Positron scattering from rare gases (He, Ne, Ar, Kr, Xe, and Rn): Total cross sections at intermediate and high energies.

Abstract

The total (elastic plus inelastic) cross sections for positron scattering from all the rare gases are reported at intermediate and high energies (20--1000 eV), where experimental data are available for comparison except for the case of radon gas. A complex-optical-potential [${\mathit{V}}_{\mathrm{opt}}$(r)] approach is employed in which the real part (static plus polarization terms) is calculated from Hartree-Fock or Dirac-Hartree-Fock target wave functions. The imaginary part of the optical potential, i.e., the absorption potential [${\mathit{V}}_{\mathrm{abs}}^{+}$(r)], is derived for each gas semiempirically from the corresponding electron absorption potential [${\mathit{V}}_{\mathrm{abs}}^{\mathrm{\ensuremath{-}}}$(r)] in the form of ${\mathit{V}}_{\mathrm{abs}}^{+}$(r)=f(k,r)${\mathit{V}}_{\mathrm{abs}}^{\mathrm{\ensuremath{-}}}$(r), where f(k,r) depends on the incident energy (${\mathit{k}}^{2}$) and radial distance (r). The ${\mathit{V}}_{\mathrm{abs}}^{\mathrm{\ensuremath{-}}}$ is taken from the work of Truhlar and co-workers. The ${\mathit{V}}_{\mathrm{opt}}$(r) is treated exactly in a partial-wave analysis under the variable-phase method. With the present form of ${\mathit{V}}_{\mathrm{opt}}$(r), we are able to reproduce experimental ${\mathrm{\ensuremath{\sigma}}}_{\mathit{t}}$ values at all energies considered here. An additional feature of the present results is that the inelastic cross sections compare very well with the measured inelastic (sum of positronium formation, excitation, and ionization cross sections) values for rare gases, where such experimental data are available. The ${\mathrm{\ensuremath{\sigma}}}_{\mathit{t}}$ for the positron-Rn system are predicted.We also discuss the correlation between scattering cross section and the atomic properties. We found that at intermediate and high energies, the positron-gas total cross section can be represented by an analytic formula ${\mathrm{\ensuremath{\sigma}}}_{\mathit{t}}$(${10}^{\mathrm{\ensuremath{-}}16}$ ${\mathrm{cm}}^{2}$)=21.16 \ensuremath{\surd}${\mathrm{\ensuremath{\alpha}}}_{0}$(${\mathit{a}}_{0}^{3}$)/E(eV) , where ${\mathrm{\ensuremath{\alpha}}}_{0}$ is the target polarizability and E is the impact energy. This simple form of the ${\mathrm{\ensuremath{\sigma}}}_{\mathit{t}}$ in terms of target polarizability works very well for highly polarizable targets such as the alkali-metal atoms and several hydrocarbon molecules. In particular, by using the above analytic formula for ${\mathrm{\ensuremath{\sigma}}}_{\mathit{t}}$, we have shown that our results for Na, K, Rb, ${\mathrm{C}}_{2}$${\mathrm{H}}_{4}$, ${\mathrm{C}}_{2}$${\mathrm{H}}_{6}$, and ${\mathrm{C}}_{3}$${\mathrm{H}}_{6}$ targets compare very well with the experimental data.