Variational Calculation of the Scattering of Electrons of Nearly Zero Energy by Hydrogen Atoms

Abstract

The cross section for the scattering of electrons by hydrogen atoms at zero energy has been calculated by using a variational principle of the Hulthén-Kohn type. For singlet scattering we have used a threeparameter trial function which reduces to an ${\mathrm{H}}^{-}$ wave function at small electron separations and which has the correct asymptotic form. To calculate triplet scattering we use an antisymmetrized version of the same trial function. The effective range for singlet scattering is determined from the scattering length already calculated and the known value of the electron attachment energy for ${\mathrm{H}}^{-}$. For triplet scattering we use an energy-dependent trial function to determine the effective range. Using the calculated values of the above parameters, we find the cross section as a function of energy for the range 0-0.02 volt.