases over an energy range from 0.5 to 60eV are presented. Measurements include the grand total ( σ GT ), Ps formation ( σ Ps ) and Grand total – Ps formation ( (σ GT -P s ) cross sections. Some preliminary DCS results will also be presented. Work on a formulation of modified effective range theory (MERT) is being undertaken to determine the value of the scattering length [1] which may be useful for identifying a bound state. Plans for experiments on metal atoms will be outlined.