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.

Electron and Positron Scattering by Non-Central Potentials: Matrix Elements and Symmetry Properties in the First Born Approximation

The Fourier transform of Cartesian Gaussian functions product is presented in the light of positron scattering. The calculation of this class of integrals is crucial in order to obtain the scattering amplitude in the first Born approximation framework for an ab initio method recently proposed. A general solution to the scattering amplitude is given to a molecular target with no restriction due to symmetry. Moreover, symmetry relations are presented with the purpose of identifying terms that do not contribute to the calculation for the molecules in the D∞h point group optimizing the computational effort. Keywords — Positron and electron scattering, Fourier transform of the Gaussian product theorem, McMurchie-Davidson procedure, Obara-Saika procedure, linear molecules .

Elastic Scattering of Electron and Positron by Radium and Radon Atoms

The Differential Cross Sections (DCS's), Total Cross Sections (TCS's) and Momentum Transfer Cross Sections (MTCS's) of electron and positron scattering by radium and radon atoms were calculated in the range of energy (5–500) eV using a total potential consisting of combining the static, exchange and polarization potentials at long distances. In addition, the correlation potential of Perdew–Zunger at short distances for electrons was used, as well as the correlation potential of Jain for positrons. The exchange potential for positrons was neglected. In this study, a good agreement with other experimental values and theoretical values of many investigators was found.