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The annihilation of positrons in gases Falk, Willie Robert

Abstract

The lifetimes of ‘free’ positrons have been Investigated (at room temperature) in. the gases N₂, O₂, CO₂, He, A, and Kr by recording the time distributions of the annihilation events. Whereas all the polyatomic gases exhibited pure exponential decay spectra, the annihilation spectra for the noble gases were more complex exhibiting an initial ‘shoulder’ followed by an exponential decay. An analysis of the results suggests that in all cases the exponential decay corresponds to the annihilation of positrons in thermal equilibrium with the gas molecules. The application of a DC electric field was found to produce marked changes in the shape of the annihilation spectra in argon. The annihilation spectrum in argon (at 10.5 atm) was investigated in detail. At zero electric field the initial portion of the spectrum is characterized by a relatively low non-constant annihilation rate, and is attributed to annihilation of positrons which are slowing down in the energy interval between the positronium formation threshold (8.9 eV in argon) and thermal energy. In this energy interval the positron can lose energy only by making elastic collisions with the atoms of the gas. A velocity-dependent annihilation rate over this energy range is suggested to account for this ‘shoulder’ in the annihilation spectrum. The time-width of this shoulder is found to be 340 nsec atm. The rest of the spectrum exhibits an exponential decay as observed in the polyatomic gases. Further investigations using applied DC electric fields (in the range between 0 to 122 V cm⁻¹atm⁻¹) revealed an increase in the mean lifetime of the ‘free’ positrons with increasing electric field. For a field of 790 V/cm and a pressure of 10.5 atm this lifetime has increased by a factor of 2. A diffusion equation governing the behavior of positrons in the noble gases has been derived and solved numerically for different cases of the elastic scattering cross section, the direct annihilation cross section, and the positronium formation cross section. A good fit to the experimental data for argon was obtained using the values 20(v₀/v)¹‧⁵πa₀², 2.25 x 10⁻⁴(v₀/v)¹‧⁵πa₀², and 5.0 x 10⁻⁵πa₀² respectively for these cross sections, where v is the velocity of the positron and v₀ its velocity at thermal energies (25°C). The form of the positronium formation cross section was taken as a step-function whose magnitude was adjusted to yield results consistent with the increase in positronium formation measured by Harder et al (1956). Further calculations are required in order to test the uniqueness of this set of cross sections. Similar experiments in helium revealed only slight evidence for the presence of a shoulder and only a small dependence of the mean lifetime on the applied electric field. This suggests that the annihilation cross section is closely approximated by an inverse velocity dependence. Preliminary investigations in krypton indicates a 'shoulder' width about § as great as in argon. The annihilation rate of the ‘free’ positrons (in the exponential region) was found to be directly proportional to the gas density for all the gases investigated except CO₂, where the annihilation rate can be represented by the equation λa = (0.852p – 0.040p²) x 10⁷/sec where p is the density of the gas expressed in terms of the density at 1 atm and 25°C. A comparison of these results to those obtained from the Dirac cross section (assuming all the electrons of the atom participate) reveals that the observed rates in N₂, O₂, CO₂ (at low pressures), He, A, and Kr are larger than the Dirac values by factors of 2.14, 1.59, 2.64, 1.91, 1.63, and 1.67 respectively.

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