Ramsauer-Townsend minimum in methane - Modified effective range analysis

Abstract

Electron-scattering cross sections in methane are analysed in the very-low energy region. The correspondence between integral elastic, elastic differential and momentum transfer cross sections is checked via a novel approach to modified effective range theory, in order to determine the depth and position of the Ramsauer-Townsend minimum. Phase shifts of the two lowest partial waves are obtained explicitly and parameterized by four coefficients with the physical meaning of the scattering lengths and the effective ranges. Using recent experiments on vibrational cross sections performed over an extended (0-180°) angular range and comparing several theories, an agreement within 10% has been obtained between experimental total and present summed (elastic + vibrational) cross sections in the whole 0.1-2.0 eV energy range. An additional check for consistency is done using two-term Boltzmann analysis to derive electron diffusion coefficients. Calculated drift velocities and transversal diffusion coefficients at 0-10 Td reduced electric field agree within 5% with experiments.