Numerical study of the dispersion relation for e--H scattering

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.

Exchange forces in dispersion relations investigated using circuit relations

We propose a novel method to compute in an exact manner the left-hand cut discontinuity of the electron-atom partial wave scattering amplitude in the complex energy plane within the static exchange approximation. Zero energy dispersion relations for electron-hydrogen scattering are computed numerically for illustration.