Elastic and Inelastic Collision Cross Sections in Hydrogen and Deuterium from Transport Coefficients

Abstract

By means of a numerical solution of the Boltzmann equation, elastic and inelastic collision cross sections have been derived for electrons in ${\mathrm{H}}_{2}$ and ${\mathrm{D}}_{2}$ subjected to a dc electric field. The cross sections for momentum transfer, rotational excitation, vibrational excitation, electronic excitation, and ionization are investigated by comparing experimental and theoretical values of transport coefficient. The same momentum transfer cross section previously obtained for ${\mathrm{H}}_{2}$ by Frost and Phelps has been found to be valid for ${\mathrm{D}}_{2}$. Good agreement is secured between experiment and theory by multiplying the theoretical rotational cross sections of Gerjuoy and Stein by approximately 1.5, provided the polarization factor of Dalgarno and Moffett is used. The final cross section for vibrational excitation of ${\mathrm{H}}_{2}$ has a threshold at 0.52 eV and a peak of 7.7\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}17}$ ${\mathrm{cm}}^{2}$ at 4.5 eV, whereas that of ${\mathrm{D}}_{2}$ has a threshold at 0.36 eV and a peak of 6.6\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}17}$ ${\mathrm{cm}}^{2}$ at 4.7 eV. The derived electronic excitation cross sections are the same for both ${\mathrm{H}}_{2}$ and ${\mathrm{D}}_{2}$. The ionization cross section was taken from the experimental results of Tate and Smith. Calculated transport coefficients for electrons subjected to crossed electric and magnetic fields, and high-frequency ac electric fields are in agreement with recent experimental and theoretical results.