Transport theory for low-energy positron thermalization and annihilation in helium

Abstract

A transport theory that explicitly incorporates loss of flux due to annihilating collisions is developed and applied to low-energy positron diffusion and annihilation. The use of more complete momentum transfer and annihilation cross sections for helium has resulted in improved descriptions of the time dependence of Z eff for positrons injected into gaseous helium. Similarly, the variation of Z eff versus E/n 0 for experiments where the annihilation region is immersed in an electric field is in closer agreement with experimental data. Inclusion of loss of flux due to annihilation was found to have a very small effect on the derived Z eff (t) for helium.

Positron Cooling and Annihilation in Noble Gases

“…f Fokker-Planck calculation of Campeanu and Humberston [14], and Campeanu [8,9] using polarised-orbital cross sections of McEachran et al [17][18][19][20][21]. g Diffusion equation calculation using model potential and enhancement-factor modified zeroth-order annihilation rate [16]. group measurement.…”

“…Understanding of positron kinetics is also crucial for the development of efficient positron cooling in traps and accumulators [10], and for a cryogenically cooled, ultra-high-energyresolution, trap-based positron beam [11,12].Despite the importance of long-standing positroncooling experimental results [5,6], there has been a paucity of theoretical studies of positron cooling in gases. Previous studies have mainly employed the diffusion or Fokker-Planck (FP) equation [8,9,[13][14][15][16]. They used semi-empirical or model cross sections, e.g., calculated in the polarised-orbital approximation [17][18][19][20][21], yielding limited success in describing the experiments.Recently, many-body theory (MBT) was used to provide an accurate and essentially complete description of low-energy positron interactions with noble-gas atoms, taking full account, ab initio, of the strong positron-atom and electron-positron correlations, including virtual-positronium formation [22][23][24][25].…”

“…Z eff (τ ) for He, Ar, Kr and Xe calculated using f (k, τ ) excluding and including loss of particles due to annihilation, initially distributed uniformly in energy (black dashed and solid lines, respectively), and including annihilation with initial energy equal to the Ps-formation threshold (magenta dotted line). Also shown for He: experiment of Coleman et al[4] (red circles), present calculation withZ eff scaled to the measured value ofZ eff =3.94 (blue solid line), FP calculation of Campeanu[14] (blue dashed-dotted line) and model calculations of Boyle et al[16] scaled toZ eff = 3.94 (green dash-dash-dotted line); Ar: experiment of Coleman et al[4,8] (red circles) and FP calculation of Campeanu[8]; Kr and Xe: experiment of Wright et al[7] (red circles) and FP calculations of Campeanu and Humberston[14] (blue dashed-dotted lines); Ne: experiment of Coleman et al[4] (red circles) and FP calculation of Campeanu and Humberston[14] (blue dashed-dotted lines). Arrows mark the calculated (black) and experimental shoulder lengths (red) τs.…”

ANTICOOL: Simulating positron cooling and annihilation in atomic gases

“…Positrons are typically produced in the laboratory at high energy (e.g., ∼ 0.5 MeV for traditional 22 Na sources, and ∼ 1 keV for nuclear reactor sources, e.g., the NEPOMUC reactor [1,2]). As they propagate through a gas of atoms or molecules they lose energy rapidly through ionization, electronic and rotational excitation, and inelastic processes such as molecular dissociation and positronium formation.…”

“…The fundamental dynamics of positron cooling in atomic and molecular gases is governed by the Fokker-Planck equation [16]. It has been the method of choice for the majority of the handful of previous theoretical calculations of positron cooling in noble gases [17,18,19,20,21,22], which have typically relied on model scattering and annihilation cross sections, and have yielded limited agreement with experiment. As first demonstrated by Farazdel and Epstein [23], a powerful and versatile alternative approach to the study of positron cooling in atomic and molecular gases is offered by Monte Carlo (MC) simulation.…”