Inversion of total and differential cross-section data for electron-methane scattering.

Abstract

The inverse scattering theory has been used to define effective local electron-methane interaction potentials. Those interactions have been obtained first by inversion of the total cross-section data as a function of energy. The WKB approximation has been used in that determination. The same approximation has been used to effect (fixed energy) inversion of differential cross-section data from electron-methane scattering for energies of 200, 300, 500, and 700 eV. The resulting interactions, which we have assumed to be purely real, are very similar and show little energy dependence. They are in good agreement with a theoretically derived potential for this system at those radii for which the inversion potentials are determined sensitively by the scattering data. In addition, the generalized unitarity theorem has been used to specify the scattering amplitude from the 700-eV data. The S function given by Legendre integration of that amplitude has been inverted to specify another purely real potential for the collision. The result is very similar to those found by the other analyses. \textcopyright{} 1996 The American Physical Society.