Total Cross Sections for Electron and Positron Scattering on Molecules: In Search of the Dispersion Relation

More than one hundred years of experimental and theoretical investigations of electron scattering in gases delivered cross-sections in a wide energy range, from few meV to keV. An analogy in optics, characterizing different materials, comes under the name of the dispersion relation, i.e., of the dependence of the refraction index on the light wavelength. The dispersion relation for electron (and positron) scattering was hypothesized in the 1970s, but without clear results. Here, we review experimental, theoretical, and semi-empirical cross-sections for N2, CO2, CH4, and CF4 in search of any hint for such a relation—unfortunately, without satisfactory conclusions.