Momentum-Transfer Cross Sections for Slow Electrons in He, Ar, Kr, and Xe from Transport Coefficients

Abstract

Momentum-transfer cross sections for electrons in He, Ar, Kr, and Xe are obtained from a comparison of theoretical and experimental values of the drift velocities and of the ratio of the diffusion coefficient to the mobility coefficient for electrons in these gases. The theoretical transport coefficients are obtained by calculating accurate electron-energy distribution functions for energies below excitation using an assumed energy-dependent momentum-transfer cross section. The resulting theoretical values are compared with the available experimental data and adjustments made in the assumed cross sections until good agreement is obtained. The final momentum cross sections for helium is 5.0\ifmmode\pm\else\textpm\fi{}0.1\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}16}$ ${\mathrm{cm}}^{2}$ for an electron energy of 5\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}3}$ eV and rises to 6.6\ifmmode\pm\else\textpm\fi{}0.3\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}16}$ ${\mathrm{cm}}^{2}$ for energies near 1 eV. The cross sections obtained for Ar, Kr, and Xe decrease from 6\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}16}$, 2.6\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}15}$, and ${10}^{\ensuremath{-}14}$ ${\mathrm{cm}}^{2}$, respectively, at 0.01 eV to minimum values of 1.5\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}17}$ ${\mathrm{cm}}^{2}$ at 0.3 eV for Ar, 5\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}17}$ ${\mathrm{cm}}^{2}$ at 0.65 eV for Kr, and 1.2\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}16}$ ${\mathrm{cm}}^{2}$ at 0.6 eV for Xe. The agreement of the very-low-energy results with the effective-range theory of electron scattering is good.